Sorglose Nacht

Overview

In Book One of his Analytics, Aristotle discusses the structure of the syllogism, his logical procedure. In Book Two, he discusses some of the properties and defects of syllogisms, and some types of reasoning that are related to syllogisms.

Outline: Book Two

1. Properties and defects of syllogism; Arguments akin to syllogism
   1. Properties
      1. The drawing of more than one conclusion from the same premises
         1. Very nice recapitulation of book one: (1) The number of figures, (2) the character and number of premises, (3) when and how a syllogism is formed, (4) what we must look for when refuting and establishing propositions, (5) how we should investigate a given problem, (6) and by what means we will attain principles appropriate to each subject.
         2. Universal and affirmative particular syllogisms yield more than one result (as these are all convertible propositions).
            1. (E.g.) Universal: Aab -> Aba
            2. (E.g.) Particular Affirmative: Iab -> Iba
            3. (E.g.) Particular Negative: Oab -//> Oba
         3. You can also get this conclusion for universal syllogisms insofar as that which is subordinate to the middle term can be inferred.
            1. Adb, Aba -> Ada, Aad
      2. The drawing of true conclusions from false premises; the first figure
         1. Given true premises, false conclusions are impossible.
         2. True conclusions (wrt fact, not reason) may be drawn from false premises.
            1. If both premises are wholly false, the conclusion can be true. (All men are stones, All animals are stones -> All men are animals).
            2. If both premises are partially false. (Some men are stones, Some animals are not stones -> Some animals are not men)
            3. If only one premise is false:
               1. When the first premise (AB) is wholly false the conclusion will be false.
               2. When AB is partially false, the conclusion can be true.
               3. When the second premise (BC) is wholly false, the conclusion can be true.
               4. When BC is partially false, the conclusion (C) can be true.
            4. If one premise is wholly and one is partially false:
               1. When AB is partially false, C can be true.
               2. When BC is partially false, C can be true.
      3. The drawing of true conclusions from false premises; the second figure
         1. In each of the above situations, in the middle figure, it is possible to reach a true conclusion from one or more false premises.
      4. The drawing of true conclusions from false premises; the third figure
         1. In each of the above situations, in the third figure, it is possible to reach a true conclusion from one or more false premises.
      5. Circluar proof; the first figure
         1. Reciprocal demonstration is when any [P1,P2,C] of a syllogism is provable by assuming the others.
         2. Reciprocal demonstration is only possible if propositions and terms [A,B,C] are convertible (cf. Book 1:A.I.2; i.e. Aab->Aba, Eab->Eba).
            1. Positive Universal: AC: Aab, Abc -> Aac. We can also prove AB by Aac, Acb ->Aab. And BC: (Aac->Aca),Aab -> Abc.
            2. Negative Universal: AC: Abc, Eab -> Eac. And then: AB: Eac, (Acb->Abc) -> Eab. Etc.
            3. Positive & Negative Particular: In the particular cases, we can demonstrate the particular premise from the universal and the conclusion, but not the other way around.
               1. E.g. if: (U)AB, (P)BC -> (P)AC –> Aba, Iac -> Ibc. And this only.
      6. Circluar proof; the second figure
         1. Positive Universal & Particular: Reciprocal demonstration is not possible.
         2. Negative Universal: Aab, Eac -> Ebc. (Aab->Aba), Ebc -> Eac, Etc,
         3. Negative Particular: Once again, the particular premise can be proved but not the universal, for the same reasons as in (A.I.5.iii) above.
      7. Circluar proof; the third figure
         1. Positive & Negative Universal: Reciprocal demonstration is not possible. (Third figure conclusions are always particular.)
         2. Particular premises are sometimes possible to prove reciprocally when the other premise is universal.
            1. Both affirmative & the universal concerns the minor extreme.
            1. Eg. Aac, Ibc -> Iac. If (Aac->Aca), Ibc -> Ibc (!Icb). This fails because we can’t prove something universal about the minor extreme, C.
            2. Eg. Abc, Iac -> Iab. Then if (Abc->Acb), Iab -> Iac. This succeeds because we can say something universal about the minor extreme, C.
         3. One premise is universal affirmative and the other negative -> Circular proof can be given.
      8. Conversion; the first figure
         1. Conversion means altering the conclusion of a syllogism to make another syllogism to prove that either:
            1. The last term cannot belong to the middle.
            2. The middle cannot belong to the last term.
            3. Aristotle will refer to this operation as “refuting a premise”.
         2. Conclusions can be converted into their:
            1. Contradictories: “to all”->”not to all”, “to some”->”to none”.
            2. Contraries: “to all”->”to none”, “to some”->”not to some”.
         3. Universal Contrary: Major extreme premise cannot be refuted universally (forces appeal to third figure). AB, BC -> Eac. –> Eac, Aab -> Ebc. –> Eac, Abc -> Oab (Felapton).
         4. Universal Contradictory : Conversion results in conclusions that are negative and particular.
         5. Particular Contrary: Neither premise may be refuted.
         6. Particular Contradictory: Both premises may be refuted.
      9. Conversion; the second figure
         1. Universal Contrary: The major extreme premise (AB) may not be refuted, but AC can. Aab, Eac -> Abc. Abc, Aab -> Aac. Abc, Eac -> Oab.
         2. Universal Contradictory: The major extreme premise (AB) may not be refuted, but AC can. Ibc, Eac -> Oab. Ibc, Aab -> Iac.
         3. Particular Contrary: Neither premise can be refuted.
         4. Particular Contradictory: Both premises can be refuted.
      10. Conversion; the third figure
          1. Universal Contrary: Neither premise can be refuted.
          2. Universal Contradictory: Both premises can be refuted.
          3. Particular Contrary: Neither premise can be refuted.
          4. Particular Contradictory: Both premises can be refuted.
      11. Reductio ad impossibile; the first figure
          1. The syllogism per impossibile is proved when the contradictory of the conclusion is stated and another (incompatible) premise is assumed.
          2. It resembles conversion, except that a conversion leverages an already-agreed to contradictory, whereas in a reduction to the impossible it is simply clear that the contradictory is true.
          3. E.g.: Aab, Abc -> Aac. Now, we pose that Eab, or Oab then Eab, Abc -> Eac. But Eac is impossible.
          4. All the syllogisms in all moods in all figures can be proved per impossibile, except the universal affirmative in the first figure. (Cf. I.A.11.c.)
             1. Example proof: Eab, Abc -> Eac. Aac, Abc -> Aab, which is impossible.
             2. Why it doesn’t work in the universal figure of the first: Aab, Aca -> Abc. Now assume Ebc. Ebc, (Aca->Aac) -> Eab, which is impossible, but the negation of Eab does not necessarily prove Aab. I think.
      12. Reductio ad impossibile; the second figure
          1. Reductio ad impossibile is possible in all syllogisms in this figure; proofs.
      13. Reductio ad impossibile; the third figure
          1. Reductio ad impossibile is possible in all syllogisms in this figure; proofs.
      14. Comparison of reductio ad impossibile and ostensive proof
          1. Reductio ad impossibile
             1. posits what it wishes to refute by reduction to a statement admitted to be false.
             2. takes one premise from which the syllogism starts and the contradictory of the original conclusion.
             3. it is necessary to suppose that the conclusion is not true.
          2. Ostensive proof
             1. starts from admitted positions.
             2. takes the premises from which the syllogism starts.
             3. it is not necessary that the conclusion is known or true.
          3. Both
             1. Both take two admitted premises.
             2. Anything that can be proved with one can be proved with the other.
          4. Figural dependencies for proving syllogisms.
             1. Proving a syllogism in the first figure by RAI and ostensive proof.
                1. If negative: Proof with the middle figure.
                2. If affirmative: Proof with the last figure.
             2. Proving a syllogism in the second figure by RAI and ostensive proof.
                1. Proof will accomplished using the first figure.
             3. Proving a syllogism in the third figure by RAI and ostensive proof.
                1. If negative: Proof with the middle figure.
                2. If affirmative: Proof with the first figure.
      15. Reasoning from opposites
          1. Possible types of oppositions
             1. Universal affirmative to universal negative
             2. Universal affirmative to particular negative
             3. Particular affirmative to universal negative
                1. Note that particular affirmative to universal negative doesn’t qualify, presumaly along the same logic as (A.I.11.d.ii). Aristotle says they are “only verbally opposed.”
             4. All the universals are “contraries”, all the particulars are “contradictories.”
          2. The first figure
             1. No syllogism can be made from opposed premises.
          3. The second figure
             1. Syllogisms can be made any opposed premise
             2. Science (B) is good, No science (C) is good -> Science (B) is science (C).
          4. The third figure
             1. No syllogism can be made from opposed premises.
             2. A negative syllogism is possible whether the terms are universal or not: Some medicine is a science (B), No medicine is a science (C) -> Some science is a not science [Iab,Eac->Oac].
          5. The types of opposites engender six sets of two premises [e.g. (A.I.15.a.i): Aab, Eac; Aac, Eab;]
          6. It is not possible to draw a true conclusion from opposed false premises.
   2. Defects
      1. Petitio principii (Begging the question)
         1. Begging the question is trying to prove something that’s not self-evident by means of itself.
         2. Basically, using A -> B -> C -> A to prove A is begging the question.
            1. When it is uncertain whether A belongs to C, and uncertain whether A belongs to B, but one assumes A belongs to B, one might be begging the original (AC) question.
            2. If in the above it turns out that B = C or B < -> C, the question is begged.
         3. Syllogisms are question-begging when either their predicates are identical or their subjcets are identical.
      2. False cause
         1. ‘False cause’ describes a situation in which the conclusion would have been reached with or without the hypothesis on which it was based.
         2. This is most obvious when the premise is completely irrelevant to the conclusion.
         3. It can also happen when the premise is related to the conclusion, but the conclusion does not follow from it.
      3. Falsity of conclusion due to falsity in one or more premises
         1. A false argument depends on the first false statement in it, be this the conclusion or one of the premises.
            1. A false syllogism cannot be drawn from true premises (cf. A.I.2.a).
      4. How to impede opposing arguments and conceal one’s own
         1. Don’t allow the person against whom you are arguing to use the same term twice in his premises. Be watchful: The middle term is necessary!
         2. Start from the outside: Assume we are set out to prove AF from B, C, D, and E. We need to prove AB and EF first, no BC. Our tricky interlocutor may attempt to start at the middle, and confound us!
      5. When refutation is possible
         1. A refutation is a syllogism which establishes the contradictory of the original conclusion.
            1. A refutation is possible only when at least one of the terms is affirmative.
            2. A refutation is possible only when at least one of the terms is universal.
      6. Error
         1. It turns out that when you do these in practice, its easy to logically know one thing and think the opposite.
            1. A set of premises like this could arise: [Aab, Eac, Abd, Acd] which entails a contradiction.
            2. This is the case with particulars too: [180 degrees, triangle, some particular triangle]. While someone can know ABC holds, she is not per-se required to think that C exists.
         2. Criticism of Meno and the theory of learning by recollection: “It never happens that a man starts with foreknowledge of the particular, but along with the process of being led to see the general principle he receives a knowledge of the particulars, by an act (as it were) of recognition.”
            1. In seeing some particular and not recognizing the universal, one can be led to error as well. E.g.: One can think [all mules are sterile, this is a mule, this animal is with foal] by simply not recalling AB in the presence of some compelling circumstantial evidence of C.
         3. These points show the three senses of “to know”, which, we will note, dictate the three kinds of error above.
            1. To have knowledge of the universal
            2. To have knowledge of “proper to the matter at hand” (of the particular)
            3. To exercise such knowledge
   3. Arguments akin to Syllogism
      1. Rules for conversion and for comparison of desirable and undesirable objects
         1. Whenever the extremes (A,C) are convertible, the middle (B) must be convertible with both.
         2. Let => equal “more preferable”. Given {x:{A,B},{C,D}} where A,B and C,D are sets of opposites:
            1. If A=>B and D=>C, then if {A,C}=>{B,D} -> A=>D
            2. Since they are opposites, A and B are in an equal relationship of preferability with inverse magnitude e.g.: (1,-1).
            3. If A=>B and D=>C, if A==D -> {A,C}=={B,D}
            4. Also the example he gives here is incredible (this being the Analytics): “To recieve affection is preferable in love to sexual intercourse. Love then is more dependent on friendship than on intercourse…”
      2. Induction
         1. Every belief comes either through syllogism or from induction (not only demonstrative and dialectical syllogisms thus far, but rhetorical syllogisms and other forms of persuasion).
         2. The syllogism that springs out of inducution, which works from a premise and a conclusion rather than two premises:
            1. [Long-lived, Bilelessness, Particular long-lived animals]: We know Aac, and Abc, so we can induce that Aab as long as C is wider in extension than B. His example is terrible. A more contemporarily comprehensible version is if we swap B for some Darwinian thing like “has been selected for in its ecosystem”.
            2. Also, this will cover syllogisms by probability: [Fire a cooked my hot dog, Fire b cooked my hot dog, Fires cook hot dogs.]
      3. Example
         1. Reasoning by example works when (in syllogism ABC) AB is proved by means of AD where D resembles C.
            1. E.g. ABCD:[Evil, making war against one’s neighbors, Athenians against Thebans, Thebans against Phocians]
            2. To prove AC, we appeal to [AB,BC] and we attempt to prove AB by appeal to AD.
         2. So, if deductive reasoning is reasoning from whole to part, and inductive reasoning is from part to whole, then reasoning by example is from part to part.
      4. Reduction
         1. Reduction involves attempting to clarify a term relationship by reducing one of the terms via another syllogism.
            1. E.g. [What can be taught, knowledge, justice]. AB is clear, but it is unclear that virtue is knowledge. But if BC is clearly equally or more true than AC, we have a reduction.
            2. So, assuming virtue is D, we can reduce the uncertain premise AC to a more certain premise set AD,CD: Aab, [Aad, Acd->Aac] -> Abc.
      5. Objection
         1. An objection is a like a premise contrary to a premise, with the exception that there are no universal/particular restrictions with regard to objections, even in, e.g., Barbara or Celarent. In other words you can validly offer a particular objection to a universal syllogism.
         2. In the attempt to raise an objection, one starts from premises which will result in a contrary conclusion.
            1. This will not work in the second figure, which cannot produce an affirmative conclusion.
      6. Enthymeme
         1. Enthymeme is a syllogism which requires an unstated assumption to be true for the premises to lead to the conclusion.
            1. Universal enthymeme (irrefutable, first figure): [To be with child, To have milk, A lactating woman]: AC,BC->AB.
            2. Particular enthymeme (refutable third figure): [To be with child, To be pale, A pale woman]: AC,BC->AB.
            3. Recall that enthymeme is not refutable in the second figure.
         2. The middle term (B) of an enthymeme may be called an index.
            1. Arguments derived from the middle term are those in the first figure, and are most generally accepted to be true.
         3. The extreme terms (A,C) are signs.
            1. It is possible to infer character from features, if we assume that (1) body and soul are changed together by natural affections, and (2) for each change there is a corresponding sign.
            2. E.g. Lions have courage, Lions have large extremities, Large extremities are signs of courage –> Tigers have large extremities…etc.
            3. An enthymeme of this type would require that, e.g. all and only courageous animals have large extremities.

