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
        2. Matter or substratum
        3. The source of the change
        4. The purpose and the good
      2. The first philosophers identified material constituting the essential part of all things (c.i.ii above) as causal: The essence of Socrates constitutes Socrates whether he is being beautiful, or musical, or not.
        1. Ancient philosophers are generally materialists (aka. one or some combination of the four elements): Yet they don’t agree on the number or nature of these principles.
      3. For those among the ancients who abide multiple causes, we have things like fire as having independent essences (c.i.i above).
      4. But /why/ do these materials form things? And how do elements cause things like beauty? Anaxagoras talked of a /reason/ throughout nature (c.i.iii?).
    4. Inadequacy of the treatment of these causes.
      1. As an exemplar for someone who had an idea, but didn’t carry it out systematically, Aristotle poses Empedocles as the first to mention the bad and the good as principles (c.i.iv?). He was also the first to pose four material elements (though he treaded them as two: fire and its opposites).
      2. But, generally (and there are some specifics here), their treatment of the causes was quite inadequate.
    5. The Pythagorean and Eleatic schools; the former recognizes vaguely the formal cause.
      1. The Pythagoreans were the first to take up mathematics; they thought that all things (justice, soul, reason, etc) were expressible numerically. Numbers were their first principle.
        1. This gives way to a principle where even and odd are two causes, and from one springs all numbers. This in turn gives way to binary cognates: even/odd, male/female, one/many, left/right, good/bad.
        2. From this we can learn that the contraries are the principles of things.
        3. Notably (later, 987:13) unique to Pythagoreans, also, is the thought that finitude and infinity are not attributes of other things, but are themselves the substance of the things of which they are predicated.
      2. In particular, what’s germane to Aristotle is Parmenides’ conception of the One:
        1. Seeing as being is everything that exists and nothing that doesn’t, it is one.
        2. But our senses show us many things.
        3. Parmenides then gives us a two-cause/principle system: hot/cold qua existent/nonexistent.
    6. The Platonic philosophy; it uses only the material and formal causes.
      1. Socrates was busying himself about ethical matters, but in seeking the universal in these, fixed his thought for the first time on definitions.
      2. Since sensible things are always changing, any common definition could not be of them, and must rather be of an Idea. Sensible things are “named after these” in virtue of their participation in them.
        1. Note: Objects of mathematics apparently fit somewhere between sensible things and Forms, since they are eternal and also many.
        2. The participation relationship as such, provides the possibility of a unique /separation/ between the one and the many.
        3. Yet, what /happens/ appears to be contrary to this, since (i.e.) a man who makes tables applies the form, and though he is one, makes many tables. (What is the argument here?)
      3. So Plato recognized two types of causes:
        1. Essential: The Forms are the essences of things, and the One is the essence of the Forms
        2. Material
    7. The relation of the various systems to the four causes.
      1. Almost everyone gets the matter causes: be it fire and water, the infinite, atoms, the great and the small.
      2. Some others have mentioned the source of movement, e.g. friendship and strife, or reason, or love.
      3. No one has expressed the essence (i.e. substantial reality) distinctly. Plato hints at it with the Forms.
      4. The good as a cause is both said and unsaid in the philosophers of movement’s causes. For those who say that the One or the existent is the good, and that it is the cause of substance, but not that is for the sake of this. It is not then a cause qua good, but only incidentally.
    8. Criticism of pre-Platonic philosophers.
      1. One cause (ie. fire or water or air) is not a tenable position, because it gives no account of movement, or essence, etc. Similarly, multiple material elements.
      2. Anaxagoras has an interestingly modern position, but is still part of a camp that deals only with the sensible, and thus, cannot offer us a compellingly complete account of ontology.
      3. The Pythagoreans, who now deal with things visible and invisible (including numbers), still only deal with the physical world, implying that they actually agree with the physical philosophers that the real is constituted by only perceptible, sensible things.
    9. Criticism of the doctrine of ideas.
      1. The Forms are nefariously difficult to prove.
        1. There’s no convincing way to prove that they exist in the first place.
        2. Further, of the more accurate arguments, some lead to Ideas of relations, of which we may say there is no independent class, and other introduce the ‘third man’ (infinite regress of forms: F1:[a,b,c]->F2[F1,a,b,c]->…)
        3. How could the substance and that of which it is the substance exist apart?
      2. The Forms are not even that beneficial if they exist
        1. The doctrine of the Forms seems to necessitate as many Forms as there are things in the world. Apparently, this will also require Forms for the negations of things.
