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

[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.