Overview

In Book One of his Analytics, Aristotle discusses the structure of the syllogism, his logical procedure.

Outline: Book One

1. Structure of the syllogism
   1. Preliminary Discussions
      1. Subject and scope of the Analytics; certain definitions and divisions
         1. The subject of the Prior Analytics is demonstration and the faculty that carries it out.
         2. Premise: a sentence affirming or denying something.
            1. Universal: Something belongs to all or none of something else.
            2. Particular: That something belongs to some or not to some or not to all of something else.
            3. Indefinite: A premise that doesn’t indicate its universal/particular status: “Pleasure is not good.”
            4. Premises are demonstrative insofar as they proceed by statement rather than questioning. Premises are offered by the arguer, rather than culled from his interlocutor.
         3. Term: That into which the premise is resolved (In “Socrates is a man” - both “Socrates” and “man”)
         4. Syllogism: A discourse in which one thing (a conclusion, consequence) necssarily follows from some other statements.
         5. Perfect and imperfect Syllogisms: Perfect syllogisms need nothing but what’s in the premises to get the conclusion. Imperfect syllogisms rely on external propositions.
         6. Inclusion and non-inclusion of terms in others: We say that one term is included in another insofar as it is predicated (e.g.) of all of another whenever no instance of the latter can be found of which the former cannot be asserted.
      2. Conversion of pure propositions
         1. Every premise is either affirmative or negative.
         2. Universal Premises
            1. Negation: Should be always universally convertible: If no pleasure is good, then no good will be pleasure.
            2. Affirmation: Convertible, but not universally: If every pleasure is good, then some good must be pleasure.
         3. Particular Premises
            1. Negative: Non-convertible: If some animal is not a man, it does not follow that some man is not an animal.
            2. Affirmation: Convertible in part: If some pleasure is good, then some good will be pleasure.
      3. Conversion of necessary and contingent propositions
         1. The same logical statuses in (A.I.2) will hold good for necessary premises.
         2. For possible premises, the same affirmative structures will hold, but the negative ones won’t. In fact, their conversion potential inverts:
         1. Negative universal possible becomes non-convertible: If it is impossible that every pleasure is good, that does not necessarily imply that it is also impossible that every good will be a pleasure.
         2. Negative particular possible becomes convertible: It is possible that no garment is white, then it is possible for nothing white to be a garment.
      4. Generally, the three conversions (inverting of subject & predicate) that are sound are:
         1. Eab -> Eba
         2. Iab -> Iba
         3. Aab -> Iba
   2. Preliminaries for the Exposition of the Three Figures
      1. II-a. The three figures of Syllogisms
         

         Figure	First Figure		Second Figure		Third Figure
         &nbsp	Pred	Subj	Pred	Subj	Pred	Subj
         Premise	A	B	A	B	A	C
         Premise	B	C	A	C	B	C
         Conclusion	A	C	B	C	A	B

      2. II-b. Terminology
         1. “Aab” = a belongs to all b (Every b is a)
         2. “Eab” = a belongs to no b (No b is a)
         3. “Iab” = a belongs to some b (Some b is a)
         4. “Oab” = a does not belong to all b (Some b is not a)
   3. Exposition of the Three Figures
      1. Proper syllogisms in the first figure
         1. Syllogisms Overview
            1. Demonstration is a form of syllogism, and not every syllogism is a demonstration.
            2. Whenever three terms are so related that the last is wholly contained in the middle, which is wholly contained in the first (positively or negatively), we have a perfect syllogism.
            3. Syllogisms are just like a formal structure for the transitive relation of propositions.
         2. Chart of first-figure syllogisms
            1. All pure syllogisms in the first figure are perfect

            2. Form	Mnemonic	Proof
               Aab, Abc ¦ Aac	Barbara	Perfect
               Eab, Abc | Eac	Celarent	Perfect
               Aab, Ibc | Iac	Darii	Perfect; also by impossibility, from Camestres
               Eab, Ibc | Oac	Ferio	Perfect; also by impossibility, from Cesare

         3. Spelling out the first-figure syllogisms
            1. All A is B, All B is C: All A is C
            2. No A is B, All B is C: No A is C
            3. All B is A, some C is B: Some C is A
            4. No B is A, some C is B: Some C is not A
      2. Proper syllogisms in the second figure
         1. Chart of Second-figure syllogisms
            1. There are no perfect syllogisms in the second figure.

            2. Form	Mnemonic	Proof
               Eab, Aac | Ebc	Cesare	(Eab, Aac)>(Eba, Aac) | Cel^Ebc
               Aab, Eac | Ebc	Camestres	(Aab, Eac)>(Aab, Eca)=(Eca, Aab) | Cel^Ecb>Ebc
               Eab, Iac | Obc	Festino	(Eab, Iac)>(Eba, Iac) | Fer^Obc
               Aab, Oac | Obc	Baroco	(Aab, Oac +Abc)|Bar(Aac, Oac) | Imp^Obc

         2. Spelling out the second-figure syllogisms
            1. No B is A, All C is A: No C is B.
            2. All B is A, No C is A: No C is B
            3. No B is A, Some C is A: Some C is not B
            4. All B is A, Some C is not A: Some C is not B
      3. Proper syllogisms in the third figure
         1. Chart of third-figure syllogisms
            1. There are no perfect syllogisms in the third figure.

            2. Form	Mnemonic	Proof
               Aac, Abc | Iab	Darapti	(Aac, Abc)>(Aac, Icb) | Dar^Iab
               Eac, Abc | Oab	Felapton	(Eac, Abc)>(Eac, Icb) | Fer^Oab
               Iac, Abc | Iab	Disamis	(Iac, Abc)>(Ica, Abc) = (Abc, Ica) | Dar^Iba>Iab
               Aac, Ibc | Iab	Datisi	(Aac, Ibc)>(Aac, Icb) | Dar^Iab
               Oac, Abc | Oab	Bocardo	(Oac, +Aab, Abc) | Bar^(Aac, Oac) | Imp^Oab
               Eac, Ibc | Oab	Ferison	(Eac, Ibc)>(Eac, Icb) | Fer^Oab