        2. Given (j.i) and (j.ii.i) it seems entirely unclear what exactly the Forms are contributing to either ontology or epistemology.
      3. A second thread, a participation relation tells us nothing about causation.
        1. How do sensible things come into existence given the existence of the Forms?
        2. Numbers cannot be Forms because Platonists speak of the One has homogeneous.
        3. How would a theory of Forms account for (e.g.) points on a line? [What’s the argument here?]
      4. The overview
        1. There’s no convincing account of the causes of movement from a theory of Forms.
        2. The proofs of oneness show not the oneness of all things, but the existence of a One in itself, which requires us to grant a lot of assumptions.
        3. It’s unclear how things combine to allow things like points, lines, and planes from numbers: These aren’t Forms, nor intermediates, nor perishable things. They seem to be a fourth class.
        4. How could we /learn/ the Forms of all things (contra Socrates’ recollection model)? How can we know “straightness” outside of straight things?
        5. Finally how can we comprehend sense-primitives with Formal concepts? (He doesn’t say this, but it’s Kant’s left-right intuition from the Prolegomena.)
    10. The history of philosophy reveals no causes other than the four.
  2. BOOK II/LITTLE ALPHA
    1. General considerations about the study of philosophy.
      1. Philosophy is the attempt to attain knowledge of truth. The (eternal) truth which causes all other truths is the sublime object of philosophy.
    2. There cannot be an infinite series, an infinite variety of kinds, of causes.
      1. There is a first principle, and the causes of things are neither (b.i.i) an infinite series nor (b.i.ii) infinitely varied in kind.
        1. Cause itself necessitates that the series of causes be bounded. If (a) every (temporal) events is caused, and (b) there is no beginning of this series, then (c) every event is an intermediate event (requiring a causal agent that precedes it), and therefore (d) nothing causes anything else. Better:
          1. A contingent being exists (a contingent being is such that if it exists, it can not-exist)
          2. This contingent being has a cause or explanation of its existence.
          3. The cause or explanation of its existence is something other than the contingent being itself.
          4. What causes or explains the existence of this contingent being must either be solely other contingent beings or include a non-contingent (necessary) being.
          5. Contingent beings alone cannot cause or explain the existence of a contingent being.
          6. Therefore, what causes or explains the existence of this contingent being must include a non-contingent (necessary) being.
          7. Therefore, a necessary being (a being which, if it exists, cannot not exist) exists.
        2. If the kinds of causes are infinite, then knowledge (this seems to mean, “complete knowledge”) is impossible, because we cannot account for/abstract from infinite types causes in finite time.
    3. Different methods are appropriate to different studies.
      1. Getting knowledge (ontology) and getting the way of attaining knowledge (epistemology) are two different things, and require different modes of discourse.
  3. BOOK III/BETA
    1. Sketch of the main problems of philosophy.
    2. Fuller statement of the problems: -
      1. Can one science treat of all the four causes?
      2. Are the primary axioms treated of by the science of substance, and if not, by what science?
      3. Can one science treat of all substances?
      4. Does the science of substance treat also of its attributes?
      5. Are there any non-sensible substances, and if so, of how many kinds?
      6. Are the genera, or the constituent parts, of things their first principles?
      7. If the genera, is it the highest genera or the lowest?
      8. Is there anything apart from individual things?
      9. Is each of the first principles one in kind, or in number?
      10. Are the principles of perishable and of imperishable things the same?
      11. Are being and unity substances or attributes?
      12. Are the objects of mathematics substances?
      13. Do Ideas exist, as well as sensible things and the objects of mathematics?
      14. Do the first principles exist potentially or actually?
      15. Are the first principles universal or individual?
  4. BOOK IV/LAMBDA
    1. Our object is the study of being as such.
      1. In order to grasp first causes/principles, we need to study being as being. We arrive at this conclusion because it must be something about being as such that is /necessary/ to the existence of things.
    2. We must therefore study primary being (viz. substance), unity and plurality, and the derivative contraries, and the attributes of being and of substance.
      1. All things that are said to be refer to a single “thing”, namely, substance.
        1. “Substance” is the stuff of being, it seems, because things are said to be insofar as they are related to (are, or are qualities of, or are negations of, etc.) substance.
        2. Hence, substance is the subject of philosophy.
      2. Now, there are as many parts of philosophy as there are kinds of substance. What we are detailing here is “first philosophy” (here, ontology).
