What is the role of logic in philosophy, mathematics, and other disciplines?

[dipungal]

I will try to make my OP based on the rules this sub-forum subscribes to, if not please inform me. Sorry.

My question is about logic. How did we acquire it? Was it evolutionary? How is it that Japanese logicians do very much the same work as white American ones do. I am asking because logic seems so fundamental to everything we do.

Does it come from intelligence?

 

[Maui]

I will try to make my OP based on the rules this sub-forum subscribes to, if not please inform me. Sorry.

My question is about logic. How did we acquire it? Was it evolutionary? How is it that Japanese logicians do very much the same work as white American ones do. I am asking because logic seems so fundamental to everything we do.

Logic, in my view, is the orderliness, structure, consistency and the relative comprehensibility of the world. It's not a propery of us but of reality, is it? If causality were broken in many ways, would we have made it thus far?

 

[Maui]

So is causality the foundation and basis of what we call 'logic'? Seeing how certain aspects and experiments of qm appear to lack a cause, it seems appropriate to remind of Bohr's (in)famous quote - "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature". Some scientists disagree and seem to accept that nature has both deterministic and emergent properties, whereas others think in terms of some systems POV(hard to follow, for me at least)

 

[MarcoD]

So is causality the foundation and basis of what we call 'logic'? Seeing how certain aspects and experiments of qm appear to lack a cause, it seems appropriate to remind of Bohr's (in)famous quote - "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature". Some scientists disagree and seem to accept that nature has both deterministic and emergent properties, whereas others think in terms of some systems POV(hard to follow, for me at least)

I really like this question since I have never read a good paper on it. Who should I read? Which experiments of qm lack a cause? I am not very proficient at physics, but so far I haven't seen experiments which don't have a causal interpretation?

My take so far is that I agree with you: Darwinistically, one would assume logic to emerge since it gives a competitive edge. But it stems to reason that it gives a competitive edge since the world, as we interact with it, seems to be causal. I don't think that needs to imply the world fundamentally is causal, at least, I wouldn't know why; then again, I wouldn't really know how causality could emerge from a non-causal world.

 

[Maui]

I really like this question since I have never read a good paper on it. Who should I read? Which experiments of qm lack a cause? I am not very proficient at physics, but so far I haven't seen experiments which don't have a causal interpretation?

Many but most importantly - the measurement problem and the general indeterminancy of qm. Others may include - radioactive decay, the EPR correlations and the impossibility to have local causality between them, etc.

In general, causality took a great hit with the advent of qm(though some may imagine that it's still deterministic but we lack the ability to ascertain the cause). There's a lot of vacuum as to how experiments of qm should be interpreted and the vacuum is full of bogus theories and suppositions that you would hardly believe. All interpretations of qm are very vague as to what they mean and if there are 20 proponents of say BM or MWI, there are usually 20 different opinions as to how it all takes place. It's all somewhat kindergarten-ish and crackpotish, but is tacitly considered 'science' by most(or somewhat scientific) so that everyone is happy in the community and doesn't go crazy(there are theories tailored to suit all tastes).

My take so far is that I agree with you: Darwinistically, one would assume logic to emerge since it gives a competitive edge. But it stems to reason that it gives a competitive edge since the world, as we interact with it, seems to be causal. I don't think that needs to imply the world fundamentally is causal, at least, I wouldn't know why; then again, I wouldn't really know how causality could emerge from a non-causal world.

We lack a basic understanding of what the constituents of reality really are(whatever they are, they don't make sense). That's by far the biggest problem before we can begin to think of going off the deep end and tackling the biggest questions like existence, reality, etc. Hence why the PHD's rarely hang around here, they don't have answers too and probably consider it a waste of time.

I spend a lot of time thinking what causality is, it seems to be a basic fact of reality that the constituents(local or nonlocal fields, etc) interact (maybe there was no other way, or there are 2 trillion universes with different properties, or god, or it all will never make sense to an ape-like creature ot whatever you want to believe in...). For some reason, the basic properties of reality are what they are(sorry this question is bigger than me, maybe someone else will give it a try)

 

[disregardthat]

I elaborated.

EDIT: However, this is off topic. I took issue with your statement the rules of logic are arbitrary in a similar manner to language. And that they lack the need for justification. Common language to formal logic is not a fair comparison.

Its a perfectly fine comparison. And you are completely missing the point. Common language is where logic is found. Logic is part of the structure of (common) language.
https://www.physicsforums.com/showpost.php?p=3621802&postcount=12

And the "inconsistencies" you are pointing out are not inconsistencies at all.

 

[Willowz]

Its a perfectly fine comparison. And you are completely missing the point. Common language is where logic is found. Logic is part of the structure of (common) language.
https://www.physicsforums.com/showpost.php?p=3621802&postcount=12

And the "inconsistencies" you are pointing out are not inconsistencies at all.