         2. Spelling out the third-figure syllogisms
            1. All C is A, All C is B: Some B is A
            2. No C is A, All C is B: Some B is not A
            3. Some C is A, All C is B: Some B is A
            4. All C is A, Some C is B: Some B is A
            5. Some C is not A, All C is B: Some B is not A
            6. No C is A, Some C is B: Some B is not A
      4. Common properties of the three figures
         1. Syllogisms always result from conversions (3.c), and changing universals to particulars affects the results.
         2. All syllogisms in the second and third figures are provable with those in the first figure. Further, it is possible to reduce all proper syllogisms to the universal syllogisms in the first figure (Barbara and Celarent).
            1. Also, the particular syllogisms in the first figure (Darii, Ferio) can be proven by those in the second figure (Camestres and Cesare respectively).
         3. In what follows, Aristotle will be doing something like this:
            1. Two necessary premises (8)
            2. One necessary and one assertoric premise (9-11)
            3. Two possible premises (14,17,20)
            4. One assertoric and one possible premise (15,18,21)
            5. One necessary and one possible premise (16,19,22)
         4. More terminology:
            1. Since this is his procedure, it is convenient to describe modal syllogisms in terms of the corresponding non-modal syllogism plus a triplet of letters indicating the modalities of premises and conclusion:
            2. N = “necessary”, P = “possible”, A = “assertoric”.
            3. Thus, “Barbara NAN” would mean “The form Barbara with necessary major premise, assertoric minor premise, and necessary conclusion”.
            4. I use the letters “N” and “P” as prefixes for premises as well; a premise with no prefix is assertoric. Thus, Barbara NAN would be NAab, Abc : NAac.
      5. Syllogisms with two necessary premises
         1. There are three classes of premise possible for a syllogism, (a) a necessary one, (b) a contingent/possible one, and (c) a simple/assertoric/pure one.
         2. With the exceptions of Baroco (5.a.4) and Bocardo (6.a.5), conclusions will be proved to be necessary by conversion (3.c).
      6. Syllogisms with one assertoric and one necessary premise in the first figure
         1. Universals: When the major premise of a first-figure syllogism is necessary, the conclusion is necessary.
         2. Particulars: When the universal premise is necessary, the conclusion is necessary.
      7. Syllogisms with one assertoric and one necessary premise in the second figure
         1. Universals: When the negative premise of a second-figure syllogism is necessary, the conclusion is necessary.
         2. Particulars: When the negative premise is both universal and necessary, the conclusion is necessary.
      8. Syllogisms with one assertoric and one necessary premise in the third figure
         1. Universals: When one of the two premises of a third-figure syllogism is necessary and both are affirmative, the conclusion will be necessary.
         2. Particulars: When the universal premise is necessary, and both are affirmative, the conclusion is necessary.
      9. Comparison of assertoric and necessary conclusions. In overview:
         1. You need at least one necessary premise to get a necessary conclusion.
         2. Assertoric conclusions are reached by two simple premises.
      10. Prelimiary discussion of the contingent/possible
          1. For Aristotle, “Possibly P” is equivalent to “not necessarily P” and “not necessarily not P”.
             1. Hence the conversion looks like Pp -> [!Np, !N(!p))]. That said, this difference has weird logical consequences.
             2. Entailments:
                1. PAab -> PEab
                2. PEab -> PAab
                3. PIab -> POab
                4. POab -> PIab
             3. Modern modal logic, contrawise, treats necessity and possibility as interdefinable:
                1. “Necessarily P” is equivalent to “not possibly not P”,
                2. “Possibly P” is equivalent to “not necessarily not P”.
                3. Like this: (i) Np -> !P(!p), and (ii) Pp -> !N(!p)
             4. Aristotle acknowledges that there is a certain sense of “possible” that is more like the modern equivalece:
      11. Syllogisms in the first figure with two possible premises
          1. PAab, PAbc -> PAac
          2. Universals: When the major premise is a universal, and the minor premise is particular, there will be a perfect syllogism.
          3. Particulars: When the major premise is particular, no syllogism is possible.
      12. Syllogisms in the first figure with one possible and one assertoric premise
          1. PAab, Abc -> PAac
          2. Aab, PEbc -> PEac
      13. Syllogisms in the first figure with one possible and one necessary premise
          1. PAab, NAbc -> PAac
          2. NEab, PAbc -> NEac
          3. PEab, NAbc -> PAac
      14. Syllogisms in the second figure with two possible premises
          1. No syllogism is possible in this combination.
      15. Syllogisms in the second figure with one possible and one assertoric premise
          1. Eab, PAac -> Eba, PAac -> PEbc
          2. Aab, PEac -> Aba, PEac -> PEbc
      16. Syllogisms in the second figure with one possible and one necessary premise
          1. NEab, PAac -> NEba, PAac -> PEbc, Ebc (otherwise it would be impossible that Aac)
          2. NEab, PEac -> NEba, (PEac -> PAac) -> PEbc, Ebc (cf. 19.a, 13.a.ii)
          3. Rule: If there is a universal, negative and necessary premise, a syllogism is possible.
      17. Syllogisms in the third figure with two possible premises
          1. PAac, (PAbc -> PIcb) -> PIab
          2. PEac, PAbc -> POab
          3. A syllogism with two negative possible premises lead nowhere.
      18. Syllogisms in the third figure with one possible and one assertoric premise
          1. Aac, (PAbc -> PEbc) -> PIab (cf. 13.a.i, 15.b)
          2. Abc, POac -> POab
          3. Whenever both premises are indefinite or particular, syllogism is impossible.
      19. Syllogisms in the third figure with one possible and one necessary premise
          1. NAac, PAbc -> NAac, PIcb -> PAab, Aab
          2. PEac, NAbc -> PAac, NAbc -> PEab (cf. 19.b)
          3. NEac, (PAbc -> PEbc) -> POac -> Oac -> Oab (* I don’t get this one. It might be wrong, but it seems like this is what he’s saying.)
   4. Supplementary Discussions
      1. Every sylllogism is in one of the three figures, is completed through the first figure, and reducible to a universal mood of the first figure.
         1. All of the above syllogisms can be reduced to the univeral syllogisms in the first figure (Barbara, Celarent).
            1. To prove A has some relationship to B, you need some C that unites them.
            2. If this is the case, in order to predicate A of B, you need to predicate either (1) A of C and C of B, (2) C of both A and B, or (3) both A and B of C.
               1. (1) Possible syllogism: [(Eac | Aac),(Ecb | Acb)]
               2. (2) Possible syllogism: [(Aca | Eca), (Acb | Aca)]
               3. (3) Possible syllogism: [(Aac | Eac), (Acb | Acb)]
            3. Which are the three figures (4-6), which we just proved reduce to Barbara and Celarent in 7-22 above.
      2. Quality and quantity of the premises of a syllogism
         1. Every syllogism requires at least one affirmitive and one universal premise.
         2. Further, one of the premises must be like the conclusion in both its affirmitive/negative quality and in terms of its necessary/possible/assertoric status.
      3. Number of the terms, propositions, and conclusions
         1. Every demonstration requires three terms and no more. (The fact that multiple minor premises can be used to assess a single conclusion does not create extra premises, but extra syllogisms.)
         2. It follows from this that every conclusion follows from two premises and no more.
         3. In the case of prosyllogisms or continuous middle terms, we can generally state that:
            1. Terms = premises +1
            2. Premises = relations of predication (e.g. A,E,I,O)
            3. When you add terms, conclusions grow proportionally where: newTerms = oldTerms++; conclusions+=(oldTerms-1);
      4. The kinds of proposition to be established or disproved in each figure.
         1. The universal affirmative is only proved through Barbara.
         2. The universal negative is proved through Celarent in the first figure, Cesare and Camestres in the second.
         3. The particular affirmative is proved through Darii in the first figure, and Darapti, Disamis and Datisi in the third.
         4. The particular negative is proved through Ferio in the first, Festino and Baroco in the second, and Felapton, Bocardo, and Ferison in the third figure.
2. MODE OF DISCOVERY OF ARGUMENTS
   1. General
      1. Rules for categorical syllogisms, applicable to all problems
         1. Individuals (Socrates) cannot be predicated of universals, but universals can be predicated of them (Socrates is human).
            1. Predicating a sensible particular (Socrates) on something else is always incidental: The white thing is Socrates.
            2. The ‘upward limit’ of predication is yet to come (Posterior 1. 19-22); we assume it now.
         2. The aspiring syllogist should collect a cache of universal premises (by comprehending relations of definition and properties).
            1. The aforementioned aspirant should take care to realize that some things that apply universally to the species are not so applicable to the genus, and while this is not the case vice versa, one should still avoid applying species predicates to a genus for propriety’s sake.
      2. Rules for categorical syllogisms, peculiar to different problems
         1. To build a syllogism, you have to look at subjects and their attributes.
         2. Suppose (1) B entails A, which entails C and D’s cannot be predicated of As and (2) E’s have attribute(s) F, can’t have attributes H, and are entailed by G.
            1. C=A, then Afe,Aac->Aae (first figure)
            2. C=G -> Iae (last figure)
            3. F=D -> Eaf,Afe -> Eae (first figure, second figure)
            4. B=H -> Aba, (Ehe->Ebe) -> Eae
            5. D=G -> (Ead->Eag),Ige -> Oae (last figure)
            6. B=G -> Aba, (Aeg->Aeb) -> Aea & Iae
         3. Hence, we must find out which terms in the inquiry are identical
      3. Rules for reductio ad impossibile, hypothetical syllogisms, and modal syllogisms
         1. What is proved ostensively may also be concluded syllogistically per impossibile and vice versa.
            1. Aba, Iae -> Ibe: But it Ebe was assumed. Hence, it must be the case that Eae.
            2. Eae, Aeg -> Eag: But Aag was assumed. Hence it must be the case that Iae.
         2. Generally, a ostensive syllogism has two true premises, and in the reductio ad impossibilie, one of the premises is assumed falsely.
         3. Hypothetical syllogims:
            1. C=G, Aeg -> Aae
            2. D=G, Aeg -> Eae
         4. The method works the same way whether the relation is necessary or possible.
   2. Proper to the several Sciences and Arts
      1. “It is the business of experience to give the principles which belong to each subject.”
   3. Division
      1. Division (cf. The Sophist) is a sort of weak syllogism - it begs the question and proves something more general than it ought.
         1. Division takes the universal as a middle term. E.g.:
            1. A = Animal, B = mortal, C = immortal, D = man
            2. Division assumes all A is either B xor C, so if D is A, then D = B xor C, which Aristotle doesn’t believe.
            3. Funny example then where B = footed, C = footless.
3. Analysis (I) of arguments into figures and moods of syllogism
   1. Rules for the choice of premises, terms, middle term, figure
      1. In attempting to select the premises, ensuring at least one universal premise and two total premises.
      2. Further, we need to discern that nothing unnecessary is assumed, and nothing necessary is omitted.
      3. This established, we need to take as the middle term that which is stated in both premises.
   2. Quantity of the premises
      1. That one premise be universal - which is to say that one term is premised of all of another term - is absolutely required.
   3. Concrete and abstract terms
      1. An easy fallacy to encounter is one in which the terms are “set out wrong”.
         1. E.g. A=Health,B=Disease,C=Man -> Eac, which is obviously wrong.
         2. Subustituting more concrete terms -> A=Healthy,B=Diseased,C=Man, we get better results.
   4. Expressions for which there is no one word
      1. Let A=180 degrees, B=Triangle, C=Isosceles triange
         1. It appears that while Aac because of Aab, there is no middle term for AB.
         2. This is because, Aristotle says, the middle must not always be assumed to be an indivdual thing, but sometimes a complex of words.
   5. The nominative and the oblique cases
      1. Terms should always be used in the nominative (man, good, contraries) and not the oblique (of man, of good, of contraries).
         1. Eg.: If Wisdom (a) is knowledge (b), and wisdom (a) is of the good (c), then knowledge is of the good. I think the problem here is just an equivocation of “is of the good”. Or maybe the translation suffers from this and the original doesn’t. Who knows.
      2. Premises ought to be understood by case: dative, genitive, accusative, nominative.
   6. The various kids of attribution
      1. Any derivation of “belonging” (”This belongs to that”) can be understood in as many ways as there are categories.
   7. Repetition of the same term
      1. When you have a term that repeats another term,
         1. A=”knowledge that it is good”, B=”good”, C=justice. * universals here to keep it simple
         2. P1: There is of the good (b) knowledge that it is good (a). (Aba)
         3. P2: Justice (c) is good (b). (Acb)
         4. But if we add “that it is good” to B (good that it is good), we still get P1, but P2 becomes sensless.
      2. Hence, if you’re going to repeat a term, add it to an extreme (A or C) and not a middle term.
         1. He is deeply confusing about this.
   8. Substitution of equivalent expressions
      1. We can exchange equivalent expressions in syllogisms.
   9. The definite article
      1. The premise “Pleasure is good” is different from “Pleasure is the good”.
      2. The use of either requires consistency in the use of the definite article.
   10. Interpretation of certain expressions
       1. The main point seems to be that “A is said of all of which B is said” is equivalent to “A is said of all the things of which B is said”, a point so lukewarm it’s hard to imagine I actually understand the passage.
   11. Analysis of composite syllogisms
       1. A composite syllogism can be composed of simple syllogisms from multiple figures; it can be internally heterogenous.
   12. Analysis of definitions
       1. Sometimes syllogisms use throwaway terms in definitions. E.g. if a given syllogism proves that water is a drinkable liquid, then we only really proved either drinkablility or liquidity (assuming the other).
   13. Analysis of arguments per impossibilie and of other hypothetical syllogisms
       1. Reduction of hypothetical syllogisms (syllogisms with at least one hypothetical premise) is impossible.
       2. Neither can arguments brought to conclusion per impossibile.
          1. These differ from (I.C.44.a) insofar as those latter require an agreement on a hypothetical premise, whereas in the former men accept the reasoning because the falsity of a premise is patent and required for the conclusion.
   14. Analysis (II) of syllogisms in one figure into another
       1. The conversion of syllogisms (cf. I.A.I.3) continues to apply, and that we can reduce complex syllogims to their components, which can in turn be reduced to the first-figure syllogisms as before, and that these can be proved reductio ad impossibile.
   15. ‘Is not A’ and ‘is not-A’
       1. The clearest example he gives of why these two phrases are different:
          1. They are not identical: “It is not a white log” is not identical to “it is a not-white log”.
          2. Nevertheless, there seems to be some relationship as it is impossible that “It is a white log” and “It is a not-white log”.
       2. Succintly, the appeal to a third term seems to be required, The general four-term logical matrix is:
          1. A=”white”, B=”not white”, C=”not-white”, D=”not not-white”.
          2. Nothing can be (1) [A,B] or (2) [C,D], but everything must be (3) either A or B and (4) either C or D. (Noncontradiction, Excluded Middle)
          3. D “follows” B: Since (4), and C cannot belong to that which B belongs (since B “carries along” A and (1)).
          4. Since C “does not reciprocate” with A, but (4), then it is possible that something could be [A,D].
          5. Since A follows C, then B and C cannot belong to the same thing.
          6. B “does not reciprocate” with D either, since (I.C.46.b.iv).
       3. Out of those five conclusions (ii-vi), only one makes sense to me: ii. The quoted language is just lost on me. Email would be great.