        1. Being and unity have a strict causal relationship (”one being” parses out to the same content as “being”). This means that the study of unity is part of the study of being, and hence falls under first philosophy’s domain. (Entails sameness, etc.)
        2. Likewise, as difference is simply the negation or privation of unity, this too must fall under the domain of our first science. Which entails of course unlikeness, otherness, contrariety, etc.
        3. Also, the history of philosophy tells us that all things are either contraries or composed thereof (hot/cold, love/strife, limited/unlimited), and hence in this way too we can see that first philosophy entails a study of being as sameness and otherness.
        4. So our first philosophy will examine being qua being, and also the attributes that belong to it qua being: prior/posterior, genus/species, whole/part, etc.
    3. We must study also the primary axioms, and especially the law of contradiction.
      1. Truths that hold good for everything there is (axioms) doubtless also belong to the domain of first philosophy. The reason is that what unites these axioms is being itself, so they are axioms that hold good for all things qua being.
      2. And here Aristotle introduces, as the fundamental axiom, the law of non-contradiction.
        1. Remember, this is a term logic: “the same attribute cannot at the same time belong and not belong to the *same subject* and in the same respect.” (My emphasis: Not subject/predicate-combo [proposition]).
    4. Fatal difficulties involved in the denial of this law.
      1. This law is so solid that no educated person should ever demand its demonstration.
      2. We can however demonstrate it negatively:
        1. Reasoning is possible because words at least one meaning. (E.g. Men are ‘two-footed animals’.)
          1. If they had several, we could create new words for each of the meanings.
          2. If they had infinite meanings, reason would be impossible. Likewise if they had none.
        2. So, if a name has one and only one meaning. This entails that “being a man” cannot mean “not being a man”.
        3. Any confusion of the signifier/signified relationship is just that: confusion. It doesn’t point to the possibility that words have multiple meanings.
      3. Given that, we understand that non-contradiction is necessary. (E.g. a man can not both be and not be a two-footed animal.)
      4. Further, this incontradictable “manness” is the very substance/essence of what it is to be a man.
        1. So, attributes are not essential (e.g. against the view that not-manness could be an attribute of a man, I suppose) because this would entail infinite predication:
          1. An accident is of a subject, not another accident: The white is not musical, the man is white and musical.
          2. But, in “Socrates is musical” both terms are “accidental to something else.” So, two senses:
            1. White is accidental to Socrates, and Socrates the white has not yet another accident.
            2. White cannot have musicality.
          3. On overview: Sense (d.iv.i.i) reduces to sense, and (d.iv.i.ii), in this an infinite number of accidents combined together is impossible; there must be substance somewhere.
        2. The end result of this is you’re just talking about infinite indeterminate subjects, all of which must be predicated by the affirmation and negation of every attribute.
          1. We say x is y.
          2. We say z is b.
          3. We say x is not z qua b. This entails x is not b.
          4. Without N/c we say x is b.
          5. This entails in turn that x is in fact z, and every other subject, etc.
      5. Two arguments in conclusion
        1. Nicely summed up: “If it is true that a thing is a man and a not-man, evidently also it will be neither a man nor a not-man.”
        2. Either N/c is true of everything, or else of nothing. If it were true of something, then the possible predicates of that would be subject to it, and so on…
      6. Two more tempered arguments
        1. Practically, we don’t see people walking off cliffs all the time, so they must be capable of some kind of judgements, and hence telling the difference between good and not-good.
        2. Additionally, there seems to be “more truth” in thinking that 4 is 5 than there is in thinking that it’s 1000. In other words, he admits of some “degree” of attributes that’s possible in things (terms). [Again, this would appear to be contra propositional logic.]
    5. The connexion of such denial with Protagoras’ doctrine of relativity; the doctrine refuted.
      1. Nonetheless, we see contradictions cropping up everywhere - aka. two men will have contradictory opinions on what is good. This can lead to a certain relativism, that all opinions are right!
      2. This is due first to a confusion about two senses of “be”: namely, something can potentially at the same time two contraries, but not actually.
      3. Secondly this confusion arises as entailed by a confusion about from whence truth comes. Namely, some think that truth arises from the sensual appearances. (Aka. they think that since things become, they are neither being nor non-being exactly, or rather both.)
