Hi everyone, welcome to another entry of our Short Attention Span Reading Group
The Text
We will study On Contradiction by Mao.
It is divided into 6 sections (7 if we count the very short conclusion), none of them will take you more than 20min to read (most will take less) :).
I think this essay can be summarized by its first sentence
The law of contradiction in things, that is, the law of the unity of opposites, is the basic law of materialist dialectics.
And this is all it studies, starting to what is the difference between dialectics and metaphysics, the law of contradiction, what are contradictions, how are they defined, what are their different types, and so on. And of course what it means for Marxism.
The biggest question I am left with after reading this essay is the place of Nature in materialist dialectics...
Supplementary material
- On Practice by Mao Tse-tung. It is significantly shorter than On Contradiction, and they both go hand in hand.
The universality or absoluteness of contradiction has a twofold meaning. One is that contradiction exists in the process of development of all things,
Engels said, "Motion itself is a contradiction." [5] Lenin defined the law of the unity of opposites as "the recognition (discovery) of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature (including mind and society)". [6] Are these ideas correct? Yes, they are. The interdependence of the contradictory aspects present in all things and the struggle between these aspects determine the life of all things and push their development forward. There is nothing that does not contain contradiction; without contradiction nothing would exist.
This is meaningless to me. You can assert that all things are a unity of contradictions, but for understood phenomena, this involves the ad hoc labeling of things and contra-things, with no perscriptive guidance except that a contradiction must be found. So what's the point? What's the use?
Bohr didn't use the law of contradictions to develop his model of the atom, so what point is there in going back and labelling the positive nucleus and the negative electrons as contradictions? Is that what it means to be a contradiction, to have opposite electrical charges? Could be! Why not? There's no more specification. Oh, or what about the matter and the binding energy; those could be labeled the opposites (what does it mean to be opposite as opposed to be distinct ). What additional benefit does the law of contradictions provide when applied to such phenomena to be able to say that the law of contradictions is meaningfully applicable.
... one of the basic principles of higher mathematics is the contradiction that in certain circumstances straight lines and curves may be the same....
But even lower mathematics teems with contradictions.
Contradiction have a specific meaning in mathematics, and these contradictions aren't those contradictions. Engel's Dialectics of Nature are replete with ad hoc labeling of contradiction that leave me as a math professor absolutely befuddled. There's no rhyme or reason to what makes something a contradiction apart from the fact that we know everything must contain one (apparently).
In mathematics: + and - . Differential and integral.
No.
In war, offence and defence, advance and retreat, victory and defeat are all mutually contradictory phenomena. One cannot exist without the other. The two aspects are at once in conflict and in interdependence, and this constitutes the totality of a war, pushes its development forward and solves its problems.
No.
I feel the law of contradicition can be more intelligibly summarized as "things are made up of other, distinct things". We've managed to rehash atomism.
To be fair, Mao isn't talking about the mathematical concept of contradiction, but the Marxist one. The invocation of positive and negative does do a lot to reduce the credibility of the text though, and my impression of it struggles to recover from that moment. It feels like philosophical astrology.
mathematical concept of contradiction, but the Marxist one
Yeah, I was trying to call attention to that, although not very clearly. So the question then is "what is a contradiction?".
Which reminds me of a particular M.A.S.H, as Hawkeye pleads to know what B.J.'s actual name is, what does B.J. stand for, B.J. replies
"Anything you want"
The focus on calling out dogmatists makes me think the text is meant more as a blow to people holding onto old ideas rather than a specific framework for understanding the world. A seriously overwritten "fuck you, everything can change, everything will change, nothing is isolated, go get your hands dirty".
That's not a uniquely dialectical conclusion though, so even if that is the case, it's couched in all so much of this drivel that everyone who agrees with the conclusion has to swallow a mountain of methodological objections and cosign it, or get lumped in with the dogmatists.
I mean, you can create a seriously overwritten “fuck you, everything can change, everything will change, nothing is isolated, go get your hands dirty” polemic in the language of literal astrology, but doing so would be somewhat self-defeating.
In that scenario, the only rationale I can come up with for writing such a simple concept in such an obtuse way is that the obtuseness is the point, either to give the concept credence because people respect many big words strung together, or to get your good-faith ideological opponents stuck in the trap of trying to understand what you're saying. Not that either of these ends are necessarily bad, and it might well have been the right thing to do for someone trying to swat down dogmatism in the party.
