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

[FlexGunship]

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

Consistent and inconsistent.
Flammable and inflammable.

 

[disregardthat]

Flammable and inflammable.

A = NOT A

This simply shows that the in-prefix is not universally considered a logical "not"-operation, as we don't mean "the opposite of flammable" by inflammable as well as "flammable". But I get your point. This isn't what we mean by logical consistency though.

It is important to note too (before we get into more peculiarities) that it is the intended (understood) meaning of the word or sentence that matters. That we can mean different things by the same word in different situations and contexts doesn't imply any inconsistency.

 

[FlexGunship]

This simply shows that the in-prefix is not universally considered a logical "not"-operation, as we don't mean "the opposite of flammable" by inflammable as well as "flammable". But I get your point. This isn't what we mean by logical consistency though.

It is important to note too (before we get into more peculiarities) that it is the intended (understood) meaning of the word or sentence that matters. That we can mean different things by the same word in different situations and contexts doesn't imply any inconsistency.

If you plan to hand-wave each example as "an exception to the rule" I'm not sure what would satisfy your conditions for exceptions to grammatical rules. Here's a different type of example where a well defined prefix is used when the root is no longer part of the language.

Counterpoint and point.
Countermand and ?.

 

[disregardthat]

If you plan to hand-wave each example as "an exception to the rule" I'm not sure what would satisfy your conditions for exceptions to grammatical rules.

This is ridiculous, you are the only one saying it's a rule. No one insists on "inflammable" meaning both "flammable" and "not flammable".

 

[FlexGunship]

This is ridiculous, you are the only one saying it's a rule. No one insists on "inflammable" meaning both "flammable" and "not flammable".

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.

 

[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.