Relevant.

The three laws are:

- Law of Identity
- Law of Contradiction
- Law of Excluded Middle — I like sushi

But maths is not given in experience - again, it is constitutive of the rational operations of the mind. — Wayfarer

The world is intelligible only because of identity and difference. The inherent logic of identity and difference grows out of our ability to distinguish one thing from another, which is obviously essential to survival and is necessary for any intelligibility at all. In our parsing of the world in terms of distinct entities the law of contradiction is inherent: a thing cannot both be and not be itself. This logic is also inherent in the law of the excluded middle; a thing is either itself or it is not. Mathematics as elaborated is not "given in experience", but on account of identity and difference, number, which is the basis of all our elaborated mathematics, is.

So, the world of our experience is logically in accordance with those three laws and mathematics, the only exception being what is observed in quantum physics experiments. But we have evolved in the "macro world" of phenomenal experience, so we should not be surprised if the "micro world of QM yields counter-intuitive results.

The unreasonable effectiveness of mathematics? My friends, it is only unreasonable that one forgets reason evolved with it.

I notice most of the answers here have to do with logic's place as already useful. I find it interesting that an inquiry on the nature or origin of logic is almost considered impossible. What is the implication of that then? Well, you can just say, "It's foundatioanal", and "it is what it is", but how unphilosophical is that? Here we have a set of tools that we use in the world to create other tools, but we don't and refuse to look at it closely? — schopenhauer1

We notice that some arguments are truth-preserving, and we call those arguments logical. What further explanation of their nature or origin would be needed?

As an analogy, consider that the major encryption schemes that underlie internet transactions rely on prime factorization. But what is the nature and origin of prime numbers such that they are so special? Simply that primes are those natural numbers that have a specific characteristic that can be exploited for encryption (namely, that they are not divisible by smaller natural numbers). Similarly, logical arguments - those with the characteristic of preserving the truth of their premises - can be exploited for various things, such as building computers, solving problems and increasing knowledge.

Of course, those definitions don't exhaust what can be learned about prime numbers or logical arguments. But I think it shows that they can be understood as perfectly natural features of the world and not as intrinsically mysterious or other-worldly.

Is logic something that the universe provides? Are we divining/discovering logic? If so, is logic just how the universe operates? If so, is this different than the idea that we are divining/discovering math? Is that the same thing being that math is also an ordering/pattern principle? Is it more foundational or less foundational then math then as it might underride math (pace early Bertrand Russell).

If math is simply something that is nominal- we make it up to help make sense of the world, why can it be used so effectively in things like generating outputs from inputs? If put to use in a technological context, it is the basis for modern engineering, science, and technology. — schopenhauer1

The traditional view would be that thought, language and the world are isomorphic, that the world itself has a logical structure that can be discerned. The modern view would be that logic is about the form of sentences, not their content. Physics, understood as applied math, would seem to locate form in the world again as suggested by slogans such as information is physical.

I notice most of the answers here have to do with logic's place as already useful. I find it interesting that an inquiry on the nature or origin of logic is almost considered impossible. What is the implication of that then? Well, you can just say, "It's foundatioanal", and "it is what it is", but how unphilosophical is that? Here we have a set of tools that we use in the world to create other tools, but we don't and refuse to look at it closely?

Is logic something that the universe provides? Are we divining/discovering logic? If so, is logic just how the universe operates? If so, is this different than the idea that we are divining/discovering math? Is that the same thing being that math is also an ordering/pattern principle? Is it more foundational or less foundational then math then as it might underride math (pace early Bertrand Russell).

If math is simply something that is nominal- we make it up to help make sense of the world, why can it be used so effectively in things like generating outputs from inputs? If put to use in a technological context, it is the basis for modern engineering, science, and technology. — schopenhauer1

I believe that logic, an internal-mind system is secondary to the external world and derived from it. I don't know if you believe in evolution but if you do then it must be that our minds, everything in it, including logic, must be mappable to external reality. We wouldn't survive and we wouldn't be able to pass on our genes if we were illogical. Of course there are some ''illogical'' thought patterns that actually help us survive but that's another topic.

