Are the laws of mathematics and logic, such as if a=b, and b=c, then a=c just constructs of the human mind, or does the universe hold an innate logical structure to it, which the physical part of the universe must abide by?
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4+1 for a great first question .. for a good discussion of a related topic see Do numbers exist independently from observers? .. there are innumerable supporters of both the 'mind dependant' and 'mind independant' ways of approaching about this topic, i think there is no better place to start than the work of Plato. Also welcome :)– Dr SisterSep 12, 2012 at 10:50
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1Vote to close: "We expect answers to be supported by facts, references, or specific expertise, but this question will likely solicit debate, arguments, polling, or extended discussion."– DBKSep 12, 2012 at 20:30
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I'm new to this forum so I don't fully understand its purpose. Should I edit to ask what have famous philosophers said on the matter, rather than asking the question directly?– KenshinSep 13, 2012 at 4:05
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Could you try to indicate how this is different from the already-existing question about whether numbers exist independently of observers? philosophy.stackexchange.com/questions/451/…– Joseph Weissman ♦Sep 13, 2012 at 4:59
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Welcome to Philosophy.SE, by the way! Just in passing: the community tends to strongly favor very specific and practical problems encountered during the study of philosophy. You may wish to review our FAQ.– Joseph Weissman ♦Sep 13, 2012 at 5:20
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The question you have linked seems very similar to mine, except asks about numbers instead of the rules of logic more generally. I'm not entirely certain that if numbers are human creations then it implies that logic is a human creation etc.– KenshinSep 13, 2012 at 6:51
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@JosephWeissman: while it touches on a similar concept, and may be interpreted as being a projection from a common 'Platonic Question Regarding Foundations Of Precise Reckoning', I would say that the questions are in practise as distinct as 'counting' is from 'reasoning'. If anything, this question is more foundational.– Niel de BeaudrapSep 13, 2012 at 14:34
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Frege wrote about this very thing, as did Aristotle (who viewed logic as a a mere tool, btw). I would argue that if these laws have no bear on the world, then our science and common sense have to go. It would involve denying number of facts. It is incredibly difficult to see how logical laws could be a mere mental fabrication without rendering reality unintelligible.– Robert LeChefNov 26, 2012 at 22:44
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@DBK Perish the thought that a question in philosophy might spark debate. Can't have that around here!– user4894Jun 1, 2016 at 17:04
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Laws of logic are human invention. They are intrinsic to languages and knowledge but not to reality. They are used in language for describing the reality.– Marino KlisovichSep 13, 2022 at 13:06
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9 Answers
The answer is: we don't know. As the user Seldom indicated, Do numbers exist independently from observers? is a very related question.
What we do know is that there seems to be an incredible correlation between logic (and mathematics, for that matter) as we see it in the human mind and the way the universe behaves. For some reason, every time I make some logical conclusion in my mind, or even a calculation, "reality" seems to agree with it. And every time we discovered a discrepancy between our logic and reality, it was because we had erroneous models/premises.
So until now, we've had so much success that we induce that the universe seems to work with some kind of correlation with logic. Of course, there are several possible explanations for this:
- Logic is a structure of reality
- Logic is an abstraction made by humans looking at reality
- Logic is a method used by humans to view and filter reality
Again, very similar to the numbers question.
Insofar as any of these relationships are defined and scoped by the human mind, so are they contingent upon the human mind.
Dependency/independency of some mind begs all the wrong questions and results in meaningful and senseless statements like "equality exists outside of space and time" and "laws of physics, equally, are part of the universe, regardless of human observation." These, in turn, result in all kinds of sloppy language.
This is not a meaningful question in logical positivism. The question of whether something "exists" or "does not exist", especially in relation to the existence of other inferred things, like human or animal consciousness, is an abuse of language in the sense of Carnap.
So this question has no answer, and it needs no answer, because it is not a real question. It's just a bunch of words you put together which fool your brain into thinking they have meaning when they don't.