        1. There’s an appeal here that things are changing only in quantity, not in quality.
          1. Note generally that the required product is to show that there’s something changeless.
        2. Not all appearances are true; people (e.g. doctors) and senses (e.g. sight) have different degrees of authority on various objects of appearance. But the appearance of (e.g.) sweetness as such will never be changed (sweetness will always be sweet).
    6. Further refutation of Protagoras.
      1. If not all things are relative, and some are self-existent (e.g. the objects of sensation), not everything that appears will be true.
      2. If a thing is one, this entails that it is in relation to either one or a definite number of things; that “that which thinks” is in relation to infinite things is impossible. (This is an argument against solipsism.)
    7. The law of excluded middle defended.
      1. There cannot be an intermediate between contradictories. If there was, saying “it is” or “it isn’t” is bankrupt of its content.
      2. Another regress: If there is a term B which is neither A nor not-A, there will be a new term C which is neither B nor not-B.
      3. So, if (4.e.iii) then everything is true, and if (4.g.i) then everything is false.
    8. All judgements are not true, nor are all false; all things are not at rest, nor are all in motion.
      1. Any of this requires us to postulate the notion of “meaning”. Namely, that we know what it is for something to be true or false.
      2. Hence, given (4.c.ii) and (4.h.i), some judgements must be true and some must be false.
      3. This dictates also that there are both motion and rest.
        1. Admitting that there is some truth in (4.e.i), and that some propositions can be true and false at different times, there must be movement.
        2. And, if everything is constantly in motion, nothing can be true. We can be assured that the former clause of the previous sentence is false by appeal to (2.b.i) [among other things].
  5. BOOK V/DELTA: PHILOSOPHICAL LEXICON
    1. Beginning
      1. The ways in which it is spoken of.
        1. The first point or the best point at which to start.
        2. The immanent (a house’s foundation) or non-immanent (parents to child) start of something.
        3. The mover/changer of something.
        4. The condition of knowability of something.
      2. What these ways have in common.
        1. They are the first point from which a thing comes to be (known).
    2. Cause
      1. The ways in which it is spoken of.
        1. The material stuff (bronze:statue) or the pattern (or essence) of something.
        2. Both the beginning (5.a.ii) and the end of something (one walks for health).
      2. What follows
        1. There are several causes of one thing.
        2. Causes and effects usually play both roles reciprocally (excercise is a cause of good health, which causes exercise).
        3. Contraries are usually causes for contrary effects (the presence and privation of the steersman:safety and shipwreck).
      3. Four senses of causes: Material substrata, essences, sources of change, ends.
      4. Genus and accident:
        1. Causes as either the individual, or the genus, or as the accidental, or as the genus that includes the accidental.
        2. Genus-causes are also inherited from parent objects (the sculpture is caused by Ron, and man, and animal, and living thing, etc.).
        3. Accidental causes are “accidentally” inherited from individuals (the sculpture is caused by Ron, who is musical, so the musical caused the statue).
      5. What these ways have in common.
        1. They may all be taken as acting or having a capacity, although this works in different ways.
    3. Element
      1. The ways in which it is spoken of.
        1. The (indivisible) primary component(s) immanent in a thing.
        2. Indivisible primary things that are useful for many purposes (aka. atoms) - cf. /elemental/.
      2. What these ways have in common.
        1. The element of each thing is the first component immanent in each.
    4. Nature
      1. The ways in which it is spoken of.
        1. The genesis, the cause of genesis (seed), and the source of the primary movement of growing things (mother:baby).
        2. (a) The primary material out of which an object is made (wood:bed), or (b) the essence of a natural object.
        3. By extension of (5.d.i.ii.b), every essence in general.
      2. What these ways have in common.
        1. The essence of things which have in themselves a source of movement.
    5. Necessary
      1. The ways in which it is spoken of.
        1. (a) That without which a thing cannot live (breathing, food) and (b) that without which good cannot come (medicine).
        2. The compulsory and compulsion (doing one’s taxes).
      2. What these ways have in common.
        1. That which cannot be otherwise than it is.
    6. One, Many
      1. The ways in which it is spoken of.
        1. One by accident (Coriscus is musical and just; musical:just)
        2. One by its own nature (continuous things: straight lines are more “one” than bent lines).
        3. One by virtue of homogenous substratum.
        4. One by virtue of participation in a genus ([horse, man, dog] qua “animal”).
        5. One by indistinguishability (Leibniz’s identity of indiscernables).
        6. Generally, one by continuity, form, or definition. (qua form: Circle is more “one” than straight line.)
        7. Beginning in number.
      2. What these ways have in common.
        1. Oneness by (a) number by essence, (b) species by definition, (c) genus by shared figures of predication, (d) analogy by relation to a third or fourth thing.