So you see, the question ''why logic works/exists?'' is explained and there isn't anything mysterious going on.

That out of the way it's important to note that logic works and is probably confined to a human scale - the part of the universe we're capable of perceiving. Some say that contradictions, impossible at the human scale, do occur at the quantum level.

@Joshs

Thermodynamics, Maxwell's equations, all sorts of electrical, chemical, and physical laws, these are the basis for much of the technology we use. These patterns of nature (i.e. laws of nature) are in-built into the system. They are not things we invented (pace a realism of some kind).

Of course, the way these patterns lead to more complex patterns (pace an emergentism of some kind), it not fully known. How combinations of patterns create systems that are more than its parts, are perhaps the most vague part of the process. We know the less complex patterns. We know perhaps, how these patterns can combine, and we know the output of more complex patterns, but how this emerging process really works in terms of less complex to more complex is harder to nail down.

But lets say one of the complexities out the less complex patterns is the pattern of evolutionary change in animal species. There is a pattern, perhaps, to how species respond to environmental stimuli and external pressures. These patterns in evolution produce patterns of behavior. Patterns for various species are conserved in what we colloquially call instinctual behaviors- ones that can produce outputs favorable for survival in a certain morphological/biological/ecological niche for that species.

Human evolutionary pressures resulted in a more plasticity. The plasticity allows for accumulated cultural learning. In this learning process, abilities to see the very patterns that compose the human, nature itself, and the very reason they can learn, are employed to recognize patterns, use linguistic encoding to symbolically represent those patterns, and then use those patterns to help in survival, find more comfort, and entertain ourselves. The superstructures of culture, institutions, and the like help glue together the accumulated cultural knowledge and learning and reinforce it in a kind of feedback loop.

Thus logic that is metaphysically composed of "natural laws" becomes logic that is creatures composed of the patterns, recognizing the very patterns they are composed of. This might be where @Banno was coming from in his idea that logic fits too well- like questioning why a glove fits so well. This also leans towards the idea that logic and math is in fact discovered.

Now, a counter of this is @StreetlightX objection that humans don't just discover natural laws, and laws that lead to technology, but other laws that are not useful in any way outside their own contained system. These are non-thermodynamic, non-Maxwell's equations, non-quantum theory, non-Boolean algebra, etc. These are mathematical systems that are fiat, made up, but are wholly functional systems in and of themselves, without mapping to any real world phenomena. In this regard, it is the pattern-finding that is primary. The output need not be useful or map to anything real. If I was to use an analogy with other animal traits, I might use the example of certain birds that reach out and move their beaks and neck to catch an egg before it rolls away. It might do this in circumstances that mimic an egg rolling. It didn't do anything "real" towards the eggs, but it kept doing its instinctual response anyways. Well, if humans are naturally problem-solving pattern-finders, this can be simply taken out of its original context for survival purposes as an exaptation of sorts. It is an ability that is there as byproduct of having the enormous amount of plasticity needed for original environmental pattern-seeking and problem-solving.

Both of you seem to be hitting at my last post.

These are mathematical systems that are fiat, made up, but are wholly functional systems in and of themselves, without mapping to any real world phenomena. — schopenhauer1

Agreed. It's very much like how life itself evolves. A trait, in this case logical ability, must have survival value. From logic evolved math which too has survival advantage but it's not necessary that ALL our mathematical knowledge have direct advantage. Some mathematics is pure abstraction I believe but these may provide indirect benefit by augmenting our logical/mathematical skills just like how play and games are very important to a child's mental development.

