Do humans have an inherent capacity to decide that a conclusion follows necessarily from premises?

[Speakpigeon]

Yes. But I am just guessing.

And what about actually casting a vote?
EB

 

[Angra Mainyu]

Here are some of the people who can't decide between "Yes", "No", Don't know" and "Doesn't make sense".

Koyaanisqatsi,
prideandfall,
loose cannon,
Bearded One,
abaddon,
couch_sloth,
Keith&Co.,
steve_bank,
J842P,
Tharmas,
Angra Mainyu.

What's wrong with them, do you think?
EB

I had chosen not to reply. I was not taking part in this thread. But you chose to attack. Why?
The reason I chose not to reply was, precisely, the way you mistreat me in our interactions. But you chose to attack me and mistreat me even though I was not taking part in the thread. I would have no interest in discussing the matter with you, regardless of whether I can figure what you meant by "inherent" or as part of human nature, and regardless of whether I can give an answer. The reason I have no interest is that discussing the matter - or, as it seems, nearly any matters - with you is stressful because of how hostile you are towards me, and I have more interesting and happy things to do with my life - and if and when I decide to engage in a stressful exchange (which I do much less often lately due to meatspace commitments), I'd rather go for things with a bigger social impact than discussions about whether we have an inherent capacity in this case.

 

[steve_bank]

EB is taking down names...muast be we are in trouble.

I am not undecided. I gave my view and my reasoning. I did not vote because in te end it is pointless. It is anoter one of EB's threads on logic that goes on forever. No interest in debate.

The basic question is without EB's formal Aristotelian logic how on Earth could humans without articulate language and writing have accomplished anything at all.

 

[Speakpigeon]

Here are some of the people who can't decide between "Yes", "No", Don't know" and "Doesn't make sense".

Koyaanisqatsi,
prideandfall,
loose cannon,
Bearded One,
abaddon,
couch_sloth,
Keith&Co.,
steve_bank,
J842P,
Tharmas,
Angra Mainyu.

What's wrong with them, do you think?
EB

I had chosen not to reply. I was not taking part in this thread. But you chose to attack. Why?
The reason I chose not to reply was, precisely, the way you mistreat me in our interactions. But you chose to attack me and mistreat me even though I was not taking part in the thread. I would have no interest in discussing the matter with you, regardless of whether I can figure what you meant by "inherent" or as part of human nature, and regardless of whether I can give an answer. The reason I have no interest is that discussing the matter - or, as it seems, nearly any matters - with you is stressful because of how hostile you are towards me, and I have more interesting and happy things to do with my life - and if and when I decide to engage in a stressful exchange (which I do much less often lately due to meatspace commitments), I'd rather go for things with a bigger social impact than discussions about whether we have an inherent capacity in this case.

I'm really sorry that it should be at all stressful. If so, I recommend that you not visit my threads.

Maybe I should say that I'm not hostile or agressive at all. I may be a bit robust in my approach but I generally like people, even those I disagree with, even in real "meatspace" life, where, arguably, it's definitely much more stressful. Still, I guess I understand, but there's not much I can do about it, accept to say sorry.

That being said, I don't buy your explanation. This thread is a poll and is therefore not primarily about debating. Voting is of the essence. Debating is optional.

And as for voting, I don't buy that you can't decide between "Yes", "No", Don't know" and "Doesn't make sense". I scratch my head and can't find any other reasonable option that would be missing.

Still, you do as you please, but I would have appreciated you input, if only the vote.

Sorry again that I can't take a different, softer, approach, and I don't believe I'm wrong on this.
EB

 

[Speakpigeon]

I am not undecided. I gave my view and my reasoning. I did not vote because in te end it is pointless. It is anoter one of EB's threads on logic that goes on forever. No interest in debate.

It's a poll, Johnny.

The basic question is without EB's formal Aristotelian logic how on Earth could humans without articulate language and writing have accomplished anything at all.

You're wrong again, on substance, Johnny.

The basic question has been spelled out: Do humans have an inherent capacity to decide that a conclusion follows necessarily from premises?
EB

 

[Angra Mainyu]

If so, I recommend that you not visit my threads.

That would not be a good idea, because then I will not know whether in a thread you will attack either me or other people I would care to defend in this venue.

Maybe I should say that I'm not hostile or agressive at all. I may be a bit robust in my approach but I generally like people, even those I disagree with, even in real "meatspace" life, where, arguably, it's definitely much more stressful. Still, I guess I understand, but there's not much I can do about it, accept to say sorry.

That being said, I don't buy your explanation. This thread is a poll and is therefore not primarily about debating. Voting is of the essence. Debating is optional.

And now you accuse me of lying. The accusation is false, and unwarranted. Voting would be unclear, because first I would need to address what you mean by "inherent", and explain my position depending on how one construes that. Moreover, voting in a public poll would risk a reply from you, what I would have wanted to avoid if I had known it was a public poll (I did not, so as far as I knew, voting would give you no info about my position, but then, since I do not understand the question, there is no proper option).

And as for voting, I don't buy that you can't decide between "Yes", "No", Don't know" and "Doesn't make sense". I scratch my head and can't find any other reasonable option that would be missing.

