Sunday, September 7, 2008

Aristotle's Theory of Scientific Demonstration: Lect. 2

This second lecture was dedicated to a brief glossing of Aristotle's Posterior Analytics and theory of scientific demonstration. It is Aristotle's own solution to a number of problems addressed by Plato regarding metaphysics, epistemology, logic/demonstration, and cognitive states. As a glossing of the text, we only covered the skeleton of this treatise's rather exhaustive inquiry into the nature of scientific demonstration. The Posterior Analytics can take years to get even a handle on its nuances, let alone assimilate its modes into solidified habitus or cognitive propositional dispositions. And it seems rather clear that this was an endevor of fundamental importance for the medievals who wrote a sundry of commentaries on this task for the purpose of apprehending every nuance. Avicenna is amongst the medievals who say the wisdom of this text, and an awareness of this influence will certainly provide an schema by which one can follow the philosophical moves Avicenna is making while attempting to explicate scientifcally on any particular subject genus.

The unity of the Posterior Analytics lies in that the question of the first chapter is dealt with again with a new solution in the last chapter of the text. The mode of knowing of the higher cognitive states as found in Plato's "Divided Line" has reached a level of maturity and precision in Aristotle.

Major contrasts in Aristotle from Plato is the diversity of sciences. For Plato there is one universal science towards the Good. All knowledge is a process on the way to knowing the Good, and to know the Good is then to have episteme. For Aristotle there are a diversity of sciences, as many as their are subject genus. This allows Aristotle to hold that one can have episteme and know nothing about the Good.

Posterior Analytics: Book I. Ch. 1

Thesis: New knowledge is acquired from/by prior knowledge

Prior Knowledge is of three kinds:

1) Of a Principle: that it is - quia est
2) Of a Proper Attribute: What it is - quid est
3) Of a Subject: Both That it is & What it is - et quia est, et quid est

Posterior Analytics: Book I. Ch. 2

Thesis: To know scientifically is to (A) know the cause of the thing and (B) know that it cannot be other wise than what it is.

There is another way of knowing, but the first topic treated is of knowing through a demonstration. Demonstration is obtained by a scientific syllogism, and the latter is that that in virtue of which, by possessing, we know something.

Demonstrated knowledge must necessarily proceed from appropriate principles that are
1) True
2) Primary
3) Immediate
4) More known than
5) Prior to, and
6) The causes of the conclusion

Note: There can be a syllogism without these requirements for principles, but such a syllogism will not be a demonstration, for it will not produce knowledge.
Digest of the Requirements of a Demonstrative Syllogism’s Principles

1) True: Principles should be true because non-being (falsity) cannot be known
2) Primary: Demonstrated knowledge must be acquired from primary principles which are indemonstrable. Primary also means appropriate to the thing known.
3) Immediate: not mediated for that would require another demonstration. Immediate means there is no other premise before it.
a) Thesis: is any immediate syllogistic principle that cannot be proved and it not
necessary for a learner to have in order to learn something.
i) Hypothesis: is a thesis that states something is the case or not.
ii) Definition: is a thesis that does not, such as “a unit is that which is
indivisible with respect to quantity.”
b) Axiom: is a principle a learner must possess to learn anything
4) More known than (and to a higher degree): not simply understood but knowing that. Also Prior and More Know without qualification, that is, as most universal.
a) To a higher degree: “for that because of which a thing exists always exists to a
higher degree” (Note: this is an aspect of the Principle of Causality)
5) Prior to: Principles must be prior by nature to the conclusion if they are the cause of it.
6) The cause: Because we know a thing only when we know the causes of it.

Posterior Analytics: Book I. Ch. 10

Principles in a demonstration are of two kinds.

Some are Proper principles and some are common to many sciences.(common by analogy: since they are used as far as the genus of things under each science extends)

Proper Principles are also those whose existence is posited and whose essential attributes are investigated by a given science.

A science posits that each of these exists and is so-and-so.
The definition of essential attributes is posited. But that each essential attribute exists is proved though the common principles or axioms and from what has been demonstrated.

Every Demonstrative Science is concerned with three things:
1) those which it posits to exist (and these are things under the genus whose essential attributes it investigates.
2) The so-called “common axioms” from which it demonstrates as from first principles,
3) The attributes, the meaning of whose corresponding terms it posits.


