Tuesday, May 27, 2008

The analytic-synthetic dichotomy

[Slightly edited]

Leonard Peikoff obtained fame within the
Objectivist community with his article 'The Analytic-Synthetic
Dichotomy.' Even though Peikoff named Kant as the namer of
this "dichotomy," somehow he becomes associated with all its
20th-century ills, many of which come from A.J. Ayer.

But the "dichotomy," which is really only a distinction, is easy to see
by mathematical example. Arithmetically contained in the concept
of the number 4 (staying with the natural numbers) is the idea of a
combination of numbers, such as 1+1+1+1, or 2+2, or 3+1. The example
most commonly taken from these is 2+2=4.

2+2 is more than just a combination, it is a synthesis (or
integration) of two numbers which equals 4. But it is analytical to
the concept of the number 4 that it consists of adding 2 and 2. This
is just a matter of going backwards (right to left) or forwards (left
to right) in the equation 2+2=4. To go backwards is to divide the
number 4 into two elements by analysis. To go forwards is to
synthesize these two elements back into the number 4.

This formulation is easily applied to the concept 'furniture' in
Rand's example at ITOE 22. Notice that Rand has done part of the work
for us already, by reference to the "constituent concepts" (sometimes
also called "constituent units" or "constituent particulars") of the
concept. Those constituents are nothing more than the various items
of furniture: tables, chairs, beds, armoires, etc. The concept
"furniture" is a product of their synthesis into that concept.
Precisely how this takes place - by differentiation and integration -
is irrelevant in this context, just as the exact mathematical process
was irrelevant to the previous example, although "integration" is
certainly synonymous with "synthesis." And by the same token, a
"constituent concept" or "unit" is the result of analyzing a "wider"
concept into its components.

At one point Rand supported my contention that integration and
synthesis are the same process: "The uniting involved is not a mere
sum, but an integration, i.e., a blending of the units into a single,
new mental entity which is used thereafter as a single unit of thought
(but which can be broken into its component units whenever required)."
(ITOE, 9)

So you have, within Rand's own epistemological context, the very ideas
of synthesis and analysis which are then later attacked by Peikoff, et
al.

The reason 2+2=4 was thought, before Kant's time, analytical or even
tautological was probably because the answer, 4, was taken for granted,
and so 2+2=4 was held equivalent to 4=4. But this ignores the process of
synthesis (or integration) by which the answer 4 was obtained which is
why Kant, in the introduction to the Critique of Pure Reason, suggested
using much larger numbers on the left side of the equation.

2 comments:

robert574 said...

I've always thought that a synthesis, in the Kantian sense, was a combining of two opposite elements, the thesis and the antithesis into one. Integration, on the other hand can involve any number of characteristics or units into a new concept. It is a mental process that involves accurately identifying the characteristics of a given number of entities and then creating a new concept based upon similarities if they exist.

4 is not the antithesis of 4, they are each like units (numbers) comprised of the same number of subunits each. When you add, you do not integrate or synthesize, you add and uniformly you come up with 8 subunits. This is counting. Adding, subtracting, multiplying and dividing are merely short cuts that facilitate and speed up the process of counting.

Synthesis, integration and counting are three different mental processes. Synthesis, in the Kantian sense, creates no new knowledge because it is impossible for thesis and antithesis to be integrated since they are opposites. I've never seen the process of synthesis in action so Kant's idea is a dead end.

Integration is a mental process that is based on the similarities of a number of units and does not involve opposites. Counting is merely the process of counting, 1, 2, 3, etc.

Peikoff ably showed that the "distinction" between the tautological and analytical was a false alternative that also was a dead end. Dead ends lead nowhere except toward confusion and intellectual disintegration which is the opposite of integration.

Show me a synthesis, a physical joining of two opposites. In reality when two opposites come close together you either get a collision (chaos) or a repulsion neither of which are a synthesis.

Rand was talking about a mental integration. She was not talking about joining thesis and antithesis. The terms thesis and antithesis are nothing more than Kant's clever way of using the concepts A and non-A which can never be synthesized. In logic A and non-A are two opposed concepts destined to always be opposed. Non-A can never change into A. It is a concept that has none of the characteristics of A. Whatever A is, non-A is not A. A is always A no matter how many times it changes forms. Whatever it is it is.

Cavewight said...

Robert,

For Kant it's not a thesis/antithesis relationship being formed by the synthesis, you must have this confused with something Hegel wrote, or perhaps with something Kant wrote on thesis/antithesis much later on in the Critique in the section on the Antinomies of Pure Reason.

To call this a "mental" process is too general because it includes the psychological; but in this case, adding numbers, or any synthesis in general, is specifically an intellectual process and not primarily psychological which might occur in the case of habitually associating two disparate events in one judgment or experience, as for Hume.

I would identify integration with synthesis, albeit abstracting from Rand's emphasis on psychology, which is prevalent throughout ITOE, focusing simply on the intellectual element involved.

I don't totally disagree with this quote from ITOE 2nd ed. p. 9 - "The uniting involved is not a mere sum, but an integration, i.e., a blending of the units into a single, new mental entity which is used thereafter as a single unit of thought..." At any rate, nobody has said anything about it being a physical integration or synthesis. I don't like Rand's use of a sloppy, non-philosophical term such as "blending." And I don't believe that Rand's choice to use that word automatically converts it into philosophical terminology.

I don't recall Peikoff denying or even mentioning any analytical-tautological distinction, although he referred to both ideas, and it is easy to see that the context was not Kant but A.J. Ayers, a philosopher whose most famous work he mentioned in "The Analytic-Synthetic Dichotomy." Furthermore, Ayers was not continuing to do Kant's dirty work for him, which is Peikoff's implication, but employing some Kantianism as he understood it in developing a theory of his own which Kant may or may not have agreed with.