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It is fair to ask whether logic is more or less a feature of nature, just as we can ask whether mass is a feature of nature. However, an answer is strongly suggested by distinguishing "facts" from "truths", in the sense of "not contradicted by fact". Sep 13, 2012 at 14:52
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@NieldeBeaudrap: The existence of logic is mathematically equivalent, modulo a choice of reasonable axioms and a small translation, to universal computation. Universal computation is measurable in nature, at least in finite approximations: we can build it, and we see it around us in biological things. This doesn't have any bearing on whether they "exist independent of consciousness" since this is not a proposition which has any bearing on the senses, or on the testable properties of logic or computation. Sep 14, 2012 at 3:33
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Computation is itself a tool. The idea that reality can be used for computation is the notion that we can harness physical processes to do something we want -- depending on the notion of intention. That intention is imposed on the tool by the user (e.g. ourselves). Inasmuch as we speak of tools, we are speaking of our own interpretation of how the universe may be harnessed to our own ends. Therefore we are speaking of a correspondance of the world with our ideas, and therefore speaks more of the relationship of our models to the things they represent, than reality in itself. Sep 14, 2012 at 3:54
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@NieldeBeaudrap: That argument would carry more weight if we didn't see natural computing machinery acting with intentionality in every cell in nature. The notion of computation does not require us doing anything--- evolution does it all by itself. Your brain is an obvious example. Sep 14, 2012 at 6:21
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There is a risk in attributing intentionality to things in reality. I'll admit that there's a philosophical problem hiding here, essentially the boundary between humanist/existentialist and materialist/mechanistic ways of speaking about the world. But remember that cells are presumably nothing but the byproduct of deep-time chemical processes which biased towards replicators; if these compute, why don't we say that all chemical reactions are computation, that gravity is computation, or that evolution is an intentional force of nature? Sep 14, 2012 at 13:24
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@NieldeBeaudrap: They are not biased toward replicators. Replication is not the main thing in evolution, computation is. Most chemical reactions are not Turing complete in bulk, they can't be programmed arbitrarily, my definition of life is when they are Turing complete. This is not an improbable event, a reasonable fraction of complex polymer reactions are complete. When a virus infects a cell, it shuts down translation. That's because it recieves a signal and it "knows" it's been infected, that's intentional. This kind of thing turns into our type of intentionality by gradations. Sep 14, 2012 at 15:31
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I don't think that's a good idea of "intentionality". Intentions, even if you want to reduce them to merely mechanical causes, can't so easily be reduced to everything that occurs in the universe. That's philosophically presumptuous and is putting the cart (a mechanistic system) before the horse (the facts of experience: even an illusion needs explaining). And computation is second to physics. Computers are physical objects operation in terms of physical laws. Computation is what humans ascribe to this artifact which mimics a mental operation. Nov 26, 2012 at 22:52
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@RobertLeChef: Computation is not necessarily second to physics, because physics invokes a notion of computation to do wave-function reduction in quantum mechanics (this is measurement). Whether this is a permanent thing in physics is a matter of debate, but I tend to believe it is. The computation doesn't mimic anything--- it is a mental operation of a primitive sort. When it is sophisticated enough, it is equivalent to that which goes on in your head. Every aspect of the human soul is a property of computers, and denying this is trivializing the transcendence of computation. Nov 27, 2012 at 0:59
No, because we form the basis of the a priori. That is, it is our consciousness which assesses and selects the building blocks of all logical systems, coming from the infinite sea* of [logically] equally-valid starting points.
(cf. Gregory Chaitin)
Basically note that we are living in a world that is certainly not self-contradictory and has rules for itself (some approximately discovered and some not even in any approximate way, maybe), but surely there should be some axioms for it to be based upon, as we can easily say something is possible (according to such axioms) and something is not possible (again according to that axioms) and such sentences are all meaningful (although there is aways the possibility that the one who says these expressions be wrong in respect to his objectives, so I am talking about the ontic knowledge and not epistemic, what really is and not what we think to know of reality). Thus, logic by its own is beyond the human kind, even humans exist based on the same logic that other things exist, they all belong to the set of possible objects in this world according to its underlying axioms, or say logic rule.
However, mathematics is perhaps the only branch of science which has not its base on witnessing the outside real world, you can imagine a set of axioms and logical rules to create your own self-consistent mathematical world, and substituting some of the axioms or logical rules by their antonym you may still be able to create another self-consistent mathematical world for your self and yet be happy with your creation. None of these logical rules may also have no counterpart in the outside world and that's it, logic exist in human minds and outside it!