Principles are of three kinds:

1) the genus concerning which something is proved
2) the attributes which are proved of the genus
3) the common axioms from which something is proved.

Posterior Analytics: Book II. Ch. 1

The things we know about and the things we inquiry about:

1) a fact
2) the reason for a fact
3) if an object exists
4) what a thing is.

Posterior Analytics: Book II. Ch. 2

When we inquire 1) whether something is or is not a fact or 3) whether an object simply exists or not, we inquire whether it has a middle or not.

Following knowledge of a fact or that a thing exists we sometimes inquiry further. We inquiry the 2) why of the fact or 4) the whatness of it, in this case we ask “what is its middle?”

In all inquiries we therefore inquire either a) whether there is a middle or b) what the middle is; for the cause is a middle and in all cases it is what is sought.

To understand the whatness of a thing is to understand the why of it


Posterior Analytics: Book II. Ch. 19

First must be acquired but not by demonstration (which would entail circularity or infinite regress cf. P.A. I. 3). Aristotle, contra the Platonic thesis, thinks that principles are not grasped by intellectual apprehension of Forms separate from the things themselves. Rather Aristotle thinks that forms can be grasped in the things themselves.

Aristotle (100a4)
  • Sense perception
  • Memory } Out these three cognitive operations arises the arts and sciences
  • Experience
To illustrate the latter cognitive transition Aristotle uses the famous metaphor of the army in a rout that suddenly makes a stand, becoming stronger and more secure as the ranks increase. A locus where this metaphor is enforced is within Aristotle's account of "incidental sensation" (cf. De Anima II. 6 418a7-418a26) Our sense-perception is of the particular but the particular itself is an instantiated form - which is universal as known, and is perceived as a particular instantiation of the universal in incidental sensation (as later commentators bring to light, e.g. Avicenna, Aquinas, etc.)



Dialectic: For Plato is a comparing and motion up a genus-species tree. However, Aristotle's account of dialectic takes on an expanded inductive inference from what we see in the Divided Line. It includes also particulars to generalization, as well as Plato's account of the motion from species to genus. Aristotle expands induction because he does not think we start with the forms but must first acquire them from the particulars which bear them in re. The particularized universal instantiations are "gathered" together prior to grasping a "real universal. The scheme of Aristotle looks something like this:

Individual -> Universals (specific) -> Universals (generic to most generic)

Induction is capped or culiminates in nous- intellectual insight. Nous should be taken here as a unified dyadic act of apprehension (concept-formation) and judgement (proposition-formation) as the Medievals will come to identify them. This account is verified in a number of Aristotelian passages; earlier in the PA I. 2 and 10 he explains propositions as divided into two species 1) definitions and 2) hypothesis. The latter has for its constituents the former. This account of the unity of the first two acts of intellect will receive a must fuller treatment in the later commentators, in particular, I will later be addressing Avicenna's treatment in his Metaphysics of the Healing Bk. I ch. 5-7.

Veracity of the Intellect in Aristotle:
In PA II. 19 we get the completed epistemic account that not only Scientia (episteme) but also intellectus (nous) are unfailingly true. Opinions, justified true beliefs, and inductions as found in sense-perception, memory, and experience are generalized or universal in a sense, in Aristotle and Plato, but they are not necessarily true as they are in nous.

We have here different intellectual habitus:
  • Scientia - as discursive and mediative
  • Intellectus - as insight and immediate


N.b. - A question is often raised in this context and I wish to provide the brief response given by my professor to this question. Due to the high epistemic status Aristotle grants this intellectual insight (nous) many question the frequency of the occasion of nous. How often do humans have insight into the essence of things? There is no unequivocal and strait forward answer to this question. One must keep in my the complexity of things man knows and the gradient of intelligibilities in things that must be actualized through human cognition and its correlative habitus. Since nous is a habitus, those who are more active in their pursuit of insight will have a greater frequency in the apprehension of natures. However, and perhaps more important, is not the frequency of apprehension but the clarity and understanding of the natures grasped, which is certainly cultivated by a habitus. In this way one can admit with Aristotle in the Ethics that there is insight (nous) occurring at the most abstract and most preliminary cognitive interfaces with real things. The most preliminary insights are no less true, just perhaps less clear and lacking in penetration to the depths of the reality they apprehend.

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