Whew. Next week, Book Two: Properties and defects of syllogism; Arguments akin to syllogism.

Overview

1. The Two Systems

There are actually two sets of Categories articulated in the Categories. The first (2.b) is four-fold, and the second is ten-fold (4.a). It is notable that there is considerable debate about the subject matter of the second system of classification (aka. whether it is a classification of (1) words or of (2) objects in the world, or as classifying (3) linguistic predicates in so far as they are related to the world in semantically significant ways).

2. A Metaphysical Note about the Second System

That there are highest kinds (categories) can be motivated by noticing the fact that the ordinary objects of our experience fall into classes of increasing generality. Consider, for instance, a maple tree. It goes something like ‘maple trees’ -> ‘trees’ -> ‘plants’ -> ‘living things’ -> and so on. Now, quite naturally any good Aristotelian will tell you that this increase in generality or extension cannot go on ad infinitum. We seem to require, then, a highest kind. The obvious appeal here is to Being.

The class that contains all and only beings must be the class with the greatest possible extension. However, in the Metaphysics, however, Aristotle argues that being is not a genus. Why? According to Aristotle, every genus must be differentiated by some differentia that falls outside that genus. Hence, if being were a genus, it would have to be differentiated by a differentia that fell outside of it. In other words, being would have to be differentiated by some non-being, which, according to Aristotle, is a metaphysical absurdity. This can generalize to any proposal for a single highest kind.

Hence, he does not think that there is one single highest kind. Instead, he thinks that there are ten.

3. The Structure of the Categories

In the Pre-Predicamenta (1-4), Aristotle discusses a number of semantic relations (1,3), gives a division of beings into four kinds (2), and then presents his canonical list of ten categories (4). In the Predicamenta (5-9) Aristotle discusses in detail the categories of substance (5), quantity (6), relatives (7), and quality (8), and provides a cursory treatment of the other categories (9). And finally, in the Post-Predicamenta, he discusses a number of concepts relating to modes of opposition (10-11), priority and simultaneity (12-13), motion (14), and ends with a brief discussion of having (15).

