Engels trying to make up contradictions to prove dialectics

[BIXX]

The man seemed to be not great with mathematics. I noticed this while reading through a bit of "anti-Duhring".

Here are some particularly bad examples:

"But even lower mathematics teems with contradictions. It is for example a contradiction that a root of A should be a power of A, and yet A1/2 = https://www.marxists.org/archive/marx/works/1877/anti-duhring/ad02.gif. It is a contradiction that a negative quantity should be the square of anything, for every negative quantity multiplied by itself gives a positive square. The square root of minus one is therefore not only a contradiction, but even an absurd contradiction, a real absurdity. And yet https://www.marxists.org/archive/marx/works/1877/anti-duhring/ad01.gif is in many cases a necessary result of correct mathematical operations. Furthermore, where would mathematics — lower or higher — be, if it were prohibited from operation with https://www.marxists.org/archive/marx/works/1877/anti-duhring/ad01.gif?"

Just because something may seem odd does not make it a contradiction. It is simply a function of mathematics. It would be a contradiction if one of them made the other one impossible, or those two true ideas acted against one another, but that's not how it works. They are simply different ways of showing the same thing.

Another failure from a single paragraph earlier: "We have already noted that one of the basic principles of higher mathematics is the contradiction that in certain circumstances straight lines and curves may be the same."

What he is referring to here is NOT a contradiction. This is referring to curved lines at great distances being so close to straight lines (as far as a human can tell) that we ignore the difference as it would e minute, almost undetectable. We ARE NOT saying they are one and the same.

If he rests his usage of dialectics on these examples AT ALL then his dialectics are particularly useless, as they are based on a severe misunderstanding of mathematics.

I'm sure there are many more examples... But seriously, why even read at that point?
If Marx made those mistakes then I'm gonna cry.

This is the specific place I got it from: https://www.marxists.org/archive/marx/works/1877/anti-duhring/ch10.htm

Thoughts?

[Dodo]

I am no expert on maths, but from my readings, Engels was more obsessed with establishing a "Marxist method" of "science". He could have had this massive confirmation bias to prove dialectics as some sort of "law of nature" as I think he seemed to claim a lot.
So he might have tried an unnecessary expansion.
From what I have seen, Marx's method did not include such bias. Marx's deal was more with looking at today, going backwards to see how we got there and creating -laws- which are not meant to be taken in a positive-universal sense.
Marx's way of dealing with law is more in line with "tendency" within the given relational framework as far as I understand.
Engels put a lot of the "laws" made up by backward reading into -positive-reading of things.

[Kronsteen]

Yes, I'm afraid Engels badly misunderstood mathematics - and the philosophy of mathematics, and the history of mathematics.

He denied the validity of irrational numbers, and infinitessimals in calculus. He also denied complex numbers, which is especially odd, as he had no trouble with the co-ordinates on his military maps. He confidently asserts that all mathematics is empirical, that in the equation "1+1=2", the two instances of "1" are "in contradiction" of some kind...and at one point seems to think Descartes invented Algebra.

It's not that he had unpopular opinions on the topic - it's that he doesn't understand the positions he's arguing against, and doesn't understand the issues under discussion.

Marx didn't make the same mistakes. He made different mistakes. In his Mathematical Manuscripts, he seems to be trying to say that, because measurements have degrees of uncertainty, so do the values of the numerals used to express them.

[La Comédie Noire]

The problem is Engels is going off common (mis)conceptions of mathematics especially his notion of calculus. A mathematics major for instance would take issue with his use of the word "contradiction" which as Ecoshock pointed out has a very specific meaning for mathematics.

In one sense Engels can't be blamed. Our understanding of Mathematics, Calculus especially, did not reach full maturity, until the late 19th and early 20th century. Papers were published around the time Engels was active, unfortunately they were of a very specialized nature.

A lot of the seeming contradictions of mathematics fade away if one speaks in a very rigorous fashion, using the tools of set theory and logic.

To give one example (this is paraphrased from Bertrand Russell) it was thought a contradiction that a part of infinity was also infinite. Much mysticism was supported by this notion of a part somehow being equal to the whole.* However, if it is rephrased "a part is similar to the whole" that is part of infinity is similar to infinity as a whole than the seeming contradiction disappears.

*And just as a cautionary tale/ example a trained mathematician would take me to task for speaking so loosely. It's just a feature of everyday language.

[Strannik]

My opinion is, that Marx uses "dialectics" as a theory of (social) knowledge - it explains how concepts and "truths" are socially produced and how they change for material reasons. In "Dialectics of Nature" Engels, for some reason, tries to turn dialectics into an ontological theory - a theory about existence.

[Ven0m]

there's one bit where engels talks about the chicken and the egg being a dialectic. the dude was a bit weird.

[Sinister Intents]

there's one bit where engels talks about the chicken and the egg being a dialectic. the dude was a bit weird.

You're banned, though you deserved it. I wish I could see this talk of the chicken and egg discussion from Engels... Anyone able to help?

[0zgurluk]

My opinion is, that Marx uses "dialectics" as a theory of (social) knowledge - it explains how concepts and "truths" are socially produced and how they change for material reasons. In "Dialectics of Nature" Engels, for some reason, tries to turn dialectics into an ontological theory - a theory about existence.