Basically what you are saying is that "truth" is a made up concept contingent on the postulates of any formal system. I'm probably misinterpreting you here, but how do you interpret Tarski's undefinability theorem?

 

[disregardthat]

Basically what you are saying is that "truth" is a made up concept contingent on the postulates of any formal system. I'm probably misinterpreting you here, but how do you interpret Tarski's undefinability theorem?

I don't understand how you got that from what I wrote. Where did I say or imply that truth is a made up concept contingent on the postulates of any formal system?

 

[MarcoD]

Its a perfectly fine comparison. And you are completely missing the point. Common language is where logic is found. Logic is part of the structure of (common) language.
https://www.physicsforums.com/showpost.php?p=3621802&postcount=12

And the "inconsistencies" you are pointing out are not inconsistencies at all.

I am not sure language is the root cause of logic. Even animals which don't have logic seem to use basic logic: i.e, see a panther => run away. Isn't that logic?

Then again, I once had a dog which used his head to open doors but never quite grasped the concept of a fully closed door.

 

[Willowz]

I don't understand how you got that from what I wrote. Where did I say or imply that truth is a made up concept contingent on the postulates of any formal system?

It must be my confusion over post 24. I'm still wondering what you mean by it. Is it that language/grammar/and logic are simply things we do (as in tautological) and as such there can be no inconsistencies?

 

[Willowz]

I am not sure language is the root cause of logic. Even animals which don't have logic seem to use basic logic: i.e, see a panther => run away. Isn't that logic?

Then again, I once had a dog which used his head to open doors but never quite grasped the concept of a fully closed door.

A little more confusion. Are you portraying logic in terms of causality?

 

[chiro]

I don't know what you mean by saying that english grammar is inconsistent. Could you give an example?

Have you ever heard of the liars paradox?

 

[MarcoD]

Many but most importantly - the measurement problem and the general indeterminancy of qm. Others may include - radioactive decay, the EPR correlations and the impossibility to have local causality between them, etc.

I never understood EPR but I always got the feeling that it just boils down to solving equations. If x = y + 2 and we measure x, say 7, then 'magically,' we know y, 5. Clueless about the theory, really, I did get somewhere with the bracket notation.

I remember an experiment with entangled particles which gave a 100% correlation between them and an exact 50/50% divide on the 'choice' of the particle to be in a specific state. As a layman, to me, that said that, well, the 100% is predictable if you're solving equations, and the 50/50% distribution would hint that the 'underlying' system should be completely mechanical because, like in decay, a system of dices which makes sure that the choices over time are 50/50% seems improbable.

Ah well, guess I should leave the explanations to you physics guys, and women, of course.

 

[MarcoD]

A little more confusion. Are you portraying logic in terms of causality?

I would think so. The original poster commented on that logic is a byproduct of language, and I wonder whether logic is not a byproduct of a causal understanding of the world.

 

[Willowz]

That would make sense. But, in that case how the heck do we do math?

 

[MarcoD]

That would make sense. But, in that case how the heck do we do math?

God, I personally do believe that math is a side effect of modeling the world linguistically, that language developed as darwinistic means of having an edge over other species, and that formal logic can be used to make the math, or our reasoning, precise. I.e., math is attaching concepts to symbols and manipulating these symbols, which is the basis of the linguistic darwinistic advantage. We advanced from sensing to attaching 'symbols' to what we sense, to uttering and writing down these 'symbols,' to manipulating those 'symbols' orderly which ultimately gave us a means to formulate hypotheses on our world. Each step, not necessarily in that order, increasing our competitive edge over others.

But in that puzzle, there is no reason for me to assume that math -or maybe, the math we developed- is anything else than an imperfect approximation of the world we interact with.

Another thing. People, you, often state we are good at doing logic and math. But honestly, if anything, the world shows that people are plain lousy at logic or math. The vast majority of people make lots of mistakes even employing basic arithmetic, and in daily life almost everyone rather defaults to primary feelings instead of logic.

We are exceptionally bad at manipulating symbols, consequently, doing math. We're just fuzzily moving symbols around, like apes playing with stones.

 

[RegressLess]

Logic has little or nothing to do with language. Animals with less developed brains do not cooperate, although it is logical because it benefits survival. However, intelligent animals such as crows and apes do cooperate.

 

[disregardthat]

Logic has little or nothing to do with language. Animals with less developed brains do not cooperate, although it is logical because it benefits survival. However, intelligent animals such as crows and apes do cooperate.

"Logic has little or nothing to do with language."

"it is logical because it benefits survival."