Kinda strikes me as a loyalty test, in the same way the Word of Wisdom is for LDS types
We're going to talk and think like this now!
I am not going to talk and think like that.
Goodbye dogmatists.
Honestly, if your goal is to produce a party bureaucracy that moves and acts as a single unit, there's worse ways to go about it...
Wait wait, I unironically think I've figured it out.
The point of these works by Lenin, Mao, and Stalin, et al, is not to make sense or to accurately describe the world, but to show how the synthesis of ideological gibberish with material action can fundamentally bring about massive societal transformations.
So when leftists go about mining these tomes for intellectual insight, they're missing the point entirely. The point isn't in the gibberish, is in how the application and context of the gibberish is used to catalyze social change.
That's funny, he just replied "John Kerry" a thousand times to my follow up.
I'd say Lenin did both. Early in his life he was doing sociology to understand Russian class relations and imperialism. Later though he would do these weird justifications to practically run the ussr which went against some of his earlier theorizing.
The point of these works by Lenin, Mao, and Stalin, et al, is not to make sense or to accurately describe the world, but to show how the synthesis of ideological gibberish with material action can fundamentally bring about massive societal transformations.
That might be a good take, do you mean it in the sense that they build in a "thinking framework" that allows people to consider and realize said massive societal transformations?
Think of it like the Book of Mormon; it isn't at all what it purports to be, and the people who wrote it knew that, but they used it as a springboard to be able to create a massive movement out of it that changed the course of history.
So Mao/Marx/Lenin would have more or less believed that Hegel is (more or less) full of shit but that it gives a near mystical/super deep appearance to whatever rigorous theory/social movement they were building, is that what you mean? I'm not necessarily disagreeing, and I can see the point of doing so, don't get me wrong. I am just not sure whether they thought Hegel was mystical "bs" or if they were carried themselves by said mystical "depth". I'd lean towards the later.
Also, I do believe there is something of value under all this, but yeah, this is belief :p
or if they were carried themselves by said mystical “depth”. I’d lean towards the later.
Sure, and I think it's plausible that Joseph Smith even came to genuinely believe and rationalize what he was doing; it's just that the content of these theoretical papers isn't what's important; thesis/anti-thesis, law of contradiction, dialectics, it's not what to take away from these historical works. The important bit, the thing to analyze, the meta-dialectic is how these theoretical works wore able to catalyze material change, and I think some of them (Lenin) may have been smart enough to realize that was the actual ballgame.
I think Lenin was smart enough to advance an intellectual argument in bad faith, because he's wasn't playing for a bourgeois intellectual win.
I think when you read Marx and Lenin in this light, especially when they go after other philosophers, you can see winks and nods of this all over the place.
I'm not saying this was definitely the case, but I like 3D Chess Lenin over unironic Dialectics of Nature Engels.
I like this angle because it doesn't matter if any particular thinkers were doing this on purpose, it reframes the creation of knowledge and the work of philosophy into something weaponizable, a pattern you can see in the neoliberal think tanks of the USA. It's impossible to ignore the leverage provided by dodgy science if it creates "knowledge" that advances a revolutionary cause.
Exactly!
The lesson isn't "the law of contradiction is present in all things"
The lesson is "If i tell people "the law of contradiction is present in all things", I can get them to shoot the tsar."
Might be the case, and it's plausible take (I guess it would be hard to prove or disprove). I do feel like Mao is quite serious when he writes On Contradiction and On Practice though, and even 30 years later is his still seriously talking about dialectical materialism.
My impression though is that there is something in there that "works". I mean, Žižek is one of the two writers who made me be able to move left, in the sense that I had some feeling something was wrong, but he helped me destroy some barriers that I wasn't able to overcome and my own, and well, I don't think we can argue that žižek does anything but dialectism (we certainly can't blame him for being too clear or too formal). I think part of the reason this worked is because it forced me to consider things in relation to each others in ways that I had not considered before, and this is what dialectical materialism is all about right, drawing all kind of connections between "things" and seeing how they come into play (through contradictions from which new things emerge yadda yadda).
