I.1 All teaching and learning result from previous cognition.

(i) We presuppose that something is (the fact); or

(ii) We comprehend what it is (the reasoned fact).

Solution to Meno's Paradox: We know in one way what we are learning, while being ignorant in another way.

I.2 Demonstrative knowledge

Demonstration=a deduction expressing knowledge. (Apodeixis = syllogismos epistemonikos)

Premises of a demonstration must be

("absolute" features") true, primary, immediate,

("relative" features) better known than (more familiar, gnorimoteron), prior to, and explanatory of the conclusion. "better known" and "prior" have two senses:

(i) closer to us, or clearer through sense-perception;

(ii) further from us, closer to the truth (closer to the universal)

Some key terms:

• proposition (protasis, premise): one part of a contradictory pair
• posit (thesis): something that cannot be proved; need not be grasped by anyone who is to learn
• axiom (axiom): ditto, but MUST be grasped by anyone who is to learn
• supposition (hypothesis): assumes something does or does not exist
• definition (horismos): does not assume something is (a kind of thesis, not a hypothesis)

I.3 It is not true that all things that are known are known by demonstration. To insist on this would result in one of two unacceptable consequences: (a) Either there will be an infinite regress, since the primitives will have to be demonstrated, on and on ad infinitum; or (b) there will be circular demonstrations. (Aristotle thinks some circular or reciprocal demonstrations are possible, involving what he calls "counterpredicables," but that these will be very limited.)

I. 4 Demonstrative knowledge is necessary, hence must be a deduction from things that are necessary. To understand this necessity, Aristotle refers us to three notions: "belonging in every case," "in its own right," and "universal":

(i) A belongs to B in every case (holds of all cases at all times)

(ii) A belongs to B "in its own right" (kath' hauto):

(1) essence of B is composed of A

(2) B is present in the account revealing what A is

(3) B is not said of A as of another underlying subject

(4) A belongs to B because of itself.

(iii) A belongs to B universally if both (i) and (ii) are true.

I.6 Demonstration must proceed from principles that are necessary (not just "reputable" or true). It must also be through a middle term that is necessary.

Brief example of a syllogism:

Comments: The syllogism has two premises and a conclusion. Each premise is a proposition with a subject term and a predicate term. In the conclusion, the subject term is C and the predicate term is A. There is also a "middle term" B, which is the term linking the C's and the A's. Hence Aristotle regards the middle term as what provides the explanation (i.e., B explains why all C's are A's.)

I. 7 You cannot prove by passing over into another kind (genos).

I.8 If propositions that ground demonstration are universal, then it is necessary for the conclusion to be eternal. (Question about demonstration about something non-eternal, like eclipses.)

I.9 You cannot know anything haplos (simpliciter) except from its own principles.

I.10 Some principles are common to different sciences, some are distinctive of a given science.

Every demonstrative science is concerned with three things:

• the kind (genos): things it posits to exist;
• the common axioms: primitives from which demonstration proceeds;
• attributes (pathe): things that will hold "in themselves" of the kind; we assume what each means (and prove that it is)

More on axioms, postulates, etc.:

• A provable but unproved assumption is a postulate;
• When accepted by the person, this becomes a hypothesis;
• Hypotheses are propositions (they assert existence or non-existence); definitions are not;
• Postulates and hypotheses are universal or particular, definitions are neither.

I. 13 Understanding the fact (the hoti) is not the same as understanding the reason why (the dihoti). You can know a fact in various ways that do not entail knowing the reason why; you may even have a demonstration of the fact but if it is not a truly "explanatory" ("causal"?) demonstration, then you still do not (really) know the reason why.

Example:

• B is A. What is not twinkling is near.
• C is B. Planets are not twinkling.
• C is A. Planets are near.

Comments: This is not explanatory; it is not because the planets are not twinkling that they are near, but vice-versa.

Sciences stand in certain relations of subordination to one another. Some seem to be more "empirical" than others. For example, geometry is prior to optics, which is prior to the study of the rainbow.

I. 14 The first figure (of the syllogism) is the most scientific: it is (allegedly) the most used, and it works best to give knowledge of essences and universals. This figure is necessary (allegedly) to supplement the other figures so as to reach immediate premises.

II.8 Knowing what a thing is = knowing the explanation of what it is.

Example: What is an eclipse? Answer: a blocking of the moon's light by the earth.

Let A=eclipse, B=blocking by the earth, and C=moon.

In this example, asking whether the moon is eclipsed = asking whether B is or is not. We have the "account" of eclipse (namely, B, the middle term), so we learn both the fact (that there is eclipse) and the reasoned fact (why) at the same time.

Alternatively we might only know the fact, not the reason.

Let A=eclipse, B=inability of moon to cast shadows, C=moon.

If it's clear that A belongs to C, then to inquire why it belongs is to inquire into what B is (blocking? rotating? extinguishing?). B is an "account" or explanation of one of the other two "extreme" terms, A (eclipse).

Another example: A=thunder, B=extinguishing of fire, C=cloud. Then we get an account of thunder as "extinguishing of fire in the cloud."

II.10 The "nominal" definition tells what a name signifies (thunder is noise, eclipse of the moon is failure to cast shadows). The "real" definition tells why this is so (thunder is noise due to extinguishing of fire, etc.). The "real" definition is read off from a demonstration (differently arranged).

II.19 All demonstration comes from pre-existing knowledge, knowledge of principles. How do we know these? They are neither innate nor are they acquired from nothing. They must be acquired through a distinctive potentiality we have. This potentiality is sense-perception. The chain goes like this:

Perception --leads to-- Memory --leads to-- Experience --leads to--Understanding.

From experience derives "understanding" of principles (of crafts or of sciences)