Aristotle and Dialectics: Are they really at odds?

[quantumdude]

Abstract
Adherents to the dialectical reasoning system started by Hegel and then adopted by Marx, Engels et al have traditionally denied that their logic is compatible with the classical formal logic of Aristotle. I argue in this thread that said incompatibility is only apparent, being due to political differences between Aristocratic and Marxist ideologies, and not actual incompatibilities in the two logical systems themselves.

Definitions of Key Terms
When I refer to Aristotle's logic, I am referring to the system of reasoning set forth by Aristotle in his work The Organon¹.

When I refer to dialectical logic, I am referring to the system of reasoning set forth by Hegel in his work The Science of Logic². This is the logic that was later adopted, altered, and applied by Marx and Engels.

Description of the Apparent Conflict
Anyone who has studied dialectics, especially the materialist brand of dialectics espoused by Marx and Engels, knows that a typical introduction to the subject begins with a statement of what is denied by dialectics: Aristotle's logic. Specifically, adherents to dialectics state that they oppose one of the cornerstones of Aristotelian logic, "A is A", which can be more formally stated as follows.

$A \leftrightarrow A$​

Dialectical materialists oppose this view, saying instead that the whole of nature is not static, but rather evolves through the struggle of opposites. The cornerstone of dialectical reasoning is schematized by the following.

$thesis \longrightarrow antithesis \longrightarrow synthesis$​

In ancient times Aristotle's logic was used to support the idea of a caste system. After all, if "A is A" then slaves are slaves and kings are kings, and never shall the two be different. Dialecticial materialists oppose this view with the observation that everything is in constant change, and that quantitative changes in any state of affairs inevitably accrue to force qualitative changes.

Conclusion: From this the dialecticial materialist concludes that "A is A" is an empty tautology and rejects it because:

1.) It is at odds with dialectics and observed reality and,
2.) It is easily used by unethical governments to perpetuate class exploitation.

The Thesis of this Thread
I contend that 1.) above is wrong, and that 2.) is the only real reason for a dialectical materialist to reject Aristotle's logic. That is, I contend that the only real reasons that Marxists et al reject Aristotle are political in nature.

Aristotle and Dialectics: United?
In the section entitled Description of the Apparent Conflict, I said:

Dialectical materialists oppose this view, saying instead that the whole of nature is not static, but rather evolves through the struggle of opposites. The cornerstone of dialectical reasoning is schematized by the following.

I deliberately put the expression "not static" in boldface to highlight where I think the resolution of the apparent conflict lies. Aristotle's syllogisms apply to various categories ("kings", "slaves", etc), but there is nothing in Aristotle's formalism that requires the contents of these categories to be static. If we take any categorical statement such as, "Jack is a blue collar worker", nothing in Aristotle's formalism breaks down if we allow the truth value of such statements to be time-dependent. This would require us to put a temporal index on any particular logical statement. So if we acknowledge that the truth value of a statement depends on time then we can say that, "A at time t is A at time t', if t=t'".

This can be stated more formally as follows.

$(t=t^{\prime})\rightarrow(A(t) \leftrightarrow A(t^{\prime}))$

Counters to this Argument
I thought this point of view was quite clever , but the wind was taken out of my sails one day when I read the following by Trotsky in his work The ABC of Materialist Dialectics³

I will here attempt to sketch the substance of the problem in a very concrete form. The Aristotelian logic of the simple syllogism starts from the proposition that 'A' is equal to 'A'. This postulate is accepted as an axiom for a multitude of practical human actions and elementary generalisations. But in reality 'A' is not equal to 'A'. This is easy to prove if we observe these two letters under a lens—they are quite different from each other. But, one can object, the question is not of the size or the form of the letters, since they are only symbols for equal quantities, for instance, a pound of sugar. The objection is beside the point; in reality a pound of sugar is never equal to a pound of sugar—a more delicate scale always discloses a difference. Again one can object: but a pound of sugar is equal to itself. Neither is this true—all bodies change uninterruptedly in size, weight, colour, etc. They are never equal to themselves. A sophist will respond that a pound of sugar is equal to itself 'at any given moment'.

I added the color for emphasis. Basically, he states that my idea here is "sophistry". But why would one say that? In physics we use this idea to great advantage all the time (time dependent functions, equal-time commutation relations, etc). For instance in dynamics we say that $F(t)=m\ddot{x}(t)$, and this statement withstands Trotsky's objection. Why should either categorical statements or the logic used to make inferences from one set of such statements to another be any different?

What this Thread Is, and What it Is Not
I am not looking for any discussion about politics, economics, or sociology. I am also not looking for any discussion of the ethics of slavery, materialism, idealism, relativity of simultaneity, or any other tangent issue that I may have mentioned in passing.

What I am looking for are reasons why Aristotle's logic is or is not really incompatible with dialectical reasoning (as opposed to apparently so). Trotsky's work is fertile ground for the one position, so we can get more into that if anyone cares to. I look forward to your responses.