You have no idea what logic is. Read a definition of logic, and you will see that logic has nothing to do with any of that which you are suggesting.

Logic is valid reasoning. It has everything to do with language.

 

[RegressLess]

Let me correct myself. Langauge has nothing to do with the origin of logic. If anything, language is born from logic. The crow reasons that if he drops a nut on a busy road, cars will break it open for him.

Is it not true that cooperation is logical? Does cooperation not benefit survival? I fail to see how I am so wrong.

 

[Maui]

I would think so. The original poster commented on that logic is a byproduct of language, and I wonder whether logic is not a byproduct of a causal understanding of the world.

I agree. And because we don't(and probably won't?) adequately understand anything about the world, 'logic' is probably just a myth and wishful thinking when applied to all aspects of reality. Our mode of thinking(the way we arrive at conclusions) could be faulty or applicable only to specific scales where causality plays an essential role.

 

[Maui]

Logic is valid reasoning. It has everything to do with language.

So is valid reasoning an innate biological part of our brains or a defining trait of reality(and its general comprehensibility)? If this will help better illustrate my question - is logic out there(dependencies and correlations waiting to be discovered and understood) or inside us?

I wouldn't agree that valid reasoning is part of language but i could be misunderstanding your point.

 

[disregardthat]

So is valid reasoning an innate biological part of our brains or a defining trait of reality(and its general comprehensibility)? If this will help better illustrate my question - is logic out there(dependencies and correlations waiting to be discovered and understood) or inside us?

We must analyze what logical reasoning is. Inductive reasoning is not logical reasoning. Logical reasoning is, in essence, operations on propositions of language. As such they are part of language and does not transcend it.

The crucial point is that it does not make sense to doubt a logical argument. Logic is determined by the correct usage of logical connectives, such as "and", "or", "not", etc...

Logic is simply the way we treat propositions.

I don't mean that, say, inductive reasoning is wrong, but I do mean that it is not logical.

 

[Maui]

We must analyze what logical reasoning is. Inductive reasoning is not logical reasoning. Logical reasoning is, in essence, operations on propositions of language. As such they are part of language and does not transcend it.

No way. Logic is also a part of reality to which you compare to find out if your reasing is faulty or valid. It's reality that decides what reasoning is valid and what is wishful thinking(otherwise we must grant the same status to the Bible as the TOE because they are both expressed in the same language terms).

The crucial point is that it does not make sense to doubt a logical argument. Logic is determined by the correct usage of logical connectives, such as "and", "or", "not", etc...

Logic is simply the way we treat propositions.

I don't mean that, say, inductive reasoning is wrong, but I do mean that it is not logical.

I don't think i have any idea what you mean to say. 2+2=4 is something you can verify against reality, so it's a valid and logical conclusion(you can do the math with apples or stones and there is no "and", "not" or "or" anywhere in it). I think you may be confusing 'logic 'and language and they are not the same thing(or did you mean to say something else?)

 

[apeiron]

I don't mean that, say, inductive reasoning is wrong, but I do mean that it is not logical.

I too have not been able to understand the grounds of your objections. Can you provide references in case you are expressing a particular school of thought here?

It seems now you are constrasting induction with deduction.

But just talking about deduction is too narrow a definition of "logic" to answer the OP, which is about how logic arose in human history - was it more found or invented?

At its broadest, saying things are logical is saying they are orderly and with pattern. The world seems to operate a certain way, and our minds are shaped to appreciate that - either by evolution, or learning, or most likely a combination/refinement of both.

Induction does seem to be the main way that brains naturally learn - generalisation from experience. Bayseian inference.

Deduction does seem to be a new level of thinking that depends on the human ability to handle syntactic structure. And so logic in this sense piggyback's on a capacity for grammar and would be exclusively human.

So there may be no essential dispute here, just a difference of terminology. You want to have a tight definition of logic, and I take a much looser one (because I'm more interested in the general issues rather than the specific applications).

 

[RegressLess]

It's difficult to understand how one can have a logical thought without language since our thoughts are comprised of words, but language had to start somewhere and it is absurd to think it would come from minds incapable of logic. Without the ability to reason, language is pointless. That was the reason I mentioned animals capable of rational thought. They do it without language.

 

[apeiron]

Without the ability to reason, language is pointless. That was the reason I mentioned animals capable of rational thought. They do it without language.

I have a whole bookcase of books that debate just this one issue.

My own view in fact is that what we call reason followed our invention of language. Which is why I just said there is a broad truth in the idea that while animals are capable of induction, only humans employ deductive reasoing.

Though yes, animals are capable of limited reasoning - when placed in the kind of experimental set-up that demands this of them, and so essentially scaffolds their mental response in the same way that language continually scaffolds our own thinking.