The unreasonable effectiveness of mathematics? My friends, it is only unreasonable that one forgets reason evolved with it. — fdrake

I think my last post here, is getting to your point as well: https://thephilosophyforum.com/discussion/comment/292353

obviously essential to survival — Janus

it is only unreasonable that one forgets reason evolved with it. — fdrake

Notice the implicit suggestion that reason can be understood through the perspective of evolutionary naturalism. After all it is only natural to assume that abstract reasoning skills would be advantageous in the Darwinian sense, in that through them 'the clever hominid' could outwit his nimble, but intellectually-challenged, competitors and predators. But I really don't think it stacks up. It's another form of biological reductionism; that everything about h. sapiens is ultimately explicable on the basis of a theory of biological origins. And ultimately, this can only lead to some form of pragmatism or utilitarianism - because it implicitly subordinates culture to biology. (This is the subject of Thomas Nagel's essay Evolutionary Naturalism and the Fear of Religion.)

Whereas through reason and language, humans are able to transcend the biological; we can understand the biological, and on one level are clearly biological organisms, but it's our ability to reason and to explore abstract truths that differentiates us from animals.

Conversely, it is exactly the capacity to reason which is criticised by some naturalist philosophers, precisely because it doesn't fit into the biological and naturalistic outlook.

obviously essential to survival — Janus

You've lifted that out of its context.

The inherent logic of identity and difference grows out of our ability to distinguish one thing from another, which is obviously essential to survival and is necessary for any intelligibility at all. — Janus

So, I'm not saying "that reason can be understood through the perspective of evolutionary naturalism." if that is taken to mean that some kind of final or absolute explanation can be found there. In any case it would be more of an explanation of the origin of reason in sensory perception, than an explanation of some purported relationship it might be thought to have to some imagined ultimate nature of the world in any kind of platonic sense.

So reason, or logic, is itself irreducible, which means it cannot be existentially explained because all explanations both presuppose and utilize it, as others have noted. I was merely trying to tease out the ways in which reason or logic, and language itself, might be thought to have evolved from our experience of a world of differences and similarities, of change and invariance. Without primordial difference and similarity (identity), change and invariance or regularity or recurrence or whatever term you like, the world could not be the world; there would be no intelligibility to begin with and hence no survival.

And that goes for animals as well as humans, of course. Animals' experiences must make sense to them in their own various ways as ours do to us, otherwise how would they function, let alone survive? It has also been demonstrated that a few kinds of animals (I'm not sure just how many) can perform rudimentary counting, so number is perceptible and makes some kind of sense to them. They must, in their own ways, select form the "buzzing, blooming confusion" of sensory input, just as we do in our own ways.

@schopenhauer1@TheMadFool

I believe that logic, an internal-mind system is secondary to the external world and derived from it. — TheMadFool

That is essentially psychologism. Arguments for psychologism haven’t really held much weight historically.

That is essentially psychologism. Arguments for psychologism haven’t really held much weight historically — I like sushi

I was offering an explanation to the query ''why logic works or fits so well with experience?'' My explanation doesn't involve psychology. It's based on evolutionary theory though.

My mistake. I thought you were implying that logic is created rather than discovered. That is basically psychologism.

no problem.

I wasn’t trying to cherry-pick, I selected it because I wanted to discuss that particular point.

So, reason, or logic, is itself irreducible which means it cannot be explained because all explanations both presuppose and utilize it, as others have noted. — Janus

Mostly me. It’s a form of the argument from reason, although I don’t proceed from there to an argument for divinity, which is how it’s usually presented.

Animals' experiences must make sense to them in their own various ways as ours do to us, otherwise how would they function, let alone survive? — Janus

But surely the point about animal behaviour is that it can mostly be accounted for in terms of stimulus and response. I don’t *think* animals could imagine how things could be different, so it’s not a matter of them ‘making sense’ of the world, but of responding to it effectively. And in fact, a lot of ‘naturalised epistemology’ wants to explain rationality in just those terms, so as to show the basic continuity of animal and human intelligence. Naturalism doesn’t recognise ontological discontinuities.

But surely the point about animal behaviour is that it can mostly be accounted for in terms of stimulus and response. — Wayfarer

Sensory stimuli must be modeled by the animal brain just as is the case with humans. It has nothing to do with "being able to imagine how things could be different" but to do with being able to recognize difference and similarity. I see no reason to suppose that humans have not evolved from common ancestors with other animals, notably chimpanzees with whom we have 99% of DNA in common. Why should the brain be any different?