Here's a thermonuclear take:
If you want to neutralize the bourgeois conditioning in someone's thought patterns, it's better to create the antithesis of that bourgeois thought pattern, resulting in something more akin to mutual annihilation rather than a mere convincing.
If the target bourgeois thought pattern isn't present in the reader's mind, the antithesis can sail harmlessly through their psyche like a radio wave through flesh.
So maybe the reason this bit of philosophy isn't playing nice with the bulk of this reading group is because those brainworms have already been annihilated.
What additional benefit does the law of contradictions provide when applied to such phenomena to be able to say that the law of contradictions is meaningfully applicable.
I think this is a fair point (I am only a few sections in though).
I certainly do wonder at times whether “opposites” would be a better word than “contradictions”, although both are used so they are probably not meant to be perfect synonyms.
I do find it interesting that the mathematical examples given (addition and subtraction, differentiation and integration) are examples of inverse process (in the mathematical sense, particularly the group-theoretical sense). In particular, I think this gels really well with the ending parenthetical in the Lenin quote with which the article starts:
the division of a unity into mutually exclusive opposites and their reciprocal relation
I don’t know what to make of it, but it definitely makes the group theory part of my brain fire up. I don’t know how much of this sort of group-theoretical thinking Lenin was exposed to, but I do find it interesting.
the division of a unity into mutually exclusive opposites and their reciprocal relation
All these writers keep dropping these words with highly specific meanings into applications where they clearly make no sense.
So lets take the rest as being fine. 1 and -1 one represent opposites (as opposed to just additive inverse?), and in their addition (unity?), you get (0). What sense does it make to describe 1 and -1 as mutually exclusive as opposed to just distinct?
I just want to preface this by saying that I am not well-read; I have read very little MLM and am not in a position to offer a coherent defense of their thoughts or writings.
All these writers keep dropping these words with highly specific meanings into applications where they clearly make no sense.
I again think this is a fair point. At the same time, Lenin writing about dialectics or Mao on contradiction are surely trying to abstract features they see common to many different things (math, physical sciences, society, etc). They can either invent new terminology, or co-opt terminology from one (or several) of these subjects. I would expect there to be some friction when the latter happens. I personally find it excusable, but I do sympathize with the spirit of your critique (or at least what I perceive it to be).
1 and -1 one represent opposites (as opposed to just additive inverse?),
I think this terminology--"opposites" or "contradictions" instead of the highly-specific "additive inverses"--would be excused by virtue of the fact that we're trying to generalize, or draw comparisons between things.
and in their addition (unity?), you get (0). What sense does it make to describe 1 and -1 as mutually exclusive as opposed to just distinct?
Perhaps in this example, it is the positiveness and negativeness which are mutually exclusive. In light of this, perhaps here the "unity" is the totality (or group) of the set of real numbers. The group as a whole decomposes into "opposites".
I do want to repeat that I would not consider myself to have even a basic understanding of what "dialectics" is. Maybe everything I've written is astrology for math nerds, and maybe Lenin and Engels did that too. But my background in math is evoking all of these vague ideas when I read some passages, and allowing me to say "OK, maybe in a given system (the additive group of real numbers, or a capitalist society) there is a feature or features we can pick out (positiveness vs. negativeness, wage-laborer vs. owner) which separates the components of our system into two mutually exclusive camps, that our system couldn't exist without these two camps, and that we can look at our system in terms of how these camps interact among and between themselves".
I also should add that these things did not immediately spring to my mind fully-formed, that your questions encouraged me to try and be more specific about vague analogies I felt. I'm also not trying to say that Mao's or Lenin's writings are faultless and that you're wrong, but I am trying to see if different framings might make more or less sense.
At the same time, Lenin writing about dialectics or Mao on contradiction are surely trying to abstract features they see common to many different things (math, physical sciences, society, etc).
“OK, maybe in a given system (the additive group of real numbers, or a capitalist society) there is a feature or features we can pick out (positiveness vs. negativeness, wage-laborer vs. owner) which separates the components of our system into two mutually exclusive camps, that our system couldn’t exist without these two camps, and that we can look at our system in terms of how these camps interact among and between themselves”.
That's sorta my point; this commonality is found only if you presuppose it. Sure you can map the language of dialectics and contradictions onto literally any field you want by squinting hard enough and assign some notion of "oppositeness" to individual elements. But why bother? Is it so unquestionably useful that I should insist on thinking only dialectically, as so many on the leftists insist?