Outline

1. Equivocations, univocations, and derivatives.
   1. Equivocations (homonyms) are things sharing a name but with different meanings. His example is a real man and a figure in a picture are called “animals”.
      1. Such words are applicable to various items in the world in virtue of the fact that those items all bear some type of relation to some one thing or type of thing.
      2. A second example of such a homonym is “healthy”: A regimen is healthy because it is productive of health; urine is healthy because it is indicative of health; and Socrates is healthy because he has health. In this case, a regimen, urine and Socrates are all called ‘healthy’ not because they stand under some one genus, namely healthy things, but instead because they all bear some relation to health.
   2. Univocations (synonyms) are things that mean the same thing and are applied to different things. His example is a man and an ox; both are “animals”. That is, they all stand under a genus; in this case, “animals”.
   3. Derivatives are things that derive their meanings from other things. His example is the way a courageous man derives his name (as such, “courageous man”) from the word “courage”.
2. Kinds of things qua predication
   1. Simple and composite expressions.
      1. Simple forms of speech are either a single subject or predicate: ox, man, wins, runs.
      2. Composite forms of speech are subject/predicate expressions: The ox runs. The man wins.
   2. Things (a) predicable of the subject, (b) present in a subject, (c) both predicable of, and present in, a subject, (d) neither predicable of, nor present in, a subject.
      1. Qua (2.b.a): ‘Man’ is predicable of the individual man, and is never present in a subject. Presence here means “contained in”.
      2. Qua (2.b.b): Think of a particular piece of grammatical knowledge. It is present (”contained”) in the mind, but is not predicable of minds (or anything?) in general. (Try also the particular whiteness of Socrates; even if some other white is qualitatively different that Socrates’, it is numerically distinct. This is what we mean by a nonsubstantial particular.)
      3. Qua (2.b.c): While knowledge in general is present in the human mind, it is predicable of grammar. Again, whiteness provides a somewhat more intuitive example. The universal whiteness is said-of many primary substances but is only accidental to them.
      4. Qua (2.b.d): These are individuals. An individual man or horse.
   3. Irritatingly, this set of distinctions rests on a circular definition (of what “present in” means) and a missing definition (”said of” or predication). Apparently, most scholars conclude that beings that are said-of others are universals, while those that are not said-of others are particulars. Beings that are present-in others are accidental, while those that are not present-in others are non-accidental. Now, non-accidental beings that are universals are most naturally described as essential, while non-accidental beings that are particulars are best described simply as non-accidental.
   4. Putting all that good work of interpretation together, we can gather that we have
      1. Essential universals (2.b.a)
      2. Accidental particulars (2.b.b)
      3. Accidental universals (2.b.c)
      4. Non-accidental particulars (2.b.d): Primary substances, individuals.
3. The Transitive property of predication and its effects
   1. That which is predicable of the predicate is predicable of the subject.
      1. ‘Man’ is predicated of an individual man. ‘Animal’ is predicated of ‘Man’. Thus, the individual man is ‘Animal’.
   2. The differentiae of species in one genus are not the same as those in another, unless one genus is included in the other.
      1. E.g. The genera ‘Animal’ has differentiae (internally-differentiating characteristics), e.g. ‘with feet’, ‘two-footed’, ‘winged’, ‘aquatic’.
      2. These differentiae do not arbitrarily apply to all genera, e.g. ‘Knowledge’.
      3. They may, however, apply, to subordinate genera, as the parent genus will be predicated of the child.
4. The eight categories of objects under thought.
   1. The (ten-fold) categories (substance, quantity, quality, relation, place, time, position, state, action, affection) are signified by simple expressions.
      1. E.g.: Substance - ‘man’, ‘the horse’
      2. E.g.: Quantity - ‘two feet long’
      3. E.g.: Quality - ‘white’, ‘grammatical’
      4. E.g.: Affection - ‘to be cauterized’. Etc.
   2. No one of these terms involves an affirmation. Positive and negative statements arise only by combination.
5. Substance
   1. Primary and secondary substance.
      1. Primary substance is that which is neither predicable of a subject nor present in a subject (2.b.iv), aka. an individual man, horse.
      2. Secondary substances are the species and genera into which primary substances fit; in the case of a man, the species ‘man’ and the genus ‘animal’ are both secondary substances.
      3. An interesting proposed secondary substance tree from the SEP:
         1. Immobile Substances - Unmoved Mover(s)
         2. Mobile Substances - Body
            1. Eternal Mobile Substances - Heavens
            2. Destructible Mobile Substances - Sublunary bodies
               1. Unensouled Destructible Mobile Substances - Elements
               2. Ensouled Destructible Mobile Substances - Living things
                  1. Incapable of Perception - Plants
                  2. Capable of Perception - Animals
                     1. Irrational - Non-Human Animals
                     2. Rational - Humans
   2. Difference in the relation subsisting between essential and accidental attributes and their subject.
      1. Essential: Predicating secondary substances of primary substances entails that the primary substance is predicated by both the name and the definition of the secondary substance. (Both “man” and “bipedal animal” - or whatever - are predicated of a man by the predication of the former).
      2. Accidental: Predicating accidental characteristics of substances of the substances themselves, however, does not entail that the substance contain the definition of its attribute. (E.g. you can say, “the man is white,” but that doesn’t mean that “the man is [the definition of whiteness]”).
      3. In overview, this model entails a twofold manner of predication, one is a definitional/essential predication-relation (used by species and genera) and the other is an accidental relation (e.g. “the man is white”).
   3. All that which is not primary substance is either an essential or an accidental attribute of primary substance.
      1. Everything except primary substances is predicable (in the sense of definition) of a primary substance, or is present in a primary substance (is an accidental attribute).
   4. Of secondary substances, species are more truly substance than genera.
      1. A more convincing account of a primary substance can be given via species than via genus.
      2. The same predication-relation that exists between primary substances and everything else also exists between species and genera. [ species:genus :: subject:predicate ]
   5. All species, which are not genera, are substance in the same degree, and all primary substances are substance in the same degree.
   6. Nothing except species and genera is secondary substance: These alone convey knowledge of primary substance.
   7. The relation of primary substance to secondary substance and to all other predicates is the same as that of secondary substance to all other predicates. [E.g. a man -> “skilled in grammar” implies “man” -> “skilled in grammar”.]
   8. Substance is never an accidental attribute; e.g. a secondary substance is never “present” in a primary substance.
   9. The differentiae of species are not accidental attributes. [’two-footed’ is not in ‘man’ (remember that /in/ here is the container definition: (2.b))].
   10. Species, genus, and differentiae, as predicates, are ‘univocal’ with their subject.
       1. This means that when you predicate any one of them, they are related both in definition and name to the children of that which is predicated of them.
       2. In other words, this means specifically that there’s an inheritance effect if you enter into one of these /specific/ chain of predication:
          1. individual (primary substance) <- species <- genus <- differentiae
          2. individual (primary substance) <- species <- differentiae
   11. Primary substance is individual; secondary substance is the qualification of that which is individual.
       1. A secondary substance is a class that can be predicated of individuals.
       2. Species and genus signify substance qualitatively differentiated.
   12. No substance has a contrary.
   13. No substance can be what it is in varying degrees.
       1. If you’re a man, you’re a man all the way, contra, say, your whiteness, which admits of variation in time.
   14. The distinctive mark of substance is that contrary qualities can be predicated of it.
       1. For any other term, contraries cannot be predicated. Later (6a:0-3) we find that nothing can admit contraries at the same time.
   15. Contrary qualities cannot be predicated of anything other than substances, not even propositions and judgments.
       1. Interestingly, he admits statements and opinions as an exception here, although he argues that it is not they themselves that undergo modification, but things external to them which retroactively modify their truth values.
       2. Hence, it is distinctive that substances seem to be internally-modifiable in a way that admits contrary qualities.
6. Quantity
   1. Discrete and continuous quantity.
      1. Discrete quantities are things like number and speech. They share no “common boundary”.
      2. Continuous quantities are things like lines, solids, time, and place.
   2. Division of quantities, i.e. number, the spoken word, the line, the surface, the solid, time, place, into these two classes.
      1. Numbers and speech are constituted by discrete packets of information.
      2. Lines are constituted by continuous points, surfaces by continuous lines, solids by continuous planes.
      3. Time, past, present, and future, forms a continuous whole.
      4. Space, likewise, is a continuous quantity, as its parts share a common boundary (this is evidenced by the fact that space can be occupied with solids: cf. (6.b.ii)).
   3. The parts of some quantities have a relative position, those of others have not. Division of quantities into these two classes.
      1. Either a quantity’s parts have a relative position, each to each, or they do not.
      2. Quantities that do: Lines (their parts are distinguishable and relative to their other parts), and hence planes, solids, and space.
      3. Quantities that don’t: Numbers, time, speech do not because they don’t have “an abiding existence”. One might say they have a relative order, but not a relative position.
   4. Quantitative terms are applied to things other than quantity, in view of their relation to one of the aforesaid quantities.
      1. E.g. A white wall is large in terms of length (solid), a speech is long in terms of time, etc.
   5. Quantities have no contraries.
      1. Terms such as ‘great’ and ’small’ are relative, not quantitative, and moreover cannot be contrary to each other (because of their reliance on a third party or external standard).
      2. That which is most reasonably supposed to contain a contrary is space. But this seems to fall apart because of a confusion of contrariness and extreme difference of degree (the weight of the universe is not the contrary of the weight of a dust mite). Interesting that he should say this and still call sickness and health contrary.
   6. No quantity can be what it is in varying degrees: Just because n is bigger than m, it doesn’t make n /more of a number/.
   7. The peculiar mark of quantity is that equality and inequality can be predicated of it.
   8. Question: “Perhaps the most interesting question concerns the fact that some of the species in quantity appear to be quantified things rather than quantities themselves. Consider, for instance, body. In its most natural sense, ‘body’ signifies bodies, which are not quantities but rather things with quantities. The same is true of line, surface, place and arguably speech. Of course, there are quantities naturally associated with some of these species. For instance, length, breadth and depth are associated with line, body and surface. But Aristotle does not list these as the species under quantity. So, in the first instance, we can ask: does Aristotle intend his division of Quantity to be a division of quantities or quantified things?”
7. Relation
   1. First definition of relatives: Relatives are explained by reference to some other thing. (E.g. “superior” implies superiority over something else.)
   2. Some relatives have contraries (e.g. virtuous/depraved) but not all (e.g. “double”).
   3. Some relatives are what they are in varying degrees (e.g. likeness or unlikeness).
   4. A relative term has always its correlative, and the two are interdependent (e.g. slave->master, double->half, greater->lesser).
   5. The correlative is only clear when the relative is given its proper name, and in some cases words must be coined for this purpose.
      1. This is a little convoluted, basically he seems to be talking about something like this:
      2. Call the condition of being a ruddered thing “rubob”. Call the opposite condition “belbob”. Something is rubob in virtue of its rudder and relative to something belbob.
      3. E.g. a “slave” is not usefully defined with reference to bipedalism. The correct correlative of a relative term (a) is what remains after all incidental attributes are removed from (a).
   6. Most relatives come into existence simultaneously; but the objects of knowledge and perception are prior to knowledge and perception.
      1. True, e.g.: Doubleness and halfness are mutually dependent immediately.
      2. False, e.g.: The objects of knowledge/perception.
   7. No primary substance or part of a primary substance is relative.
   8. Revised definition of relatives, excluding secondary substances.
      1. The fact that a thing is explained with reference to something else does not make it essentially relative. (This is the argument against ‘head’ and ‘hand’ as candidates for categorization as relative.)
         1. Question: How do we distinguish between those things about which we are just confused and need new terminology (7.e) and the case when something that requires something external in its explanation is actually not relative?
      2. There’s an appeal to intuition now, (if a man knows something is beautiful, he knows that than which it is more beautiful). I frankly don’t see how this is a helpful criterion though, given the whole “rudder” problematic.
   9. It is impossible to know that a thing is relative, unless we know that to which it is relative.
      1. He concludes that no substance is relative in character, but again I am still stuck up on rudders.
   10. Overview: “Perhaps the most straightforward reading of Aristotle’s discussion is the following. He noticed that certain predicates in language are logically incomplete - they are not used in simple subject/predicate sentences of the form ‘a is F’ but rather require some type of completion. To say ‘three is greater’ is to say something that is incomplete - to complete it requires saying what three is greater than. Nonetheless, Aristotle accepted a doctrine according to which properties in the world always inhere in a single subject. In other words, although Aristotle countenanced relational predicates, and though he certainly thought that objects in the world are related to other objects, he did not accept relations as a genuine type of entity. So, Aristotle’s category of relatives is a kind of halfway house between the linguistic side of relations, namely relational predicates, and the ontological side, namely relations themselves.”
8. Quality
   1. Definition of qualities: “that in virtue of which people are said to be such and such.”
   2. Different kinds of quality.
      1. Habits and dispositions
         1. Habits are more lasting and firmly established than dispositions.
         2. Knowledge and virtue, e.g., are habits.
         3. On the other hand, heat and cold, disease and health are dispositions.
         4. Habits are dispositions, but not vice versa.
      2. Capacaties
         1. Capacities are predicated of a person in virtue capacity (nice). E.g. being a good runner or boxer.
         2. There is also a kind of health that is less a disposition (e.g. I am healthy at the moment), and more of a capacity towards health (e.g. I am a healthy person generally).
      3. Affective qualities (distinction between affective qualities and affections)
         1. Affective qualities and affections are like: sweetness, bitterness, whiteness, blackness, heat and cold.
         2. Affective qualities are actually capacities to produce affections “in the way of perception.” These are things like sweetness and heat, which are capable of producing affections in the senses.
         3. Contrarily, affections are like pallor and flushing (in skin). This is again reliant on a more permanent/less permanent distinction. Affections are caused by affectors (shame/fear). So the white of Socrates when he sees a ghost is an affection, and the white of my walls is an affective quality.
         4. There are also affective qualities and affections of the soul. Of the former: temper, insanity, irascibility as constitutional. Of the latter: the same list as a temporary state. We can say that affective qualities are pathologies of affections.
      4. Shape, etc. (Rarity, density, etc. are not qualities)
         1. Straightness, curvedness, triangularity or octagonality are qualities.
         2. Rarity and density, roughness and smoothness because these are actually composite attributes: roughness is due to the unevenness of an array of parts, sparseness because of the distance between parts, etc. These are not intrinsic, and thus not qualities.
   3. Adjectives are generally formed derivatively from the names of the corresponding qualities (e.g.: the quality ‘whiteness’ nominates the adjective ‘white’).
      1. The alternative to that is when things derive names from sciences (e.g. the ‘boxer’ derives his name from the science of ‘boxing’, as the innate capacity for boxing, as a quality, has no name).
   4. Most qualities have contraries
      1. Usually: justice/injustice, whiteness/blackness
      2. Not always: Red, yellow
      3. If of two contraries one is a quality, the other is also a quality.
   5. A quality can in most cases be what it is in varying degrees.
      1. In the case where it is debatable whether it can (e.g. justice), we can at least say that subjects can possess most qualities in varying degrees.
      2. Qualities of shape are an exception to both of these rules (8.e, 8.e.i).
   6. The peculiar mark of quality is that likeness and unlikeness is predicable of things in respect of it.
   7. Habits and dispositions as genera are relative; as “individuals”/(species?), qualitative.
      1. While knowledge, e.g., as a genera is relative (to something) - knowledge is always knowledge of something, a particular branch of knowledge (say, musicology) is not relative to anything.
      2. Furthermore, if something should happen to be both a quality and a relation, this wouldn’t really hurt anything.
9. Action and affection and the other categories described.
   1. Action and affection both admit of contraries and of variation of degree (heating/cooling, being glad/being vexed).
   2. Position we understood back in (7.d-e), when we “stated that such terms derived their names from those of the corresponding attitudes.”
   3. Time, place (’in the Lyceum’), state (’shod’, ‘armed’) are easily intelligible.
10. Four classes of opposites.
    1. Correlatives: ‘Double’ and ‘half’.
       1. Correlatives are defined in reference to each other: A double is two times its half, knowledge is grasping an object.
    2. Contraries: ‘Good’ and ‘bad’. (Some contraries have an intermediate, and some have not)
       1. Tautologically defined: The ‘good’ is not ‘the good of the bad’ (qua 10.b), but ‘the contrary of the bad.’
       2. There are some contraries that are mutually exclusive (odd, even) and some that aren’t (blackness, whiteness).
    3. Positives and privatives: ‘Blindness’ and ’sight’.
       1. Positives and privatives reference the same subject (blindness and sight reference the eyes).
       2. Also, it is “a universal rule” that positives are the “natural” state of things. We don’t refer to blind chairs, because they are not missing sight in any significant sense.
       3. The terms expressing possession and privation (’being blind’) are not the positive and the privative (’blindness’), though the former are opposed each to each in the same sense as the latter.
       4. Similarly the facts which form the basis of an affirmation or a denial are opposed each to each in the same sense as the affirmation and denial themselves.
       5. Positives and privatives are not opposed in the same sense in which correlatives (10.a.i) nor contraries (10.b.i) are opposed.
       1. Viz. contraries: (1) Positives/privatives are not like contraries with no intermediates because in the case of the latter, one or the other has to be present in the “subject in which they naturally persist.”
          1. His examples are health/sickness and odd/even. You get odd/even: Every number has to be either odd or even entirely. His argument is that there exists a subject who has not advanced to the state in which sight is natural, and thus is neither seeing nor blind in the sense set forth in (10.c.ii).
       2. (2) They are not like contraries which have intermediates because in the latter, only one of the two contraries need be in a subject which is constituted by that quality (e.g. fire must be hot, and hence not cold. Otherwise, things can be in the middle of the hot/cold spectrum.)
          1. The appeal here is that - while it is not necessary per se for a given subject - once said subject has reached a stage in which sight is natural, it will either see or be blind.
          2. This contra contraries with intermediate stages, for which (a) it is never necessary that one or the other be inherent in a subject, and that (b) in the special cases, if one or the other should be present, it will not admit of its intermediate or its contrary.
       3. Also contra contraries, there can be no change from one state (e.g. privation) to its opposite.
11. Affirmation and negation: ‘He sits’, ‘he does not sit’.
    1. These are distinguished by from other contraries by the fact that one is always false and the other true.
       1. Opposite affirmations seem to possess this mark, but they do not. Eg. [”Socrates is ill”, “Socrates is well”] will always contain only one true and only one false statement if Socrates exists.
       2. Contra (10.d.i), the set [”Socrates is ill”,”Socrates is not ill”] always contains one true and one false statement, regardless of the existential status of Socrates.
12. Contraries further discussed
    1. Evil is generally the contrary of good, but sometimes two evils are contrary (e.g. defect, excess).
    2. When one contrary exists, the other need not exist (when “Socrates is well” then manifestly not “Socrates is ill”).
    3. Contrary attributes are applicable within the same species or genus (whiteness and blackness require a body, disease and health, a living body).
    4. Contraries must themselves be within the same genus (white and black->color), or within opposite genera (justice,injustice->virtue,vice), or be themselves genera (good and evil).
13. The word ‘prior’ is applicable:
    1. To that which is previous in time.
    2. To that on which something else depends, but which is not itself dependent on that something else.
    3. To that which is prior in arrangement.
    4. To that which is better or more honorable (he’s “first in my book”).
    5. To that one of two interdependent things which is the cause of the other and not the other way around. (The being of j:The truth of the proposition “J is.”)
14. The word ’simultaneous’ is used:
    1. Of those things which come into being at the same time. (”Double/half” cf. 7.f)
    2. Of those things which are interdependent, but neither of which is the cause of the other. (”Double/half”, cf. 10.a.i)
    3. Of the different species of the same genus (’animal’: ‘winged’,'terrestrial’,'aquatic’).
15. Motion is of six kinds: Generation, destruction, increase, diminution, alteration, and change of place.
    1. It is obvious that five of the six are distinct kinds; the exception is alteration. One may feel like alteration implies other types of movement.
       1. This is not the case, apprarently, insofar as a square can increase but not alter (qua square). Hence it is does not directly alteration or diminution, which it seemed to initially.
    2. Rest is the contrary of motion generally, but the contraries of the specific kinds have their contraries in other kinds (e.g.: generation/destruction, diminution/increase).
       1. The contrary of change seems to be either rest in place or change in the reverse direction.
       2. The contrary of alteration seems to be either stability of quality (rest) or change of quality in the reverse direction.
16. The meanings of the term ‘to have’.
    1. With reference to a habit or disposition (”he has a pleasant temperment”).
    2. With reference to quantity (”he has a height of six feet”).
    3. With regard to possessions and parts (”he has a coat”, “he has two hands”).
    4. With regard to content (”the jar has wine”).
    5. With regard to a wife/husband, which Aristitotle concludes is the most remote meaning of “having”, since it really parses out to “lives with”.