So reason, or logic, is itself irreducible, which means it cannot be existentially explained because all explanations both presuppose and utilize it, as others have noted. I was merely trying to tease out the ways in which reason or logic, and language itself, might be thought to have evolved from our experience of a world of differences and similarities, of change and invariance. Without primordial difference and similarity (identity), change and invariance or regularity or recurrence or whatever term you like, the world could not be the world; there would be no intelligibility to begin with and hence no survival. — Janus

Sounds like the assertion that claiming there is no objective truth is itself making a truth claim.
As I wrote in earlier posts, according to phenomenology since Husserl, you've got it exactly backwards. Existence is irreducible, and logic presupposes it. There are explanations which precede logic, of which logic is just a historical derivative mode , and not a necessary one. Such explanations do not assume the law of non-contradiction. Differences and similarities are not opposites, they are both implied in every meaning. Invariance is not opposed to change, it is the effect of a constructive activity that maintains itself over time as the same differently. In order to be invariant, a meaning has to reflectively turn back on itself so that it can persist as itself. The effect of exposure to context guarantees that this reflexive move exposes any meaning to alteration of sense. Thus invariance is always the invariance of a meaning whose sense begins to drift at the moment of its turn back on itself in reflection. So the illusion is created of pure invariance only because this continual drift of sense of a meaning is subtle enough that most dont notice it. From this inattention to change within identity was born the concept of pure invariance and the law of non-contradiction.

If I have you stare at an object or say a word over and over again , at the end of this exercise you will declare that the object stared at or the word repeated continues to be the same object or the same word throughout the time frame. But what you likely would not have noticed is that the SENSE of the meaning of the object or word wandered very slightly over that period of time. To claim that this is just a subjective effect and can be separate from what we know of real world objects (and ideal conceptual objects) misses the point that our notion of real world objects is derived from subjective experience.
Logic's assumption of invariance and non-contradiction depends on ignoring these facts.
And physics can ignore them not because the aspect of the world it studies functions differently than subjectivity, but for its own convenience and due to its theoretical limitations it uses a vocabulary that masks these facts.

And physics can ignore them not because the aspect of the world it studies functions differently than subjectivity, but for its own convenience and due to its theoretical limitations it uses a vocabulary that masks these facts. — Joshs

The problem is, this invariance "works" for predictive models and technological problems. The usefulness of the logic is then what matters. Also, there are fields I am sure, that take into account the variance you describe, and put back the subjectivity in the equation, such as quantum mechanics and relativity, etc.

On a more basic level, tribesman probably see patterns in their everyday living and make note of it in their technology across generations. Agriculture became a pattern that started the idea of living with more coordinated effort to draw water for the crops and animals. This kicked off engineering, and the problem-solving that it needed. Then from engineering we can go to pure logic and math by the time of the Greeks. Other civilizations had their own mathematical systems based on astronomical pattern seeking. So it's the seeing of patterns and problem solving, and having a language to index it all that gave logic its natural force perhaps. All of these patterns are from the evolutionary patterns that helped shape our species, which themselves are from other patterns, down to patterns of laws of nature. Its patterns all the way down man. Our species are just pattern recognizers because of our brain's plastic nature of learning and ability to accumulate cultural knowledge.

Ugh, this is starting to look too similar to @apokrisis :meh:

Somewhere on some other planet orbiting some very distant star, maybe in another galaxy, there could well be entities that are at least as intelligent as we are,” he said. “Suppose they have very different sensory apparatus — they have seven tentacles, and they have 14 funny-looking little compound eyes and a brain shaped like a pretzel.” Nevertheless, Dr. Gell-Mann said, we can be confident that these creatures would discover the same fundamental laws. Some people believe otherwise, he added, “and I think that is utter baloney.

Obituary for Murray Gell-Man, discoverer of the quark.