This is my biggest problem with dialectics of nature and I've had long discussions on the discord about it. It's all based in presupposing the universality of contradiction and adhoc finding it. There's no reason to do it and as a theoretical computer science person, yeah the math analogies are laughable. The whole western marxist tradition basically chucked dialectics of nature as not a useful thing and I'm inclined to agree with them. Look up a paper called on engles intentions in the dialectics of nature, it sums up the now century long debate on the whole thing really well.
Doing dialectics with history served the purpose of making a theory of history to interpret, and make predictions, and morally situate ourselves. Finding the contradiction in a rock or some mathematical object serves no purpose as far as I can tell.
Imagine a scholar, upon realizing that any given word might be mapped, with some level of difficulty and precision, to the Greek language, proudly proclaiming "Every text is fundamentally Greek".
I agree with your point, and that section on the universality of contradiction bothered me quite a lot.
I think the problem comes from the very unclear concept of "thing". It is to say the least very ill defined, and because we don't know what "things" are then Mao is forced to try to find random examples here and there that are missing the target completely (like all his discussion on nature, and his attempt to find examples in mathematics).
That being said, you cannot just say "no" to this quote
In war, offence and defence, advance and retreat, victory and defeat are all mutually contradictory phenomena. One cannot exist without the other. The two aspects are at once in conflict and in interdependence, and this constitutes the totality of a war, pushes its development forward and solves its problems.
I understand the problem with mathematics, not with this specific quote. On the contrary, in this quote I think this approach is particularly valid.
I feel the law of contradicition can be more intelligibly summarized as “things are made up of other, distinct things”. We’ve managed to rehash atomism.
There you are missing his point. He is not just saying that "things are made up of other things", that would be tautologically pointless. He is saying that any "thing" (I have a very immature theory on how to define 'thing' and I am not ready to develop it but I will share it one day here, because I think we should strive to clarify that point), that is developing is developing because of inner contradictions (and in this case I think it would be correct to see contradictions as instabilities) that try to reach some equilibrium, and only when this equilibrium is reached on all aspect of the thing then the thing can stop evolving. For example, in the case of a war, the war stops developing when a peace treaty is signed (and many of the contradictions inherent to the war might be transferred to the peace of course), and for a peace treaty to be signed, some of the contradictions of the war must have been resolved (either one side crushing another, or a stalemate, etc...).
What is synthesis? You have all witnessed how the two opposites, the Kuomintang and the Communist Party, were synthesized on the mainland. The synthesis took place like this: their armies came, and we devoured them, we ate them bite by bite. It was not a case of two combining into one as expounded by Yang Hsien-chen, it was not the synthesis of two peacefully coexisting opposites. They didn’t want to coexist peacefully, they wanted to devour you.
This is a quote from "Talks on questions of philosophy" that gives an example about what he means regarding war
In war, offence and defence, advance and retreat, victory and defeat are all mutually contradictory phenomena. One cannot exist without the other. The two aspects are at once in conflict and in interdependence, and this constitutes the totality of a war, pushes its development forward and solves its problems.
Because these are not meaningfully contradictions, they are just distinct things. You can have a battle that is a tactical victory but a strategic defeat. That's not a contradiction. You can retreat toward enemy positions from another force in maneuver warfare. Nor do these two "contradictions" incorporate the totality of warfare. To advance and retreat, you can add static warfare.
thing that is developing is developing because of inner contradictions that try to reach some equilibrium, and only when this equilibrium is reached on all aspect of the thing then the thing can stop evolving. For
It's developing (what does that even mean?) because of the relations between it's distinct sub-things. You can call those contradictions and dialectics if you like but it's just rehashed atomism and the notion of dynamical processes in the most roundabout way possible.