Overview

To Aristotle, there is no higher moment of Natural Philosophy than the study of the Soul. In Book One, we get an overview of the historical thought about the soul. The three principles of the soul handed down to us historically are that (a) it is the source of movement and (b) sensation, and that (c) it is composed of elements. Aristotle refutes (a) and (c) in turn, and we seem to be left in the position of “starting over”.

In Book Two, we do in fact start over, trying to understand the Soul phenomenologically. We find that the soul has certain faculties: the nutritive, the appetitive, the sensory, the locomotive, and the power of thinking. All besouled things have at least one of these, and some have all. The plan moving forward is to analyze each of these faculties in turn. The remainder of Book Two addresses the nutritive, appetitive, and sensory functions of the soul.

Book Three treats, in turn, (1) “common sense”, or that which allows us to discriminate between sense objects of different sensory domains, (2) the imaginitive function of the mind (the name which marks out the domain of the “knowing soul”, as opposed to the sensing soul), (3) the practical function of the mind, and (4) the motive function. At the conclusion, it is decided that the Touch is “the essential mark of [animal] life.”

1. BOOK ONE
   1. The dignity, usefulness, and difficulty of Psychology.
      1. Knowledge of the soul is knowledge with the higest dignity. Knowledge of the soul tells us something about truth, and something about Nature, insofar as it is in some sense the principle of animal life.
      2. This knowledge, though, is nefariously difficult to attain. First, we need to know which summa genera (categories) the soul lies (is it a substance, quantum, etc). Is it potential or actual? Is it divisible? Are all souls part of one soul? Etc.
      3. Also, are all the dispositions of soul actually dispositions of the soul/body complex?
         1. It seems they are: passion, joy, fear, pity, courage, loving and hating, etc. are all produced in varying intensities that are not strictly correlative to the stimuli; apparently, this entails that these dispositions rely in some sense on an already-existing bodily state, at least in degree.
         2. Even clearer, we sometimes find ourselves, in the absence of any external cause of terror, feeling terrified.
      4. This seems to entail that soul-based dispositions are definable materially.
   2. The opinions of early thinkers about the soul.
      1. Historically, movement and sensation have been thought to be the reliable indicators of a soul-infused object.
         1. Many philosophers have viewed soul as the condition of possibility for all movement, or as the self-moving thing.
            1. Also, many of these philosophers have thought that soul and mind were the same thing.
         2. Other philosophers took perception itself to be the most characteristic attribute of the soul.
         3. Generally, those in both camps define the soul as constructed by an element (e.g. fire) or elements.
   3. Refutation of the view which assigns movement to the soul.
      1. Not only is (1.b.i.i) impossible, but it is in fact impossible that movement be an attribute of the soul.
      2. Things can be moved in two ways: (a) indirectly - by something else, or (b) directly - by its own power.
      3. Further, there are four species of movement: (a) locomotion, (b) alteration, (c) diminution, and (d) growth.
      4. If the soul is self-moving, its “moving-itself-ness” must be essential to it, and if so, because all (1.c.iii.a-d) above require place, the soul requires place.
      5. Since the soul moves the body, and the body moves by locomotion, it would seem to entail that the soul is itself moveable in space:
         1. If it is self-moving, it seems that it could aka. leave the body, which would imply the possibility of the resurrection of animals from the dead.
         2. It seems most likely that if the soul is at best incidentally moved by the body.
      6. In the sense where we think of mind and soul as the same thing, we realize that if infinite movement were coextensive with the soul, the mind would be infinitely moving (circularly, as Plato wants it in the Timaeus), which doesn’t seem to be the case as all practical instances of thinking possess very definite limits.
      7. If we can now agree that movement is not essential to the soul, movement must be contrary to the soul’s nature.
      8. Also, all views of the soul want to join it to a body without adding any specification of the reason of their union.
   4. The soul not a harmony.
      1. Another account is that the soul is a harmony: (a) a blend or composition of contraries, and (b) the body is compounded out of contraries. This is absurd because:
         1. There are many composite parts, variously compounded.
         2. All body parts (bone, muscle, etc) are different ratios of elements, so in order for the soul to be the composition of these elements, we appear to require multiple souls/harmonies to compose a body.
         3. E.g.: Is the soul identical with the ratio of elements, or is it something “above” this? Is love the cause of any and every mixture, or only those in the right ratio? Is love this ratio itself, or something “above” it? Etc.
      2. And now we know that the soul cannot be a harmony (1.d.i) nor can it be moved in a circle (1.c.vi). Yet it seems that it can be moved incidentally, and further it can power its vehicle (the body). In no other sense can the soul be moved.
         1. Qua those who say that the soul can be angered ([self-]moved to anger), this is as inexact as saying that the soul weaves webs or builds houses.
   5. The soul not moved with non-local movement.
      1. The case of mind is different, but in order to understand the mind as properly material, we only have to make the analogy to sight; both of these men lose with age, as their material elements disintegrate.
         1. So it seems clear that a disposition of the soul is not responsible for the incapacities of old age, but one of the body.
      2. Thus, finally, it is clear that the soul cannot be moved at all, and as such, certainly cannot be self-moving.
   6. The soul not a self-moving number.
      1. This hypothesis is by far the most unreasonable one yet, as it falls prey not only to the fallacy that the soul can be moved, but also to the ontological confusion that the soul is a number.
         1. How could a unit be moved? By what agency? What sort of movement would it be?
         2. Also, 1 divided in half equals a different unit, but plants and animals, when divided, are thought to retain the same soul in each segment.
   7. The soul not composed of elements.
      1. At this point, (1.b.i.i-1.b.i.ii) are refuted. What remains is to examine 1.b.i.iii. The reason for this doctrine is that its proponents think that only like can know like (i.e. only something composed of elements can know something composed of elements, i.e. bone or man).
      2. There’s nothing to be gained by the soul being composed of elements unless there are also various formulae of proportion consummate to the “recipe” for a soul. Even worse is that the recipe would have to contain the recipes of all the objects of its knowledge, which seems very unlikely.
         1. An ugly consequence of this is that it makes mortal souls more complete than the God-soul, as the God-soul is unable of knowing strife, but the mortal soul is.
         2. Continuing with the argument forwarded in (1.g.ii), we now ask: Why not just say everything has a soul? If everything is formed out of elements, each thing must certainly /know/ one or several or all of the elements.
         3. The anti-materialism argument: Mind is the primary thing, and these elemental-souls require matter to be more primary than mind!
      3. Secondly, if the soul is (i.e.) a substance, how will it know other types of beings (qua Categories: qualia, etc.)?
      4. Continuing the argument of (1.b.i.i-1.b.i.ii), then:
         1. If you consider the soul as the source of movement, and souls as the province of animals, you aren’t accounting for animals that don’t move/locomote.
         2. Further, if you want the soul as the perceptive faculty, you have to contend with the fact that while plants live, they aren’t endowed with either locomotion or perception, and most animals have no reason.
   8. The soul not present in all things.
      1. Some thinkers say that the soul is intermingled in the whole universe, but if so:
         1. Why/by what mechanism does it in some cases form an animal and not in all cases?
         2. Both ways you can answer this question lead to a paradox.
   9. The unity of the soul.
      1. Finally, some hold that the soul is divisible. But if this is the case, what holds its parts together? Surely not the body, it seems clear that the contrary is true (when the soul departs, the body decays).
      2. This argument also falls victim to the third man argument. If some unifying agency holds the soul together, is /that/ one or multipartite? Etc.
      3. From the plants argument (1.g.iv.ii), we know then that the soul is homogenous (it doesn’t have distinct parts) and that it is divisible (i.e. the smallest bit of soul is still homogenous soul).
      4. Finally, it seems that this principle in plants is a kind of soul, since it seems to be the only principle holding plants and animals together. Therefore, while it appears that soul is /necessary/ to perception, perception does not constitute soul. Neither locomotion, needless to say.
2. BOOK TWO
   So much for our predecessors’ views. Let’s make a completely fresh start:
   1. First definition of soul.
      1. Substance (determinate “what is”) is: (a) matter/potentiality - the stuff that makes up stuff - and (b) form/actuality/essence - that in virtue of which ‘this’ is ‘this’ as such, and (c) the combination of both.
         1. Of form/actuality, there are two grades, e.g. knowledge and the exercise of knowledge.
      2. Bodies are substances in the sense of (2.a.i.c: a composite) above.
      3. But, the body cannot be soul; the body is the subject or matter to the soul’s form. But form is actuality, and thus the soul is the actuality of a body thus characterized.
         1. In the first sense: of knowledge possessed; as waking corresponds to actual knowing (the exercise of knowledge).
         2. In the second sense: of knowledge possessed but not employed; sleeping.
      4. Thus the soul is the “first grade of actuality of a natural organized body.” Hence the soul/body distinction is meaningless: It is like asking whether the wax and the shape of the wax are one.
      5. More simply, soul is the essence of the thing. But this still requires having in itself the power to move itself.
         1. This power (”soulness”) is first-grade (essential) actuality, contra (2.a.iii.i), which is more second-grade (instrumental) actuality - more like the actuality of the axe.
      6. So, as the pupil + the power of sight constitutes the eye, so the body + soul constitutes the animal.
         1. From which it follows that (at least parts, if it has parts, of) the soul is inseparable from the body.
         2. Which leaves us with the problem of whether the soul is the actuality of the body in the sense that the sailor is the actuality (i.e. actuator) of the ship.
   2. Second definition of soul.
      1. Let’s now see what emerges from (a): we’ve discovered the conclusion of the syllogism, but we need to prove the ground (middle term).
      2. We know that what has soul differs from what doesn’t insofar as it displays life.
         1. Displaying life seems to be constituted by the power of self-nutrition.
         2. Displaying animal life seems to be constituted by sensation, namely touch.
      3. We have no evidence as yet about mind, which seems to be a very different kind of soul (eternal vs. perishable: “it alone is capable of existence in isolation from all other psychic powers.”).
      4. However, we are quite sure at this point that the soul (a) cannot be without a body (it is the actuality of the body), and (b) cannot be a body (it is something relative to a body), so:
         1. We can say that soul is an formulable essence of something that possesses a potentiality of being “besouled”.
         2. This leaves us needing a specification of what kind of body can be “besouled”.
   3. The faculties of the soul.
      1. We’ve mentioned the following powers of the soul: the nutritive, the appetitive, the sensory, the locomotive, and the power of thinking. All besouled things have at least one of these, and some have all.
         1. Certain of these entail others; i.e. all animals with the sense of touch have the appetitive power.
         2. There is no soul apart from the forms so enumerated. Hence, the desire for a general definition is destined to fail (qua. “figure”), and we must handle the problem on a species-level.
      2. So, the best way to define the soul is to give a definition of each of its forms.
   4. The nutritive faculty.
      1. Since nutrition (and reproduction, which he considers inseparable from the former) is the only factor common to all souls, we start there.
         1. Reproduction is an attempt to reach the divine, by the creation of an unbroken current of the same specific life flowing through a discontinuous series of individual beings united by descent.
      2. The soul is the cause of the body in three senses: It is (a) the source or origin of movement, (b) the end, (c) the essence of the whole living body.
         1. (c) is obvious since the essence of anything is the ground of its being, and in the case of living things, the ground of their being is life, and the soul is the source of life (by definition).
         2. (b) is manifest since Nature acts in a purposive way.
         3. (a) is maintained insofar as (i) qualitative change occurs via sensation, and (ii) quantitative change (growth and decay) occur via self-nutrition. Hence, all change comes from the soul.
      3. An account of food: The consumer of food transforms the food into itself.
         1. Historically, some thinkers have said that food is contrary to the thing which consumes it.
         2. Others have said that like is consumed by like.
         3. Aristotle will resolve this difference by saying that the former is undigested food, which is transformed into the latter by digestion.
      4. So, we can say that what is fed is fed because of the soul.
      5. The process of nutruition involves three factors: (a) what is fed, (b) that with which it is fed, and (c) what does the feeding.
         1. (c) is the first - earliest and most indispensible kind of - soul.
         2. (a) is the body, besouled.
         3. (b) is the food.
      6. But remember (qua 2.d.i.i) that the end of all this is reproduction, so the first soul is the reproductive soul, powered by a faculty of nutrition.
   5. Sense-perception
      1. Sensation in general relies on something outside itself as its object.
      2. Why do we not perceive the senses themselves as well as the external objects of sense?
         1. Or, why do the senses require objects since they are presumably made of the same elements as their objects?
         2. Sensitivity, then, must be a kind of potentiality (like, say, flammability).
      3. “Perceive” above as (a) the ability to perceive (a closed eye) and (b) actually seeing (something).
         1. Thus, sense must have both potential and actual senses too.
         2. Further, there are three “potentialities” here: The potential (e.g.) of a wild chimpanzee to communicate something linguistically, and the potential of someone sho speaks English to communicate something something linguistically, and someone actually saying something.
      4. Being “acted upon” by some (sense object, e.g.) also has two senses: (a) the extinction of two contraries (e.g. of food via digestion), or (b) the transformation of something like from potentiality to actuality by an actual thing (e.g. learning).
         1. The potentiality of (2.e.iv.b) also has two senses, e.g.:
            1. The way we might say that a boy may become a general.
            2. The way we say the same of an adult.
   6. The different kinds of sensible object
      1. There are three kinds of objects of sense:
         1. What is perceptible by a single sense (a “special object”: color, sound, flavor).
         2. What is perceptible by any and all senses (”common sensibles”: movement, number, figure).
         3. An “incidental object”: Something like “the son of Diares”, whose essence/concept is incidental to its perceptible qualities (i.e. a white object).
         4. (2.f.i.i-ii) are directly perceptible, (2.f.i.iii) is indirectly perceptible (or it relies on another facultly of perceptiblility -Pt).
   7. Sight and its object
      1. The object of sight is visible, which is to say that it is (a) color and (b) a certain kind of object that can be described in words but which has no single name (see below).
      2. If we want to understand color, we have to understand light:
         1. Light is the proper color of what is transparent (e.g. air, water), and exists wherever the potentially transparent is excited to actuality (by fire, he says; elements, we are thinking he means).
         2. Reflective things are bracketed here. Suffice it that what is seen in light is always color.
      3. The mechanics of seeing are like this: Color sets the air into movement, which comes into contact with the sense organ, which it sets in movement.
         1. This mechanism can be abstracted to describe the function of all senses: Sense object -> Medium -> Sense organ.
            1. The apparent difference between sight/smell/sound and touch/taste will be handled later.
   8. Hearing and its object
      1. Two kinds of sounds, actual (e.g. music) and potential (e.g. an instrument). Note that this distinction will be repeated for all senses, but not further noted.
         1. Actual sound requires two bodies with potential sound and a space between them.
      2. Voice is a kind of sound characteristic of what has soul in it.
         1. Voice is a sound with meaning.
   9. Smell and its object
      1. The reason why smell is more elusive to us than (2.g) and (2.h) is because our sense of smell is inferior (to our others, to that of other animals).
         1. This is evidenced by the fact that smell does not seem to give us clear knowledge (qua sight, hearing), but instead only the confused sensations of pleasure or pain.