References
1. The Organon, by Aristotle.
2. The Science of Logic, by Hegel.
3. http://www.marxists.org/archive/trotsky/works/1939/1939-abc.htm , by Trotsky.

 

[ahrkron]

I completely agree. Some time ago I posed the same question to a long-time socialist. As an answer, I got pretty much the first two paragraphs from Trotsky's "ABC".

As far as I can tell, "dialectic logic" does not offer any new structure or method for the extraction of correct conclusions. It rather seems as a politically motivated reminder about the fact that [bold]change[/bold] has to be thought about and accounted for in your premises.

Aristotle's logic does not have an explicit representation of time-dependency, but neither does it preclude its use in the propositions used.

Also, the "quantity-quality" issue is an interesting feature; to me, it sounds as an incorrect description of change, in the sense that it seems to assume the cathegories that define "quality" as absolute, instead of looking at them as the result of perception, language evolution and convenience.

 

[Royce]

Originally Posted by Leon Trotsky
I will here attempt to sketch the substance of the problem in a very concrete form. The Aristotelian logic of the simple syllogism starts from the proposition that 'A' is equal to 'A'. This postulate is accepted as an axiom for a multitude of practical human actions and elementary generalisations. But in reality 'A' is not equal to 'A'. This is easy to prove if we observe these two letters under a lens—they are quite different from each other. But, one can object, the question is not of the size or the form of the letters,

Joe is a living human being. He is a dynamic ever changing system.
There is never a time when Joe is exactly as he was, is or will be at any other time. Yet, so long as Joe is alive he retains his identity. Joe is always Joe and Joe can never be anything other than Joe so long as he is alive. Joe = Joe just as A=A. I don't think that this is Sophistry

... since they are only symbols for equal quantities, for instance, a pound of sugar. The objection is beside the point; in reality a pound of sugar is never equal to a pound of sugar—a more delicate scale always discloses a difference. Again one can object: but a pound of sugar is equal to itself. Neither is this true—all bodies change uninterruptedly in size, weight, colour, etc. They are never equal to themselves. A sophist will respond that a pound of sugar is equal to itself 'at any given moment'.

If I am the initiator of a syllogism, argument or discussion, a pound of sugar is a pound of sugar because I say it is. I define it as such. I identify it as such and for the purpose and duration of the discussion it is "a pound of sugar".

If we go beyond the original scope of the statement, a pound of sugar will still be a pound of sugar so long as it is implied, necessarily contained within, in the premise. This is true regardless of what the actual substance or amount may be. This is again not sophistry but the rules of logic.

We cannot reason, as is shown here daily, without knowing the terms and conditions about which we choose to reason. If A is (=) NOT A, it is then 1. a meaningless statement; 2. unknowable; 3. undefinable or 4. a paradox and reasoning is impossible.

( I have yet to read or study the links its been a while and I'm sure that I have only read brief synopsis of Hegel and Trotsky. This is only my thoughts off the top of my head.)

 

[selfAdjoint]

I added the color for emphasis. Basically, he states that my idea here is "sophistry". But why would one say that? In physics we use this idea to great advantage all the time (time dependent functions, equal-time commutation relations, etc). For instance in dynamics we say that , and this statement withstands Trotsky's objection. Why should either categorical statements or the logic used to make inferences from one set of such statements to another be any different?

And in physics we have both kinematics and dynamics to describe and delimit just what we mean by time evolution. Aristotle has nothing that will do this; when you make his categories time dependent you must add something radically non-Arittelian to be able to use them in that form.

Hegel did propose a logical method of describing time evolution; that is what the dialectic does. I am not sure it does it very well, but that is another whole discussion.

 

[ahrkron]

Hegel did propose a logical method of describing time evolution; that is what the dialectic does.

Does it? I have never seen a description of how it suggests to describe time evolution. I'm not saying that it doesn't; just that whenever I tried to understand what new procedures it had, I only found political rhetoric and texts criticizing the non-dialectical approach.

 

[quantumdude]

And in physics we have both kinematics and dynamics to describe and delimit just what we mean by time evolution. Aristotle has nothing that will do this; when you make his categories time dependent you must add something radically non-Arittelian to be able to use them in that form.

I don't see why. The only job that Aristotelian logic needs to do is define which set of inferences from one set of statements to another is valid. If I give categorical statements a time index and admit that their truth values are time-dependent then I don't see why the criticism against "A is A" is appeased, and why the time evolution mechanism is even necessary. For instance if A(t) refers to Joe's economic class:


A(1995)=Joe is a blue collar worker.
A(2005)=Joe is a white collar worker.


then in order to evaluate the soundness of an argument containing those statements I only need to know their truth values and the rules for making valid inferences. I don't need to know how Joe got from one state to the next, only that he did get from one state to the next.

Also I'm not saying that Aristotelian logic is identical to dialectical logic, only that it is compatible with it.

Hegel did propose a logical method of describing time evolution; that is what the dialectic does. I am not sure it does it very well, but that is another whole discussion.

Would that be in The Science of Logic? Admittedly, I haven't read the whole thing.