I think an important thing to note here is that even the concepts of strategic defeat or tactical victory or the totality warfare are themselves abstractions defined by the interaction between preconceptions of said terms and the processing/analysis of new experience in relation to the preconceptions and related concepts/context. Sure there are external definitions you could reference, but the mental representation of concepts aren't external definitions. The systems of processing and preconceptions are both in constant states of update and are, in of themselves, made up of a totality of inputs dependent on all the interconnected systems of perception, memory (which includes the aforementioned external definition), abstraction, etc... and ultimately the material conditions (whether it be genetics or environment). There is constant feedback from top to bottom and bottom to top; abstraction is necessary to contextualize/perceive experience of the concrete and abstraction arises from interactions between distinct experiences of the concrete. Furthermore, you can't just call it a dynamic process because the experiential, emergent nature of consciously interacting with said concept is irreducible. We have limited attention and cannot consciously perceive the totality from which the reified experience of consciousness arise. Whether it be top-down or bottom-up, we never experience the totality of our entire conceptual mapping nor the experience of physical phenomena from which they arise and which they contextualize; but we still interact with, make judgements, and alter the relationships between concepts arising from such processes despite our ignorance. The act of interacting with a concept (even so much as inquiring as to the nature of its existence as a one's own internal concept) in consciousness, more generally working memory, changes it's relationship to its context all while being unaware of the totality of its context. Even if we could fully map out all neural activity and their feedback loops, we couldn't confirm that these complex systems of input, memory, abstraction, perception etc. actually informed conscious thought in the manner in which we might predict/model due to the failure of introspection. And even if we could miraculously overcome this in study, the resulting knowledge would alter the relationship between all concepts with the inclusion of this new concept(s) informing all others.
I agree that Mao might fail in a metaphysical sense. However I think at least some of what Mao talked about with this work is super interesting in viewing the construction of mental representation of the world. As someone who has spent a decent amount of time studying cognition, I do find a lot of what I read here to be really fascinating in relation to what I've learned/researched.
I'm not sure if I explained this very clearly, but this is difficult shit to explain and deserves way more time and effort (which is actually something I am working on). I would ideally want to go into the models and studies I'm basing a lot of these claims on, but if you're interested I can try to come back and go into it sometime. I think my choice of terms is kinda shitty and something I want to work on. I also would would like to note that I'm not super well informed on Mao, just read this a few days ago and it's the first of anything I've read related to Maoism.
I don't disagree with any of the above, but I think the above blows the whole "materialist" bit of dialectical materialism out of the water. I know Marx and his descendants made efforts to distinguish themselves from "vulgar" materialists, but when you shift the goal from trying to describe the world to trying to describe the irreproducible interaction of the the concrete and abstract in consciousness, you're actually giving up the whole materialist ballgame and adopting a purely abstract or idealist perspective.
I lean more instrumentalist/pragmatist, so I can kinda just shrug at the forays than verge toward the realism/anti-realism debate.
I don't know if I'd call it purely idealist, it is determined by the evolutionary factors of Cognitive development and environmental adaptation. However I agree with the general idea with what you're saying and I think I'd lean more pragmatist. HOWEVER I'm very interested in the concept of Class Consciousness, what that actually could be (outside of the essentialist view that people will just see commonality and deduce nor it being a unique universal concept constant across all peoples), how could it form, and what historical/material and Cognitive factors could be involved. I mean there have been tons of examples of people acting in class interest, and with what I've said obviously they all didn't just follow some internal logic or well structured mode of recognition. Investigation of that requires understanding this process of abstraction. I guess I'd say the important thing in my mind isn't the specifics of the abstractions in of themselves, rather how abstraction arises in response to specific environments and Cognitive systems. Abstraction is only necessary to explain commonality between the previously unconnected, so there are some subset conditions in which commonality is witnessed leading to abstraction. We may never be able to actually map them out, but I think we can try to identify mechanisms that contribute to their arisal if that makes sense
it is determined by the evolutionary factors of Cognitive development and environmental adaptation.
Is that actually how it is, or is that just our abstraction for explaining and analyzing the mixture of abstract theoretical models with concrete empirical observations?
That's what I mean by the whole materialist ballgame getting washed away. Once you set about analyzing everything in this manner, even, your tools for analysis are up for grabs to be analyzed in this manner. So now we've got abstractions of abstractions and it all seems very divorced from the material world it's supposedly grounded in.
100% agree. You wanna shoot me some readings/vids you'd recommend on instrumentalism/pragmatism? At first glance it seems like a good way to explain my own views in general
Dewey's work provides a good primer on the notion if you want to check it out here on SEP
By development he means the typical "thesis/antithesis/synthesis", and this is where the contradiction is, between the thesis and the antithesis, and the development is this new synthesis that emerges from both the thesis and the antithesis.