↪TheMadFool
My mistake. I thought you were implying that logic is created rather than discovered. That is basically psychologism. — I like sushi

Ah, OK. ... Does that make me a psychologist, then? :wink: For I believe that maths and logic were created by humans. They were created for a purpose (or for a number of purposes), and they match those purposes so well - like the glove has five fingers - because we built them that way! We wanted a tool to help us manipulate shapes, making it easier for us to build houses and castles. So we didn't create geometry randomly, we did it with significant focus, to achieve a purpose, and we succeeded.

I dunno what your position is regarding psychologism. This may help you clarify:

3. Examples of Psychologistic Reasoning
Although the exact definition of ‘psychologism’ was itself part and parcel of the Psychologismus-Streit, most German-speaking philosophers, from the 1880s onwards, agreed that the following arguments deserved the label ‘psychologistic’ (I shall write PA for ‘psychologistic argument’):

(PA 1) 1. Psychology is defined as the science which studies all (kinds of) laws of thought.
2. Logic is a field of inquiry which studies a subset of all laws of thought.
Ergo, logic is a part of psychology.
(PA 2) 1. Normative-prescriptive disciplines — disciplines that tell us what we ought to do — must be based upon descriptive-explanatory sciences.
2. Logic is a normative-prescriptive discipline concerning human thinking.
3. There is only one science which qualifies as constituting the descriptive-explanatory foundation for logic: empirical psychology.
Ergo, logic must be based upon psychology.
(PA 3) 1. Logic is the theory of judgments, concepts, and inferences.
2. Judgments, concepts, and inferences are human mental entities.
3. All human mental entities fall within the domain of psychology.
Ergo, logic is a part of psychology.
(PA 4) 1. The touchstone of logical truth is the feeling of self-evidence.
2. The feeling of self-evidence is a human mental experience.
Ergo, logic is about a human mental experience — and thus a part of psychology.
(PA 5) 1. We cannot conceive of alternative logics.
2. The limits of conceivability are mental limits.
Ergo, logic is relative to the thinking of the human species; and this thinking is studied by psychology.
Who actually held these views, indeed whether anyone did, was hotly contested at the time, but it seems reasonable to attribute PA 1 to Theodor Lipps (1893) and Gerardus Heymans (1894, 1905), PA 2 to Wilhelm Wundt (1880/83), PA 3 to Wilhelm Jerusalem (1905) and Christoph Sigwart (1921), PA 4 to Theodor Elsenhans (1897), and PA 5 to Benno Erdmann (1892). We might also note a couple of quotations that for many authors at the time were paradigmatic expressions of psychologism. The bulk of the first quotation comes from Mill's Logic and has already been quoted in the last section:

So far as it is a science at all, [Logic] is a part, or branch, of Psychology; differing from it, on the one hand as the part differs from the whole, and on the other, as an Art differs from a Science. Its theoretical grounds are wholly borrowed from Psychology, and include as much of that science as is required to justify its rules of art (1865, 359).
And Theodor Lipps held that

… logic is a psychological discipline since the process of coming-to-know takes place only in the soul, and since that thinking which completes itself in this coming-to-know is a psychological process. The fact that psychology differs from logic in disregarding the opposition between knowledge and error does not mean that psychology equates these two different psychological conditions. It merely means that psychology has to explain knowledge and error in the same way. Obviously, no-one claims that psychology dissolves into logic. What separates the two sufficiently is that logic is a sub-discipline of psychology (Lipps 1893, 1–2).

https://plato.stanford.edu/entries/psychologism/

Thanks for that. It seems psychologism is a way of claiming that every branch, sort or style of knowledge is part of psychologism. It's just a land-grab by another name! :smile: Maybe I'm not one of them, then. :up:

But I still maintain that maths and logic were created, not discovered.

That is a psychologistic argument then.