      3. “Many” will be the opposite of these.
    7. Being
      1. The ways in which it is spoken of.
        1. Accidentally. By unessential attributes: musical, white.
        1. Synthetic predication: Both belong to the same thing, and this is.
        2. The subject of which the attribute is predicated is.
        3. The attribute which is predicated on a subject is.
      2. Essentially: By their own nature.
        1. By the categories (inc. analytic/tautological predication).
      3. A statment that is true. (”Socrates is musical.”)
      4. That which is potentially and actually (the half line is in the line, we still call the first corn sprouts corn).
    8. Substance
      1. The ways in which it is spoken of.
        1. The simple bodies (earth, fire, water, etc); everything else is predicated on them.
        2. That which, being a subject’s unpredicated attribute (e.g. an animal’s soul) and its cause.
        3. The enabling condition of an individual, the loss of which would entail the loss of the individual (e.g. plane to line).
        4. The essence or definition of a thing.
      2. What these ways have in common.
        1. The ultimate substratum.
        2. The separable nature of the shape or form of each thing.
    9. The same, Other, Diffferent, Like, Unlike
      1. The ways in which it is spoken of.
        1. The same as accidental (coincidence of attributes in an individual). Aka. the musical man is the same as the musical.
        2. The same by their nature: Sameness as a unity of treating many as one (these Warhols) or one as many (my “self” qua mind/body dualism).
        3. Different: (a) things which though other are the same in some respect, (b) those whose genus is other, to contraries, etc.
        4. “Like” things have the same attributes in every respect, or many same attributes, those whose quality is one, sharing in the most salient attribute(s).
    10. Opposite, Contrary, Other in species, The same in species
      1. The ways in which it is spoken of.
        1. Contradictories and contraries, relative terms, qua privation and possession.
        2. Contrary:
          1. Attributes differening in genus that can’t belong at the same time to the same subject
          2. The most different of things in the same genus
          3. The most different of attributes/things in the same subject/faculty
          4. The most different absolutely or in genus or in species.
          5. Things which being in the same genus have a difference (”man and horse” via animals).
    11. Prior, Posterior
      1. The ways in which it is spoken of.
        1. Empirically
          1. Prior: Some things because they are nearer to some (absolute, natural or referential) beginning.
          2. Posterior, because they are farther.
          3. Beginnings can be spatial, temporal, qua movement (boy:man) or power, or in arrangement.
        2. Qua Knowledge: Prior in definition (e.g. universals).
        3. The attributes of prior things are prior: Straightness (attribute of line) is prior to smoothness (attribute of plane).
        4. Metaphysically: E.g. for Plato, this Forms would have been prior to concrete particulars.
      2. What these ways have in common.
        1. Generally, prior things can exist without posterior things but not vice versa. (And again, in some ways, the same things may alternately occupy prior and posterior positions in relation to each other.)
    12. Potency, Capable, Incapacity, Possible, Impossible
      1. The ways in which it is spoken of.
        1. The (a) intrinsic or extrinsic source of movement or change, (b) the condition of possibility for (a) - its capability, (c) the capability of performing /well/ [white men can’t jump], (d) the states in virtue of which something is unchangeable.
        2. Capacity is the intrinsic ability of something for (a)-(d) above, and incapacity is its opposite.
        3. The possible is that which is not of necessity false, and the impossible is that which is (of necessity false).
    13. Quantum
      1. The ways in which it is spoken of.
        1. That which is divisible into two or more constituent parts, each of which is “one” and “this”.
        2. This can be either a plurality if it numerable, or a magnitude if it is measurable.
          1. Plurality: divisible into non-continuous parts.
          2. Magnitude: divisible into continuous parts.
        3. This can, like most of these things, be essential or accidental (that to which musicality and whiteness belong is a quantum).
    14. Quality
      1. The ways in which it is spoken of.
        1. The differentia of essence (e.g. man is an animal of a certain quality).
        2. In mathematics: E.g. factors of a number. (”6″ is the quality of six, where “2×3″ and “3+3″ are some of its quantitative attributes.
        3. All the modifications of substances that move (E.g. hot or cold, white or black) which, when changed, alter the substance.
