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

[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?

 

[disregardthat]

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

I said that inductive reasoning is not logical reasoning. I can hardly believe anyone would say otherwise. In what sense is: "I have only seen green leaves", hence "leaves are green" a logical argument? It is not, and it is non-sense. It is not a logical argument and a logical conclusion, but a whole new game with different rules and different applications.



Take a logical argument, you will never find any reason to verify it. Rather, the meaning we give propositions confine themselves to logical laws (we force them to), and in such a way logic must be valid reasoning.

 

[Maui]

I said that inductive reasoning is not logical reasoning. I can hardly believe anyone would say otherwise. In what sense is: "I have only seen green leaves", hence "leaves are green" a logical argument? It is not, and it is non-sense. It is not a logical argument and a logical conclusion, but a whole new game with different rules and different applications.



Take a logical argument, you will never find any reason to verify it. Rather, the meaning we give propositions confine themselves to logical laws (we force them to), and in such a way logic must be valid reasoning.

Well yes, as soon as i put on my philosophy shoes your point seems clearer to me. In a certain sense, the base of knowledge is philosophy(recently there was a thread in the General forum about it and nobody is disputing that).

But what i was objecting to was your perceived and implied stance that language and logic were one and the same(maybe i got this part wrong?)

 

[disregardthat]

But what i was objecting to was your perceived and implied stance that language and logic were one and the same(maybe i got this part wrong?)

As I have said before, logic is part of the structure of language, it is the way we treat propositions. Our logic forces the meaning of propositions to confine itself to the laws of logic. As in the example with the man standing in the room; we force the meaning of 'standing in the room' to be mutually exclusive with not standing in the room. The sense we give the propositions: "he is standing in the room" and "he is not standing in the room" must confine itself to this the moment we acknowledge them as propositions, and "not standing in the room" as the logical negation of "standing in the room". There is nothing to verify and nothing to dispute. I have never said logic and language they are one and the same, that doesn't make much sense at all.

 

[Maui]

As I have said before, logic is part of the structure of language, it is the way we treat propositions. Our logic forces the meaning of propositions to confine itself to the laws of logic. As in the example with the man standing in the room; we force the meaning of 'standing in the room' to be mutually exclusive with not standing in the room. The sense we give the propositions: "he is standing in the room" and "he is not standing in the room" must confine itself to this the moment we acknowledge them as propositions, and "not standing in the room" as the logical negation of "standing in the room". There is nothing to verify and nothing to dispute. I have never said logic and language they are one and the same, that doesn't make much sense at all.

Does everyone else but me understand what he is trying to say?

 

[apeiron]

Does everyone else but me understand what he is trying to say?

If I do, it seems too restrictive a view.

Ordinary language is in fact tolerant of ambiguity and fuzziness. Terms are not rigidly defined but are contextual.

So whether a person standing in the threshold of a door is "inside", or "outside", the room is a matter of interpretation, a semantic judgement. Further information is needed to push our judgement towards some stronger conclusion.

This is why people invented things like paraconsistent logic - to try to deal with vague cases like standing in the doorway, where the principle of contradiction does not apply.

Disregardthat is arguing that the Law of the Excluded Middle is emboddied in logical operatives like "not". So by definition, the language of logic is set up to ignore the usual real-life semantic judgements we want to make. And by doing that, it makes itself a purely syntactic device.

But that is a radical refinement of natural language, not the way that natural language actually is.

Natural language is semantics plus syntax. Just as we can say that "natural logic" is broader than simply deductive reasoning, and conventionally includes inductive reasoning.

Deductive reasoning needs to start with generalisations (If all x are y...) and induction is necessary to form those generalisations in the first place.

 

[Maui]

How is this proving that logic is part of the structure of language instead of language being a part of the logic we keep discovering in nature?

My dog knows quite well that when i am not in the room, i can't be in the room(he doesn't keep on sniffing around for me for hours). My dog knows no language, so the example seems out of place - the dog "forces the meaning of 'standing in the room' to be mutually exclusive with not standing in the room".

If logic was simply a part of the structure of language, how would progress be possible or science or space travel? You clearly need language to build a database of knowledge but language is a just a tool for communicating. Nothing more.

 

[disregardthat]

Ordinary language is in fact tolerant of ambiguity and fuzziness. Terms are not rigidly defined but are contextual.

So whether a person standing in the threshold of a door is "inside", or "outside", the room is a matter of interpretation, a semantic judgement. Further information is needed to push our judgement towards some stronger conclusion.

Logic has nothing to do with the definition of terms. That is a matter of interpretation as you say, and depends on context and so on, but as I am trying to point out our interpretation of propositions must confine themselves to the laws of logic. We simply won't accept a interpretation of propositions which does not satisfy our laws of logic. Judgement in general is a far wider concept than logical conclusions, and I don't see the point of insisting on that all (or many) types of judgement must be logical, which your objective seems to be. But the motivation for this seems unclear to me.

Science is not limited to logical deduction (after all, there are no necessities in science), so I don't see your point here Maui. Scientific inquiry is not the same as logical inquiry...

What is essential to logical reasoning, unlike other types of reasoning, is its convincing aspect of necessity. There must surely be a sharp boundary with what we traditionally think of as logical deduction and other types of reasoning. My point is that the necessity of logical conclusions is not accidental nor surprising at all.

 

[Willowz]

Well, if you're going to say that language is logic then you commit yourself to some problems of linguistics.

Further, if we say that math is also a language and therefore included into the area of logic, then you haven't said anything meaningful about logic.

Just that logic is "something we do".

 

[MarcoD]

I personally can follow Apeiron but mostly don't have the foggiest idea what Disregardthat is talking about. Maybe it would help if you would confine your ideas a bit more to smaller subjects?

 

[disregardthat]

Well, if you're going to say that language is logic then you commit yourself to some problems of linguistics.

Where do I say that? You have insisted two times I have, so please, point it out for me.

 

[Willowz]

Where do I say that? You have insisted two times I have, so please, point it out for me.

I might have misunderstood you. I concede, it's not worth arguing over.

 

[pam53146]

logic problem

1. There are necessary truths. For, assuming that there are no necessary truths, there are no necessary connections between premises and conclusions. But there are no valid arguments if there are no necessary connections between premises and conclusions; and there are valid arguments.

N = there are necessary truths
C = there are necessary connections between premises and conclusions
V = there are valid arguments

Can someone please help me get started. I need to put this in argument form and symbolize it.

Thank you,
Pam

 

[Evo]

1. There are necessary truths. For, assuming that there are no necessary truths, there are no necessary connections between premises and conclusions. But there are no valid arguments if there are no necessary connections between premises and conclusions; and there are valid arguments.

N = there are necessary truths
C = there are necessary connections between premises and conclusions
V = there are valid arguments

Can someone please help me get started. I need to put this in argument form and symbolize it.

Thank you,
Pam

You will need to start a Homework Thread in "other sciences" Homework Help. Please be sure to list everything that you have come up with on your own and where you need help.