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Adherents to the dialectical reasoning system started by Hegel and then adopted by Marx, Engelset alhave 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 toAristotle's logic, I am referring to the system of reasoning set forth by Aristotle in his workThe Organon^{1}.

When I refer todialectical logic, I am referring to the system of reasoning set forth by Hegel in his workThe Science of Logic^{2}. 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 isdeniedby 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.

[itex]A \leftrightarrow A[/itex]

Dialectical materialists oppose this view, saying instead that the whole of nature isnot static, but rather evolves through the struggle of opposites. The cornerstone of dialectical reasoning is schematized by the following.

[itex]thesis \longrightarrow antithesis \longrightarrow synthesis[/itex]

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 affairsinevitablyaccrue 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 Marxistset alreject Aristotle are political in nature.

Aristotle and Dialectics: United?

In the section entitledDescription of the Apparent Conflict, I said:

I deliberately put the expression " Tom Mattson said:Dialectical materialists oppose this view, saying instead that the whole of nature isnot static, but rather evolves through the struggle of opposites. The cornerstone of dialectical reasoning is schematized by the following.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 thatrequiresthe 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 statments to betime-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.

[itex](t=t^{\prime})\rightarrow(A(t) \leftrightarrow A(t^{\prime}))[/itex]

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 workThe ABC of Materialist Dialectics^{3}

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 [itex]F(t)=m\ddot{x}(t)[/itex], 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? Leon Trotsky said: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'.

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 notreallyincompatible 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 [Broken], by Trotsky.

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# Aristotle and Dialectics: Are they really at odds?

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