So of course, in the material world there is the difficult task of finding what is the thesis and antithesis of, in your example, a battle, a war, a victory etc. In your example
You can have a battle that is a tactical victory but a strategic defeat.
That is already the synthesis step of the battle, the thesis and antithesis were the two opposing armies and their goals and objectives. And I think this illustrates the hardest part of this discussion, is that it's hard to figure out what should be the "thing" studied, and what are its contradictory aspects, and that the more concrete the situation is (unlike for example the abstract system construct of "capitalism" vs its material realization) the harder it is to pinpoint these.
By the way, regarding the unity of opposite, I think I might have found something worth studying on ncatlab: https://ncatlab.org/nlab/show/adjoint+modality and there is also https://ncatlab.org/nlab/show/Aufhebung
I did not read them yet (although I did read a few pages of a different paper that also formalizes the unity of opposites through adjoint functors, it made sense, but then there was the reverse question: how can I take this formalism and use it in the real world?)
Goddamn this is ridiculously abstract. I feel like I have exerted all my mental energy for the afternoon in just trying to grasp it, much less trying to apply it outside of the given examples.
Any section that stands out as particularly unclear/obscure? I certainly can't say I got it all, and discussing specific points might help clear them out for everybody
I'm studying the colonization of the Americas right now, and the foremost example I can think of is how the conflict between slavers and the enslaved created whiteness, an identity that brought more people — jews and the white working class — onto the side of the slavers, transforming the contradiction from european slaveholders vs. the enslaved into whites vs. everyone else.
The principal contradiction changes only subtly, while the principal aspect of the contradiction — the ruling class into whites — changes radically, and with it the secondary aspect is changed in response: the enslaved becomes non-whites, a new superset.
My question is what insight does this provide? These concepts are laid out in the text I'm reading without deploying the language of On Contradiction.
I gotcha, so I'm mixing levels of abstraction in that example, and need to pull back to a broader perspective.
If I were to say then that slaveholding mercantilism transformed into white supremacist mercantilism by way of the existential threat of a slave revolt, and the internal possibility of whiteness is the lever upon which this force acted, would that be a more appropriate framing for Mao's conceptualisation of contradiction?
Right, I think we're thinking along essentially the same lines, it's just a matter of phrasing
Haiti was exactly the point I wanted to bring up, but wasn't sure how, I think this is a very clear point!
Finished reading it, I am knowledgeable with regard to Hegel (and in fact the only time I tried reading Hegel I quickly gave up), but all the discussion about Haiti was super interesting thank you. I can see how it connects with our discussion with this passage
At first consideration the master's situation is "independent, and its essential nature is to be for itself"; whereas "the other," the slave's position, "is dependent, and its essence is life or existence for another."81 The slave is characterized by the lack of recognition he receives. He is viewed as "a thing"; "thinghood" is the essence of slave consciousness-as it was the essence of his legal status under the Code Noir (PM, p. 235). But as the dialectic develops, the apparent dominance of the master reverses itself with his awareness that he is in fact totally dependent on the slave. One has only to collectivize the figure of the master in order to see the descriptive pertinence of Hegel's analysis: the slave-holding class is indeed totally dependent on the institution of slavery for the "overabundance" that constitutes its wealth. This class is thus incapable of being the agent of historical progress without annihilating its own existence
That's really well put and @vertexarray I think this part might interest you too
Not at all, thank you for the resource, will read it over the week end, it will be a welcome break from plain books
Engels said, "Motion itself is a contradiction."
How is motion itself a contradiction? What things contradict each other?
Motion itself is a contradiction even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it.
The denial of a unique instantaneous position for a given time t flies in the face of pretty much all of kinematics.
You literally could not write a displacement function (because multiple positions at time t indicates the relation is not a function), and thus couldn't calculate velocity or acceleration as the derivative of that displacement function.
idk how fair it is to judge those claims based on their usefulness to kinematics.
That's true, but then I'm left to wonder how we're supposed to judge it's usefulness. If you're describing a model for the nature of motion, what are you after if not empirical adequacy?
The denial of a unique instantaneous position for a given time t flies in the face of pretty much all of kinematics.