That is a psychologistic argument then. — I like sushi

According to psychologism, everything is a psychologistic argument, n'est ce pas? :smile:

Any help if I admit to presenting an argument that the psychologists also agree with? :wink:

@StreetlightX@Banno
Frege tried to prove that math is reducible to logic and invented "formal" logic as a result. Russell and AN Whitehead tried early on to do a similar project. Many would say Russell himself with his initial paradox and later with Godel and his incompleteness theorem blew this project up- that a manageable set of of axioms can explain all of arithmetic. Neo-logicists try to pick up where Frege left off, but with Russell and Godel's contradictions and inconsistencies in mind.

Why might it be important to tie math to logic? Because while mathematics is not a kind of empirical knowledge we get through the senses, scientific knowledge does work this way. But math is not empirical, it can be done without any knowledge of experience of the world "outside" (gathered from the senses). However, math even if doesn't originate in experiential knowledge, is uniquely useful for experience. You need it to understand the theories of empirical sciences.

By reducing math to logic, it grounds math in a very practical way that humans parse the world (logic). Logic seem much more empirically-based even though it may not be purely empirical. It is closer to human experience than pure math is. Thus, we can see the importance of the project Frege was working on in terms of how math works so unreasonably well in the empirical world (it is based on a more empirically usable system of logic).

However my question goes a bit deeper than that. It is asking why logic itself is so useful. Why does logic work so well? I provided an evolutionary approach for logic's efficacy. This approach tried to demonstrate that patterns in nature (metaphysical statement), by way of some emergentism, have created a being that has pattern-recognizing abilities (epistemological statement). My critique of my own argument is explanation of how emergence works. I've always had a problem with emergence, especially in ideas of theory of mind. However, taking away that tricky problem, it is kind of a basic theory. That is to say, patterns by necessity create more patterns and beings that recognize those patterns. First, it was primitive problem-solving and pattern-recognition, but as accumulated knowledge grew over time (by way of the very basic adaptation that humans developed of accumulating cultural knowledge), logic itself becomes more refined and applied to other sets of problems. All the minutia we monger comes from this.

Edit: An interesting addendum would be that creatures have to follow a "logic" of instinctual norms that more-or-less fit ecological setting (or extinction), or be plastic enough in its ability to recognize patterns (not instinct but cultural and other times of more plastic learning) in order to survive. Due to the necessity of patterns, humans couldn't survive any other way since we evolved such a high degree of plasticity. It would be almost a contradiction for there to be an animal with this much plasticity to not have pattern-recognition and problem-solving skills and eventually logical inferences.

No need to label you as being this or that. Psychologism isn’t a philosophical position just merely a means to distinguish types of argumentation as far as I can tell.

But I still maintain that maths and logic were created, not discovered.

I don’t know how you can. If you offer proof you do so via logical truths. If you claim to need no proof you do so by some necessity you view as illogical?

I would not say I created the world when I was born, I was ‘simply’ born and found myself on a voyage of discovery - and distinguished experiential phenomenon due to faculties of logic coherence. I wasn’t born and then decided to invent logical systems in order to comprehend my surrounding that I couldn’t comprehend or have any comprehension of comprehending prior to creating logic. Get it? Can you argue against that? Would be nice if you could in some useful way.

I would say I created the world when I was born, I was ‘simply’ born and found myself on a voyage of discovery - and distinguished experiential phenomenon due to faculties of logic coherence. I wasn’t born and then decided to invent logical systems in order to comprehend my surrounding that I couldn’t comprehend or have any comprehension of comprehending. — I like sushi

Neither logic nor maths was invented by one person. And neither was invented, I suspect, by someone newly-born, as your text sort of implies (but I doubt you intended that :wink:). We found ourselves in a world we didn't understand, and we gradually crafted tools to help. Gods and religion came first, and other ideas followed. Your text seems to say that we are born with "faculties of logical coherence", just as we are born with legs. I don't think this is so. Otherwise, our paleolithic predecessors would have been logic-users, long, long before the Greeks laid down their foundations for logical thinking.

You also seem to say that, without logic, we could not formulate logic. But when put as I just did, I think the shortcomings of that argument are clear?

I doubt we’re talking about the same thing at all. Never mind.