      2. What these ways have in common.
        1. Properly: The differentia of the essence.
        2. Vulgarly: The modifications of things that move.
    15. Relative
      1. The ways in which it is spoken of.
        1. Reciprocal relations to a common term. E.g. As 1/2:2 or 1/3:3 qua 1.
          1. This can be definite (qua above) or indefinite (e.g. “many times n”).
          2. All these relations refer to unity/likeness/sameness.
        2. Active to passive. E.g. As that which can heat to that which can be heated.
        3. “…as the measurable to the measure, and the knowable to knowledge, and the perceptible to perception.
      2. What these ways have in common.
        1. (5.p.i) & (5.p.ii): Something’s very essence (thing that heats, half of one) includes a reference to something else.
        2. (5.p.iii): Something else’s essence (an inch) includes a reference to it (measurability, knowability).
      3. Finally, this all works by extension: Medicine is relative because its genus, science, is.
        1. And this extension can be accidental (white is relative if the same thing happents to be double [a relative term] relative term) or essential (equality).
    16. Complete
      1. The ways in which it is spoken of.
        1. That outside of which it is impossible to find any of its parts.
        2. That which cannot be improved upon.
        3. Things which have attained their end.
    17. Limit
      1. The ways in which it is spoken of.
        1. The last point of each thing; the first point beyond which it is not possible to find any part, and the first point within which every part is.
        2. The form of a special magnitude (e.g. in a thing that has magnitude).
        3. The end, substance, or essence of each thing (the limit of an object is equivalent to the limit of its knowability).
    18. That in virtue of which, In virtue of itself
      1. “In virtue of which…”
        1. The form or substance of each thing (a man is good in virtue of the good itself).
        2. The proximate subject in which it is the nature of an attribute to be found (color in a surface).
        3. For what end? (”In virtue of what has he come?”)
        4. What is the cause? (”In virtue of what has he wrongly inferred…”)
        5. In reference to position (e.g. ‘at which he stands’ or ‘along which he walks’)
      2. “In virtue of itself”
        1. The essence of each thing (”Callias is in virtue of himself Callias”).
        2. Whatever is present in the thing (”Callias is in virtue of himself an animal”).
        3. Whatever attribute a thing receives in itself directly or in one of its part (”The surface is white in virtue of itself”).
        4. That which has no cause other than itself (”Man is man in virtue of himself”).
        5. Whatever attributes belong to a thing alone.
    19. Disposition
      1. The ways in which it is spoken of.
        1. The arrangement of that which has parts, in respect of either place or potency or kind.
    20. Having or habit
      1. The ways in which it is spoken of.
        1. “Having”: The relationship between the haver and the had. Evidently, we cannot have this having, in virtue of an infinite regress.
        2. A disposition of one who is (well or ill) disposed (e.g. “a health habit”).
        3. A portion of such disposition.
    21. Affection
      1. The ways in which it is spoken of.
        1. A quality in respect of which a thing can be altered (white, sweet, etc.)
        2. The one of these alterations actually accomplished.
        3. Especially, injurious alterations actually accomplished.
        4. And hence, misfortunes in general.
    22. Privation
      1. The ways in which it is spoken of.
        1. Something none of the attributes a thing might naturally have (even if the thing would not naturally have it). “The plant is deprived of eyes.”
        2. A special case of (5.y.i) where the thing would naturally have it (a blind man vs. a mole).
        3. The violent taking away of something.
    23. Have or hold, Be in
      1. Have or hold, to be in something
        1. To treat a thing according to one’s own nature (”fever has him”).
        2. When something is present in something receptive of it (”the bronze has the form of a statue”, “he has a disease”).
        3. The container of something (”the casks hold the wine”).
        4. Something that hinders something else from moving or acting (”the pillars hold up the roof”).
    24. From
      1. The ways in which it is spoken of.
        1. As from matter: (a) from the higest genus (all meltable things come from water), (b) a statue comes from bronze.
        2. As from the first moving principle (fight from abusive language).
        3. As a part from a whole (a verse from the Illiad), or the whole from a part (words from letters).
        4. Something comes from something insofar as it comes from a part of it (”Plants come from the earth”).
        5. Following in time (night comes from day).
    25. Part
      1. The ways in which it is spoken of.
        1. That into which a quantum can in any way be divided.
        2. Of the parts in (5.bb.i.i) only those which measure a whole.
        3. The elements into which a kind might be divided apart besides quantity (species are parts of genus).
        4. The elements into which a whole is divided (as “bronze cube” and “statue” are to “bronze”).
        5. The elements in a definition (the genus now as part of the species).
    26. Whole, Total, All
      1. The ways in which it is spoken of.
        1. That from which is absent none of its natural parts.
        2. That which contains things and these things form a unity:
          1. The whole of living things includes [man, horse, god].
          2. Something is whole by nature (a tree, I suppose).
        3. Quanta to which position makes a difference are wholes (say, a person), those to which it does not are totals (water). See (dd) below.