         2. This is parallel to our sense of taste; the exception is that taste is more discriminating, since it involves touch.
         3. So much is our sense of smell confused, that we often describe smells out of a felt likeness to tastes (aka. we describe honey as smelling sweet because it tastes sweet and we end up associating that with smell, in absense of a “real” vocabulary of smells).
   10. Taste and its object
       1. Taste is directly reliant on touch. The thing that touches the tongue must be liquid/dissovable.
       2. The organ of taste must be able to become assimilated to its objects, so it must be a non-liquid capable of “liquidizing” - aka. becoming moist.
       3. Similar to the categories of smell, tastes are either (a) bitter/saline or (b) sweet/succulent. From (2.k.iii.a-b): Pungent, harsh, astringent, and acid.
   11. Touch and its object
       1. It is a problem whether touch is one sense or a group of senses.
       2. There is another problem about what the organ of touch is (the flesh? or is that the medium of touch, the real organ situated further inward?).
       3. A third problem is whether all senses are taking place in the same way (e.g. through touching the medium). Aristotle will say yes to this one.
          1. Basically, if you place a white thing on the eye, you can’t see the whiteness, etc. Hence, senses need media. Hence, the flesh is not the organ of touch, but rather the medium.
       4. Finally, we can’t percieve a mean of hotness and coldness (or, e.g. blackness and whiteness), we rather only percieve hotness exclusively or vice versa.
          1. This seems to imply that sense itself is a ‘mean’ between any two opposite qualities of objects as determined by that sense.
   12. General characteristics of the external senses
       1. Overview: What is a sense?
          1. A sense is that which has the power of receiving into itself the sensible forms of things without the matter.
          2. An organ of sense is that in which (2.m.i) is seated.
       2. An explanation of plants, then, is that they don’t contain within themselves the means of contrary qualities.
       3. Finally, as to the question of whether objects of sense can affect bodies without the proper sense organs:
          1. Light, sounds, smells leave bodies quite unaffected, what does affect bodies is the media (the air, e.g.) of these objects of sense.
          2. For example, the visual effect of lightning doesn’t split a tree trunk, the air affected by the phenomenon does.
          3. Senses, then, are just observers of the resultant changes in the media of sense-object transmission.
3. BOOK THREE
   1. The number of external senses
      1. How can we be sure that there are just five senses?
         1. Touch covers any potential comers viz. sensation by contact, and thus all other senses are handled through a medium.
         2. Assume that for every sense there needs to be a sense organ, which is made of the same element as the medium through which the object of sense passes (eyes of water, ears of air, noses of one or the other).
         3. Given that no sense organs seem to be made of earth alone (except maybe those under the domain of touch), and further either none or all of them contain fire, then all the possible sense organs are possessed by well-formed animals.
         4. This argument assumes that the four elements are those of the world, and there is no other.
      2. The common sensibles (2.f.i.ii) are percieved by two qualities contemperanously. If there were special sense organs, our perception of the common qualities would always be incidental (aka. we couldn’t tie whiteness to Cleon’s son perceptibly).
         1. We do posess a general sensibility which enables us to perceive them directly.
         2. This “percipient sense” is what allows us to tie two individual sense-data (yellow, bitter) together in a single perception.
         3. That we have many senses instead of just one (a) provides determinacy, and (b) reveals the distinction between common sensibles and special sensibles.
   2. Common sense
      1. The question of whether a sense can be self perceptive (aka. is it by sight that we know we are seeing?)
         1. The appeal to hallucination: Sight (or the eye) itself must be colored, since it can experience color/vision without the material of the thing (think of a red apple).
      2. Further, like a thing may have a sound without (actively being) sounding, so a thing may have hearing without (actively) hearing.
         1. That said, actively sounding and hearing are the same event: “Since the actualities of the sensible object and of the sensitive faculty are one actuality in spite of the difference between their modes of being, actual hearing and actual sounding appear and disappear from existence at one and the same moment, while as potentialities one of them may exist without the other.”
         2. Hence, the relationship of actual sensation (between sensor/sensed) is a ratio: Objects of sense are pleasant in sensible extremes, and painful in excess.
      3. But how do we discriminate between sense objects of different sensory domains (aka. whiteness and sweetness)?
         1. There has to be some faculty that has access to the experience of both whiteness and sweetness.
         2. This has to be done simultaneously.
   3. Thinking, perceiving, and imagining distinguished.
      1. Remember our two faculties of the soul, (1) local movement and (2) thinking/perciving/discriminating.
      2. Thinking is akin to perceiving, for in both the soul discriminates and is cognizant of something that is.
         1. Thinking has - historically - even been identified with perceiving, although this doesn’t seem to account for the possibility of error. Unless:
            1. Whatever seems is true (there is no truth/appearance distinction).
            2. Error is contact with the unlike (although it is also widely accepted that only like can know like, and likewise error).
         2. Hence, perceiving and practical thinking are not identical. (Just think: the former is universal to all animals, the latter quite rare.)
         3. Further, speculative thinking (imagining) is also different from perceiving.
            1. In discrusive/practical thinking we are called to form judgements, in which we are constrained by truth and falsity, contra the more “free” terrain of imagination.
            2. Also, we can imagine things that will stimulate us similarly to perceptions, but which don’t endanger us.
         4. Hence, thinking is divided into thinking as judgement (3.e-h) and thinking as imagination (3.d).
   4. Imagination
      1. Imagination is not sense:
         1. Sense is either a faculty or an activity (sight, seeing), imagination takes place in the absense of both (e.g.: in dreams).
            1. Visions appear to us even when our eyes are shut.
         2. Sense is always present in animals; imagination is not.
         3. Sensations are always true; imaginations are for the most part false. (Saying that we “imagined it to be a man” is an indicator of its sense-falseness.)
      2. What is it?
         1. It’s not knowledge or intelligence, for it can be false, while the former cannot.
         2. It is not opinion, because opinion involves belief (which entails conviction, which entails reason).
            1. Hence imagination cannot be opinion in any way combined with or mediated by sensation.
         3. But, imagination is still held to be moved by sensation, and hence impossible without sensation.
            1. This movement must be necessarily (a) incapable of existing without sensation, and (b) incapable of existing except when we perceive.
            2. That in which it is found may contain phenomena both active and passive.
            3. It (the movement which spurs imagination) may be either true or false.
         4. The reason for (2.d.ii.iii) is that imagination relies on combined objects of common sense, so
            1. While single-sense-objects cannot be false (aka. whiteness is white).
            2. Second- (what is white is this or that) and third- (attributes of second-: movement, magnitude) degree objects of sense may be subject to sense-illusion.
         5. Hence, imagination must be a movement resulting from an actual exercise of sense.
   5. Passive mind.
      1. Now to turn to the thinking and knowing part of the soul. What differentiates this part, and how does thinking take place?
      2. Mind must be related to what is thinkable as sense is to what is sensible. Since (a) everything is thinkable, then, and if (b) like can only think like, and (c) the soul admits no admixture, then mind, “before it thinks, [is] not actually any real thing.”
         1. Hence, it cannot be blended with the body, lest it acquire some quality.
         2. Hence, the intellective soul is a place of potential forms.
      3. Extreme experiences of mind (very clear thoughts) seem to have the opposite effect of extreme experiences of sense (very loud music); they make the forthcoming thought more acute, and not confused.
         1. Once the mind has taken the shapes of all its objects of knowledge, it moves from the first kind of passivity to the second (cf. 2.e.iv.i): the mind is then able to think itself.
         2. Insofar as the realities the mind knows are capable of being separated from their matter (straightness vs. something straight), so also are the powers of the mind. (I wish I had an example here.)
      4. A possible objection: If mind is thinkable per se and what is thinkable is like the thinking thing, then either (a) mind belongs to everything, or (b) mind will contain some element common to all thinkable things.
         1. Qua (3.e.iv.a): Mind is /potentially/ like whatever is thinkable.
         2. Qua (3.e.iv.b): Mind is thinkable in exactly the same way its objects are: it is the potentiality of immanence as such that allows all things (speculative and materiality alike) to be thinkable. And what is mind if not the potentiality of immanence?
   6. Active mind.
      1. Since in every class of things we have (1) a matter which is potentially all the particulars included in the class, and (2) a cause which is productive in the sense that it makes them all (e.g. 2:1 as art:material).
         1. In (3.e.ii) above, we described mind as something which takes the form of its objects.
         2. In addition to this, we need a positive state which “makes” things (like light makes colors).
      2. While potential knowledge is prior in time in a subject to actual knowledge, not so in the universe.
         1. “When mind is set free from its present conditions” (when is this?) “it appears as just what it is…this alone is immortal and eternal…and without it nothing thinks.”
         2. What on earth is that referring to? I have to guess that its point at the sort of disembodied cosmological mind - mind as such - that is God. Or maybe our individual minds join up to the universal mind at death? All our souls are part of one big soul-mass, which distributes itself amongst life?
         3. Note: In the “Generation of Animals” Aristotle speaks of an intellect that enters “from without” (GA 736 b 27).
   7. The double operation of mind.
      1. Falsehood always involves a synthesis of two objects of mind (single sense-perceptions are always true).
         1. The unifying/synthesizing faculty is mind.
      2. The mind is capable of identifying simple (indivisible objects) as well.
      3. This unification of (3.g.i) can occur with actually or theoretically unified/divided objects (note that dividing the unified and unifying the divided work the same way here):
         1. Actual: The mind can divide an actually undivided length (in a similarly undivided time): In this instance, it can (e.g.) divide it in half (the object has no parts until it is divided), which also divides the time into the time in which there are two and the time in which there is one.
         2. The object of thought and the time in which it is thought here are only incidentally divisible. They also contain some indivisible unity, which gives us the time and the length as such.
         3. The best thing I can come up with here is that to have a simple line (or two), you have to have a simple time. As soon as you complicate the line (by, say, splitting it) you need complex time or the relation of contraries (one and two lines).
      4. In overview: That which cognizes must be characterized actually by one and potentially by the other of two contraries. (E.g. the cognition of evil or black.)
   8. The practical mind, and the difference between it and the contemplative.
      1. Here we get some light on (3.f.ii.ii): “…in the universe [potential knowledge] has no priority even in time; for all things that come into being arise from what actually is.”
         1. So, simple objects of sense (2.f.i.i) and knowledge (3.g.ii) - perceptions - are like bare asserting or knowing.
         2. Complex objects of sense and knowledge (movement, pain) are arrived at by negation or “quasi-affirmation” (qua 3.g.iii).
      2. The thinking soul uses images as the contents of perception. (They are like, e.g. the air that modifies the pupil for the soul: (perception-objects -> images -> soul).
      3. Let the single-sense faculties unified by (3.b.iii) be C and D where A and B are their sense objects.
         1. A:B :: C:D (aka. sweet:hot :: taste:touch)
         2. This is ostensibly how the thinking soul uses images to create judgements, which in turn lead to actions (pursuit/avoidance).
         3. Note that this is a faculty exclusive to the speculative mind. (See 3.c.ii-iii)
   9. Comparison of mind with sense and with imagination.
      1. In summary, the soul is in a way all existing things:
         1. Sensation is in a way what is sensible
         2. Kowledge is in a way what is knowable
         3. Knowable and sensible things are exhaustive of all things.
         4. The question now is: What is the way in which this is true?
      2. Within the soul, the faculties of knowledge and sensation are potentially the knowable/sensible.
         1. These potentialities must be either the things themselves or their forms.
         2. The former is impossible (viz. the stone). It must be the forms.
         3. Hence, the soul is analogous to the hand: As the hand is a tool of tools (a tool for using tools), the mind is the form of forms and sense the form of sensible things.
      3. Hence (how?):
         1. No one can learn anything in the absence of sense.
         2. When the mind is actively aware of anything, it is so through an image.
      4. Imagination is different from assertion and denial, as the latter require a synthesis of concepts.
         1. In what way do concepts differ from images?
         2. Must we not say (he asks) that concepts are not images, though they necessarily involve them?
   10. Problems about the motive faculty.
       1. Remember (again, from [3.c.i]) our two faculties of the soul, (1) originating local movement and (2) discriminating.
       2. Now, what is it in the soul that originates movement? Is it a part or the whole thing?
          1. If we have to break up the soul we’re going to stick with the old schema (2.c.i):
             1. The Nutritive
             2. The Sensitive
             3. The Imaginative/Practical (3.c.ii-iii, 3.h.iii.iii)
             4. The Appetitive
       3. Let’s start with a restricted subset of movement: What generates forward movement in the animal?
          1. It seems like the appetitive and the imaginative faculties would motivate the animal to move.
          2. It can’t be the nutritive faculty (since plants share that), nor the sensitive (for there are animals with sensation which don’t move).
          3. It can’t be the calculative/specutlative mind, for this doesn’t think things which are practical.
          4. In short, it is desire that is moves us.
          5. But we observe that something else is required to produce action in accordance with knowledge, as appetite is “too incompetent to account fully for movement.”
   11. The cause of the movement of living things.
       1. In short, it appears that the appetites and the imaginative part of mind (shared by all animals, that is, the non-rational part) motivate all movement.
       2. The practical mind is stimulated by the object of an appetite. Both practical mind and appetite are end-oriented.
          1. This ultimately means that when the imaginative/practical facility originates movement, it does so on behalf of an appetite.
          2. Thus the origin of movement is the appetitive faculty of the soul.
       3. All movement involves (a) that which originates the movement, (b) that by means of which it originates it, and (c) that which is moved (the animal).
          1. (a) may mean either something which is itself unmoved (the realizable good) or else something which is at once moves and is moved (the faculty of appetite).
       4. To sum up, insofar as an animal is capable of appetite, it is capable of self-movement. It is not capable of appetite without possessing imagination (either calculative or sensitive).
       5. Three modes of movement are possible:
       1. That in which the appetites overpower wish (gluttony)
       2. That in which the wish overpowers the appetites (restraint)
       3. That in which appetites overpower appetites (the dog drops the bone in the water)
   12. The faculty of knowing is never moved but remains at rest.
       1. The domain of knowledge is the universal, not the particular.
4. The mutual relations of the faculties of the soul, and their fitness for the conditions of life.
   1. To wrap up: All besouled things have the nutritive faculty.
   2. All animals have the sensitive faculty.
      1. Further, animals require touch specifically in order to survive (touch is a condition of being embodied).
      2. That is why taste is a sort of touch; it is the sense of the tangible and nutritious.
   3. It is clear that the body of an animal cannot consist of a single element, as it requires touch.
      1. The element of touch is earth, so earth-constitution is a requirement for embodiment.
      2. Additionally, touch must be composed of other elements, since it is capable of perceiving (e.g. hot/cold).
      3. This will also explain why when an excess of sensation is presented to any other sense (very loud noise, etc.) it simply destroys the specific sense-organ, but when an excess of touch (burning, etc) is given, it destroys the animal.
   4. Touch is “the essential mark of [animal] life.”