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1That we live in a world that is not self-contradictory could as easily be a consequence that we built logic to reason about the world we see. The world consists of facts, not truths; truth is a question of the correspondence of our utterances to fact. That logic doesn't give us contradictions about the world — because it is feasible to find 'essentially correct' assumptions to reason from — indicates that logic is fit for purpose. Sep 13, 2012 at 14:47
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I do not agree with you, the word has been existed in a self-consistent way before human being come to it, if we were some super-existences to be able to also talk about facts yet we could talk about the possibles and impossibles of this world, indeed, if the world was not self-consistent it could not survive until we could experience it, there MUST exist an inherent logic behind this world defining its possibles and impossibles, it is according to that logic that nothing can exist in this world unless its anti-thing is absent in the same world.– owariSep 14, 2012 at 23:26
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The act of studying the possibles of this world is Science, although for non-super-xistences like us it is only epistemically about the truths and not facts, so only would bring about approximate knowledge of this world, its contained existences and the rules governing them (like their evolutions in the course of time, inter-relations and etc), and thus the logic behind it. (With the exception of mathematics branch of Science.)– owariSep 14, 2012 at 23:29
I believe that the laws of mathematics are independant of thought. The names, symbols, etc that we assign to numbers are irrelevant, but the ratio between the radius and circumference of a circle, for example, are constant whether we observe them or not.
The laws of physics, equally, are part of the universe, regardless of human observation. We spend time and effort trying to figure out what they are, not inventing them.
I would like to believe, also, that the laws of logic are similarly imutable. The way we express them make it feel like they are human inventions, but I believe they are constant facts of reality that we discover and decide on conventions to express, rather than creating and enforcing rules on reality.
We would not observe water flowing uphill (observe, not just perceive), or 1 individual object coming together with another and forming a group of 3. However, when it comes to logic, it is possible to perceive actions which seem to be founded on a belief that defies logic, making it easier to think that it is human-created.
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1That the ratio of a perfect circle's circumference to it's radius is constant is a result of Euclidean geometry. But there are no perfect circles (only approximately perfect ones); and it turns out that geometry isn't Euclidean (only approximately so). So that 'perfect truth', at least, is about fairy tale creatures which are wishful versions of what we encounter in reality; they are human constructs which are extremely useful caricatures, but not real phenomena. Sep 13, 2012 at 14:39
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I'm not convinced that there's no such thing as a perfect circle in nature, but the existance of one is irellevant to the point being made... However on this: "That the ratio of a perfect circle's circumference to it's radius is constant is a result of Euclidean geometry." - we will have to disagree. The ratio between the two measurements is constant, regardless of the number system used, or any other variable. It is not a "result" of anything but the two measurements involved.– RynoSep 14, 2012 at 9:38
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1Are you aware that the ratio is not in fact constant in hyperbolic geometry, or spherical geometry? Of the uniform geometries we know, it is only constant in Euclidean; and as General Relativity indicates that geometry is not Euclidean, there ought to be real-life instances — near massive bodies for instance — where the ratio is not 2 pi. Thus it is not clear on what theoretical basis you can claim that the ratio is constant in real life, except if you're speaking of the limited domain of everyday experience, in which geometry is approximately Euclidean. Sep 14, 2012 at 10:55
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and does it scale? at plank distances, is a circle even physically meaningful? If some of the speculations regarding quantum gravity is correct, the spacetime fabric would be awash with topology change. Sep 25, 2012 at 8:23
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But maybe that what we find to be the rules which you believe are the objective rules that constitute the world and everything is just a model in our brain, and all models are wrong - but some models are useful.– scravyOct 10, 2012 at 23:39
It's not like you can take a telescope or microscope and "see" logic. The "laws" of logic don't mean anything except inside a mind. Just as the "laws" of physics are only meaningful inside a mind (brain). They represent our understanding.
I think logic is not a "thing", its a process and activity of a mind/brain. It's like saying "seeing" exists without eyes or "running" exists without legs. Something has to be "doing" the logic.
Let's start with computers. What do computers do, if not logic?
I decided that they don't, and here is my argument, based on a definition of logic: logic is a form of thinking that attempts to solve a problem by manipulating meaningful symbols via formal rules and processes, to get a meaningful result.
So, whatever is happening in a computer, it's not really logic until someone has used it to solve a problem and/or assigned meaning to the symbols being manipulated by the logical mechanism. And a computer can't do that part of logic without a human (yet).