    27. Mutilated
      1. Totals (qua [5.cc.i.iii] above) cannot be mutilated. You can’t mutilate water, or six, or fire.
      2. Wholes, on the other hand, can. You can chop off a man’s arm, and he ceases to be “whole”.
    28. Race or genus, Other in genus
      1. The ways in which it is spoken of.
        1. A continuous generation of formally similar things (the race of men).
        2. The thing which first brought things into existence (Hellenes come from Hellen, they are her race).
        3. The extensional concept (e.g. ‘plane’ to all planar figures).
        4. The substratum of the qualities; the part of the definition whose differentiae gives the qualities of a participating particular.
    29. False
      1. A false thing:
        1. Cannot be put together (is non-existent).
          1. Always: “the diagonal of a square is = its side”
          2. Sometimes: “I am done taking notes on Aristotle”
        2. Representations (a sketch, a dream) that are not the things the appearance of which they produce in us.
      2. A false account:
        1. “A false account is not an account of anything, except in a qualified sense.”
        2. A true account attains to the essence or accidental qualities of a thing. A false account is the opposite of this.
      3. A false man:
        1. A person who is fond of false accounts (5.ff.ii) for their own sake.
    30. Accident
      1. The ways in which it is spoken of.
        1. That which can be asserted of something (S) but is neither necessary nor usually part of S.
          1. Accidents thus have indefinite or chance causes.
        2. All that attaches to each thing in virtue of itself but is not its essence.
          1. E.g. that a triangles’ add up to 180 degrees. (Spurious, I know, but that’s what he says.)
          2. Hence this type of accident may be eternal, but no accident of the other sort can ever be.
  6. BOOK VI/EPSILON
    1. Distinction of ‘theology’, the science of being as such, from the other theoretical sciences, mathematics and physics.
      1. Most sciences (wissenshaft) “bracket” the question of being in total, and deal with on particular aspect of being.
        1. The natural/physical sciences are “theoretical” sciences, and focused on one particular sort of being. Namely, the concrete stuff of nature/the world, or stuff as it is embedded in concrete particulars.
        2. Mathematics is also theoretical, but whence its objects are to be categorized (qua existence/being) is still unclear.
          1. That said, it is clear that some mathematical theorems consider things eternal/unmoveable/etc., but A wonders if that shouldn’t more properly be the domain of another science.
          2. Some part of maths also deals with things that are eternal but which are nonetheless embedded in concrete particulars (he appeals to the movements of the planets).
        3. The third theoretical philosophy is theology. This will be the most important of the three, assuming that there is some kind of immovable substance. If there is, “theology” will be first philosophy.
    2. Four senses for ‘being’. Of these (i) accidental being is the object of no science.
      1. Recapitulating, Being is (a) accidental, (b) true (’non-being’ being the false), (c) figures of predication, (d) potential or actual existence.
      2. Accidental being (6.b.i.a, 5.g.i.i) cannot be treated scientifically.
        1. Accidents are those things which are not always or for the most part so.
        2. Science is either of that which is always or is for the most part. How else would it be learnable/teachable?
    3. The nature and origin of accident.
      1. Accidental things exist, for otherwise everything that is will be necessary (aka. it would be necessary that Socrates is musical). I think this is basically done by the law of the excluded middle.
      2. I think that what happens here is that he says that in one sense (contra 6.c.i) everything will happen of necessity, because of the causal deterministic nature of the world. So accidents have first causes too, although determining these causes is a sticky wicket.
    4. (ii) Being as truth is not primary being.
      1. Being as truth and falsity (6.b.i.b, 5.g.i.iii) is not the subject of philosophy either. Truth and falsity are determined in thought, and thus being in this sense is a distinctly second-stage type of being.
      2. For the record, though these notes stop here, we are now prepared to consider “being qua being”, obviously either in terms of (6.b.i.c) or (6.b.i.d).