The linked essay has another example of a supposed impossibility, though the proof needs a bit of filling in:
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 square root of minus one 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 square root of minus one?
In its operations with variable quantities mathematics itself enters the field of dialectics, and it is significant that it was a dialectical philosopher, Descartes, who introduced this advance. ...
It's correct that there are no real numbers that are the square root of negative real numbers. It's a real proof by contradiction if it's filled out properly.
How would it have been if they'd said to Descartes that complex numbers flew in the face of pretty much all of arithmetic? Because I know that complex numbers had opposition after they were invented.
(because multiple positions at time t indicates the relation is not a function)
A function can in fact take a set of positions (or some other type of thing containing multiple positions) and produce a new set of positions. Perhaps it's merely a useful simplification to say that there's a unique position.
We know that we can never find out exactly where a particle is due to the uncertainty principle and we know that we can't distinguish things that are separated by less than a Planck length, so is it possible even in principle to empirically determine for sure whether or not particles have a single instantaneous position?
It is a contradiction that a negative quantity should be the square of anything
It's not though.
It’s correct that there are no real numbers that are the square root of negative real numbers.
Sure, but you're changing what he is saying. Saying that the "square root of negative integer is a real number" is a contradiction. Saying "the square root of -1 is an imaginary number" is not a contradiction, it's a stipulative definition of i.
A function can in fact take a set of positions (or some other type of thing containing multiple positions) and produce a new set of positions. Perhaps it’s merely a useful simplification to say that there’s a unique position.
Functions by definition produce a single unique output for a given input. To say that something is in two places at one is to say that you can't describe motion as a function of time, which is the opposite result of kinematics. See the second image in the linked section.
We know that we can never find out exactly where a particle is due to the uncertainty principle
That's not what Heisenberg's uncertainty relation says. And wouldn't matter anyway because epistemic uncertainty is different than ontological non-existence. Not knowing the exact position doesn't not proscribe the existence of an exact position.
Sure, but you’re changing what he is saying.
Engels isn't a mathematician. To demand that he get correct every detail of a proof he may have heard once and that he has no training to reproduce is a bit overblown when the conclusion is correct and the true proof that he's obviously referencing would have been produced historically.
Functions by definition produce a single unique output for a given input. To say that something is in two places at one is to say that you can’t describe motion as a function of time, which is the opposite result of kinematics. See the second image in the linked section.
This is blatantly incorrect. Function outputs don't have to be unique. That's an injective function. If functions produce one output, that one output doesn't have to be a single number, it can be a single set of positions. You can have a function that takes in the starting set of positions and produces the resulting set of positions.
That’s not what Heisenberg’s uncertainty relation says. And wouldn’t matter anyway because epistemic uncertainty is different than ontological non-existence. Not knowing the exact position doesn’t not proscribe the existence of an exact position.
You must be having an argument with someone else in your head, because my point was that we can't know for sure whether or not particles have single positions, not that single positions are proscribed.
You're confused
A function f from a set X to a set Y is defined by a set G of ordered pairs (x, y) such that x ∈ X, y ∈ Y, and every element of X is the first component of exactly one ordered pair in G.
Function outputs must be unique for a given input. At time t, the position function must have a exactly one output. That can be a vector if you like, but it must always be the same vector for the same given t.
You're confusing this with one-to-one, which would be to say the position at every time must be different than every other time. Which is not what I'm talking about, because I've always been focusing on some given time t
my point was that we can’t know for sure whether or not particles have single positions
Yeah, well your buddy Engels here knows they can't, because of dialectical gibberish. And you're still using a popscience misrepresentation of the inequality. The position of a quantum particle can be known to an arbitrary high position (i.e, as exactly as you want). That just has consequences for our knowledge of the momentum.
You are apparently unaware that sets can contain sets, so the element of set Y in your definition can itself be a set, so the output of a function can be a set.
The position of an arbitrary particle can't empirically be known as exactly as you want because there are limitations to measuring devices, as you are apparently also unaware.
You are apparently unaware that sets can contain sets, so the element of set Y in your definition can itself be a set, so the output of a function can be a set.
Nope, like I said, it can be a vector, or a set, if you like. But it's always going to be the same unique set for a given input
limitations to measuring devices, as you are apparently also unaware.
Which has also nothing to do with the uncertainty principle; it's independent of any sort of technological limitations.