Consider the abacus. It can't do math until you have assigned a meaning (ie, number) (in your head) to each of the beads being moved. Without a human to interpret their meaning (ie, "read" the results), it's just a bunch of clay beads moving around on a set of rods. The same thing can be said of Babbage's calculating machine.
And it's the same with computers. Until the results of the (much more complex) electronic manipulations in the computer is interpreted or assigned meaning, it's not really doing logic, or solving a problem. Without a human to interpret (assign meaning to) the results, it's just a bunch of electrons moving around.
For example, an open circuit could just as easily mean "true" as "false" The meaning is assigned as a convention, and the rest of the computer is built based on those conventions. ASCII character 45 could just as easily mean "Z" as the letter "A".
In addition, there is the issue of defining the problem that is to be solved. This is another step in performing logic that computer's can't currently do. They have to be programmed to solve specific (human) problems.
Yes, they seem to have done a lot of thinking for you, but the problem the computer is solving was defined and programmed into the computer by a human, and the results of all that computer processing are meaningless without a human to read or interpret it (ie, consume the output), so I say computers are not really performing logical thinking.
In the future, computers may be able to be self-aware, emergently conscious, capable of reflection, progamming themselves, and assigning meaning to their own results. In the meantime, they are an extension of, and a tool for, human thinking. They have been described as our "external brains".
When humans read, they are assigning/giving meaning to symbols on paper or some other media. When humans think, they are manipulating mental symbols (concepts). Logic (and math) is the manipulation of mental symbols following formalized rules, in order to to solve a problem.
So what do I mean by "meaning"? Meaning is context. Concepts are only meaningful in the context of simpler concepts they are built up from. That is how sophisticated ideas are constructed. That is how we learn, by gradually increasing the complexity of our concepts.
Some possible implications: Logic and Math are not something "out there" that we "discover". The rules of logic and math are "constructed" by us, as our mental processes becoming more and more abstract and formalized. This is why logical thinking is hard, and takes practice.
I also agree with the "embodied mind" theorists that many if not most of our simpler concepts are understandable and can only come from the experience (ie, context) of living in physical bodies. For example, the concept of "color" is not meaningful without color vision, and a brain that is hard-wired to interpret it for us.
Nevertheless, I do think that logic and math are saying something universally "true" and non-relative to our human condition, in the sense that I think that if aliens were found, they would have developed logic and mathematically systems that are very similar, if not identical to our own (thanks goes to Carl Sagan for that idea). The more abstract our math and logic become, the more universally "true" they become. But, that truth cannot exist outside of a thinking mind. It's not "out there" to be discovered, it's "in here" and constructed, by hard thinking.
Of course, what is amazing, and almost mystical, about logic and math is how well things "in here" allow us to predict and accurately manipulate things "out there". That reality can be abstracted, and those abstractions re-applied back to real things is amazing. As Einstein once said "The eternal mystery of the world is its comprehensibility."
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Welcome to Philosophy.SE! The post is basically just an opinion. I would suggest editing it, citing sources and making more concise. Also, consider that the gist of what you suggest is already captured by other posts, and upvote those instead of adding a new post. Jun 6, 2016 at 20:12
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Well, duh. Why would I need to document and cite, if it's my own opinion? Oct 18, 2018 at 13:28
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Pleas see philosophy.meta.stackexchange.com/questions/474/… ... the community consensus seems to be to discourage answers. Oct 22, 2018 at 17:42
logic is a tool used by beings capable of reasoning, we use this tool to create valid reasoning and to understand valid reasoning, so when a human observes the universe he uses this tool to create a valid reasoning to explain what he is seeing, math is the lenguage we use to understand how natural phenomenons work, natural phenomenom exists with or with out humans the way natural phenomenoms work is the same with or with out humans, mathematics is the language we use to translate the way this phenomenomswork into human understanding, so logic and math are correlated but they only exist when theres is a mind to use them.
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so are you saying the law of identity is fundamentally not true? That's going to be a little hard to accept for certain classes of natural objects.– virmaiorJun 13, 2014 at 23:58
How can anything NOT be a creation of the mind? Just ask yourself this: IMAGINE no humans existed. Where would logic reside? Where would reason, truth, morality and numbers reside?
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1You're missing an important just in your answer to the question here. The question OP asks is if they can be just constructs of the human mind. The question you answer is whether they are also constructs in the human mind. Or at least you haven't spelled out anything else.– virmaiorJan 16, 2015 at 3:16