Overview

The first six books of Aristotle’s metaphysics serve to give the problem of being its historical and theoretical context. Book I discusses the definition and purposes of philosophy, and gives a short recapitulation of its history. Book II seeks to address in advance concerns about Aristotle’s metaphysics, by making the argument against the possibility of an infinite regress. Later in the Metaphysics, this will be developed into the famous argument for God. Book III provides a sketch of the main problems of philosophy. Book IV details a few additional premises of Aristotle’s argument, namely the arguments for the principles of non-contradiction and the excluded middle. Book V is a philosophical lexicon, giving the meanings of 30 key philosophical terms. Book VI, finally, leads into the main argument (given in parts VII-IX), by excluding two of the senses of Being detailed in Book V as the proper object of study for metaphysics.

1. BOOK I/BIG ALPHA

   1. The advance from sensation through memory, experience, and art, to theoretical knowledge.
      1. Since we all desire to know, we rejoice in our senses. Particularly in sight.
      2. Sensation gives some animals memory, and those which have memory and hearing can be taught.
      3. Humans also have art and reasoning.
      4. Art arises when from many notions gained by experience, one universal judgment may be made (not particular, e.g. medicine good for all people with symptom n, not just Socrates).
      5. Nonetheless, it must be remembered that art can only be applied to particulars (aka. one cures Socrates, not disease y).
      6. Wisdom, though, is in knowing why the thing is so, and not simply in knowing that it is.
      7. Hence, Wisdom is knowledge about certain principles and causes.
   2. Characteristics of ‘wisdom’ (philosophy).
      1. Generally wise people: can know many things (although not necessarily in detail), can know hard things to know, can teach well, etc.
      2. Things far from the senses are hardest for men to know. Knowing these universals is a good indicator of wisdom.
      3. The most worthy of knowing among these are the first principles and causes. This is philosophy.
      4. There is no doubt straightaway that this is not “a science of production”, but rather a slow, arduous process of uncovering.
      5. There may also be some concern that philosophy’s objectives are either beyond human means or that their achievement would make God jealous.
         1. Not so: “God is thought to be among the causes of all things and to be a first principle…”
         2. Not so: “such a science either God alone can have, or God above all the others.”
   3. The successive recognition by early philosophers of the material, efficient, and final causes.
      1. Causes are spoken of in four senses:
         1. The essence/substance