And as I say, there is a huge literature that argues this both ways. So regardless of which side you want to argue, there is plenty of source material to call upon.

 

[RegressLess]

when placed in the kind of experimental set-up that demands this of them

Orangutans and chimps have been known to hunt with spears. Crows attract large predators in the direction of prey so that they can get the leftovers. All of these animals have learned the benefit of tribalism. These are all examples of reason in natural environments, not some experimental set-up.

 

[apeiron]

Orangutans and chimps have been known to hunt with spears. Crows attract large predators in the direction of prey so that they can get the leftovers. All of these animals have learned the benefit of tribalism. These are all examples of reason in natural environments, not some experimental set-up.

But is this displaying inductive reasoning or deductive reasoning?

As a Peircean, I would also want to bring in abductive reasoning here - the kind of creative leaps of the imagination which do seem part of our naturally evolved cognition, which means that even animals have more than inductive reasoning, even if they still have less than deductive reasoning.

So yes, I know of the evidence for animals being smart, being co-operative. But that is precisely why it demands great care to account for how humans are actually different.

 

[RegressLess]

But is this displaying inductive reasoning or deductive reasoning?

As a Peircean, I would also want to bring in abductive reasoning here - the kind of creative leaps of the imagination which do seem part of our naturally evolved cognition, which means that even animals have more than inductive reasoning, even if they still have less than deductive reasoning.

So yes, I know of the evidence for animals being smart, being co-operative. But that is precisely why it demands great care to account for how humans are actually different.

I don't know how we could tell by which means they come up with these rational concepts. I'd love to see some research on that. However, I'm fairly convinced that the human ego is the only significant difference between us and the rest of the great apes.

 

[apeiron]

Orangutans and chimps have been known to hunt with spears.

I agree this is a cool fact ...

But also, it is credited to mimicry - so inductive rather than deductive reasoning really. Even if it is still a remarkable thing.

...our long-armed cousins do indeed show a remarkable ability to mimic our behaviour.
This individual had seen locals fishing with spears on the Gohong River.
Although the method required too much skill for him to master, he was later able to improvise by using the pole to catch fish already trapped in the locals' fishing lines

.

http://www.dailymail.co.uk/sciencet...n-attempts-hunt-fish-spear.html#ixzz1f9YUfgDX

 

[RegressLess]

But also, it is credited to mimicry - so inductive rather than deductive reasoning really. Even if it is still a remarkable thing.

Well, you got me there, but what about this: Chimps spearing bush babies

 

[apeiron]

Well, you got me there, but what about this: Chimps spearing bush babies

Again, that is impressive, but inductive. It is a natural extension of an existing behaviour. Poking and smashing are ways to make things happen. Grabbing a rock or a stick are easy habits to learn from experience and observation.

But note that crediting animals with powers of inference is actually something here. For a long time, the null hypothesis championed by the Behaviourists was that learning was purely associative.

So the claim was that animals essentially did random things and accidentally discovered the way to make things happen through reinforcement feedback. The world shaped up their behaviour to look clever. But there was no "leap of insight" - despite what the rival Gestalt school of psychology was arguing at the time, based on its own observations of primate problem solving.

So yes, the modern view is now much more willing to grant animals the ability for sudden insight - to be able to think this kind of thing has worked in the past and could be applied right now to achieve my goal.

Yet then there is the lack of syntax, and consequently a lack of "strong deduction" in animal reasoning. So there are the similarities, but also the critical differences.

A grammar-handling brain is able to do something different. All higher animals could be said to reason, to be in some way logical thinkers. But it comes in flashes of intuition and goal-oriented experimentation. It is not structured and guided by conscious abstractions.

 

[RegressLess]

So the claim was that animals essentially did random things and accidentally discovered the way to make things happen through reinforcement feedback. The world shaped up their behaviour to look clever. But there was no "leap of insight" - despite what the rival Gestalt school of psychology was arguing at the time, based on its own observations of primate problem solving.

Poking and smashing are ways to make things happen. Grabbing a rock or a stick are easy habits to learn from experience and observation.

These two ideas sound similar...

If their minds work in such a different way, how do you explain Koko, the gorilla who speaks with sign language? Sure, it's an extraordinary circumstance, being that she interacts with humans daily, but could the type of mind you ascribe to these "lesser" creatures do that?

 

[apeiron]

These two ideas sound similar...

If their minds work in such a different way, how do you explain Koko, the gorilla who speaks with sign language? Sure, it's an extraordinary circumstance, being that she interacts with humans daily, but could the type of mind you ascribe to these "lesser" creatures do that?

Koko and all similar experiments have demonstrated that animals in fact can't master generative syntax. You have to be prepared to consider here both what they can do, and what they can't.

 

[RegressLess]

No comment on the "these two sound similar" part?