I agree. I earlier thought by 'unique', you meant unique in the sense that no other input produced the same output, but I see that I was mistaken. Since I see what you mean, I don't know why you said it, because I never implied that a function could give different outputs for the same input. The same output set would always be produced for the same input set in what I said.
Now that we're agreed that a function can output a set, a set of positions at a point in time can be transformed by a function into a set of positions at a later time, meaning that it's theoretically possible for kinematics of a more complicated variety to handle the motion of particles with multiple simultaneous positions.
As far as the uncertainty principle, I may or may not be wrong about it, but my main point stands: empirically, we don't know whether moving particles have unique instantaneous positions or not because we can't measure to the exactness needed to determine that. Theoretically, this seems to be the case as well, which is why I mentioned the Planck length.
One possible alternative would be that it could be that the particle occupies all the positions of a too-small-to-measure segment along the direction of travel, for example. I'm not saying that this is the case. I'm merely trying to give the benefit of the doubt to Engels. I don't want to summarily dismiss his work just because it doesn't meet my preconceptions of how kinematics work.
Now that we’re agreed that a function can output a set, a set of positions at a point in time can be transformed by a function into a set of positions at a later time, meaning that it’s theoretically possible for kinematics of a more complicated variety to handle the motion of particles with multiple simultaneous positions.
Of course it's possible to describe all motion in such a formalism, but why?
Imagine a particle moving in R^1 at 1 unit/second that occupies, at time t=0, the position x = 0. How would you meaningfully write the motion of this particle as a multi-valued function, and what is the benefit of doing so, apart from shoehorning in Engels' conclusion?
I don’t want to summarily dismiss his work just because it doesn’t meet my preconceptions of how kinematics work
It's not that it doesn't meet ones preconceptions; It can be made compatible with any physical/mathematical theory, and any physical mathematical theory can be made compatible with it. But that's true of essentially any axiomatic assertion on the nature of things, so I don't know what makes the law of contradiction/the dialectic particularly meaningfully.
As far as why I personally proposed that formalism, it was because you claimed that multiple positions implied a non-function relation, which isn't necessarily the case.
I mean it does; can you write a set of ordered pairs describing the motion of the particle above at certain points in time that
- Occupies more than 1 place at a given time
- Is a function
And if so, how and why?
Sure.
As for how, the first element of the ordered pair is a set of starting positions. The second element of the ordered pair is a set of ending positions. ({start_0, ...}, {end_0, ...}). The function is, of course, a set of these ordered pairs where each ordered pair's first element is unique in the set.
The X in your definition of function is the same set as Y: the set of sets of positions.
As for why, just to demonstrate that the statement was incorrect.
No, I mean actually do it for the above problem set up. With the actual numbers.
You mean to write the infinite set of ordered pairs of infinite sets? No, I can't quite do that, as it would take infinite time.
Not all of them, just a few of them. I think I know the solution you're couching in the abstract terms above, and I want you to explicitly lay it out so we can look at how absurd it is.
Let's say at t = 1, t = 1.5, and t = 3.
It doesn't quite matter how absurd it appears to you. What matters is that it fulfills the definition of function you said it didn't.
Sure it matters. I've already acknowledged you can shoe-horn the assertion into any system. But I've also pointed out that this makes the assertion meaningless.
So now I'm looking to see if you can provide me a kinematic example of a particle moving in R1 occupying two places at once, where the second point it's occupying isn't meaningless nonsense.
I don't care what you acknowledge. I can see that a function can take a set of positions and produce a set of positions, and that's good enough for me.
As far as how it could be done in that hypothetical world: you move each position according to how far the velocity says it would move and you return the set of results.
[Edited because this webpage is wildly closing the editing field and either deleting or submitting the contents of it]
As far as why? Generality for the theory. No one cares what kinematics says about the movement of particular dust particles on a particular exoplanet, but it's nice to know that kinematics works generally. The same would be true for dialectics.
The point of dialectics is what can be predicted usefully from it, I think. I'm still new to it, so I'm still waiting to see what that is. The thing about motion isn't that useful, it's more a thing about making the theory general, but there should be results that are useful.
I haven't read the relevant Engels work but I imagine he's invoking Aristotle's arrow paradox.
I don't think Mao understands what metaphysics actually is.