Another option: I do not understand what you mean by "inherent".
Note that this is not at all the same as 'I do not know'. I might or might not know the answer to the question. I just do not know what the question is (though I can make approximate guesses based on other things you said).
This is also not the same as 'makes no sense'. For all I know, it might.

The part about human nature helps, but is not enough. But I will try once more, under that interpretation:

Please understand "inherent" to signify that it is in our nature. We have two legs because of our nature but some will be missing one or two because of the imponderables of life.

Okay, so according to that, the question is: Is the capacity to tell whether an argument follows from premises part of human nature?
If you mean that, then I do not know. A previous question (under that assumption) is: Is language part of human nature? Is it like having two legs, or a moral sense, or an epistemic sense that allows us to make intuitive probabilistic assessments, acquire beliefs, etc.? (which I would argue do not require language, and are part of human nature). Or is it a technology, like fire? To put it in a different way, a human without legs is malfunctioning considerably. A human (I'm talking about adults) without a moral sense is malfunctioning massively. A human that makes no intuitive probabilistic assessments and/or fails to acquire beliefs is malfunctioning much more massively still, and probably will die very soon. A human without fire may not be malfunctioning. It depends on why she does not have fire. Is a human without language malfunctioning?
I do not know. The jury is out, as far as I know. If the answer is "no" (i.e., not always), then clearly, a human who cannot tell whether a conclusion follows necessarily from premises is also not always malfunctioning. On the other hand, if the answer is "yes", then there are further questions.

Now, one could ask whether a person who has language but fails to have the capacity to tell whether an argument follows from premises without learning, is malfunctioning. That, however, would be the wrong question when it comes to saying whether something is part of human nature (it would make all sorts of highly specialized things part of human nature, given that one can always asked whether someone who has acquired such-and-such expertise fails to do something further).

 

[Speakpigeon]

Please understand "inherent" to signify that it is in our nature. We have two legs because of our nature but some will be missing one or two because of the imponderables of life.

Okay, so according to that, the question is: Is the capacity to tell whether an argument follows from premises part of human nature?
If you mean that, then I do not know.

OK, fair enough, you think you don't know. Take some more time and cast your vote. It's just a poll. Sometimes simple questions receive surprising answers. We all learn from the answers from others.
EB

 

[Angra Mainyu]

Please understand "inherent" to signify that it is in our nature. We have two legs because of our nature but some will be missing one or two because of the imponderables of life.

Okay, so according to that, the question is: Is the capacity to tell whether an argument follows from premises part of human nature?
If you mean that, then I do not know.

OK, fair enough, you think you don't know. Take some more time and cast your vote. It's just a poll. Sometimes simple questions receive surprising answers. We all learn from the answers from others.
EB

Thinking more about it would be of no help, without further input from you regarding the meaning of the question you asked. I already explained what I think my position is, conditioned to the hypothesis that you meant to ask whether it is part of human nature. If that is what you mean, then the answer is clearly that I do not know, because I do not have sufficient information to know whether language (the kind that is relevant here; i.e., that allows people to make arguments with premises) is part of human nature. Consider, for example, a troop of chimpanzees. They do have, in a sense, a language of sorts - they have vocalizations that allow them to communicate to some extent with each other, pass on information, etc. However, they do not have the sort of language that would allow them to make arguments with premises and a conclusion. So, it is not part of chimp nature to have the capacity to decide (or, more precisely, to ascertain) whether a conclusion follows from premises.

Of course, humans are not chimpanzees. Every human community that we are familiar with, has language. Then again, every human community that we are familiar with, has fire. But knowing how to make fire is not a part of human nature. Rather, it is a technology (or rather, many technologies) that was (were) learned many times, and passed on to other generations, etc. There might be a community without fire - an unethical but possible experiment could easily be set up -, without any sort of malfunctioning.

So, the question is:

Q: Could there be a human community without language (of the sort that is relevant here), without any (relevant; i.e., blindness is not relevant) malfunctioning?
If the answer to Q is 'yes', then the capacity to ascertain whether a conclusion follows from premises is not part of human nature.
If the answer to Q is 'no', then the capacity to ascertain whether a conclusion follows from premises might or might not be part of human nature, though I would say it very probably is (with some caveats).

Since I do not know whether the answer to Q is 'yes' or 'no', then I reckon do not know whether the answer to your question is 'yes' or 'no'...as long as my interpretation of your question (based on your statement "Please understand "inherent" to signify that it is in our nature. We have two legs because of our nature but some will be missing one or two because of the imponderables of life." and its context) is correct.

On the other hand, if my interpretation of your question is not correct, then I do not understand your question, so I do not know whether I know the answer. Moreover, in that case, thinking more about that will not help, since I do not have any further input from you. For that reason, I would ask you:

1. Is my interpretation of your question correct? Equivalently, is your question whether the capacity to ascertain whether a conclusion follows from premises, part of human nature? If so, please let me know, so that I vote "I do not know".
2. If your answer to 1. above is 'no', then if you want further input from me regarding your question, I will need further input from you regarding what you mean by that question.

 

[steve_bank]

OK, fair enough, you think you don't know. Take some more time and cast your vote. It's just a poll. Sometimes simple questions receive surprising answers. We all learn from the answers from others.
EB

Thinking more about it would be of no help, without further input from you regarding the meaning of the question you asked. I already explained what I think my position is, conditioned to the hypothesis that you meant to ask whether it is part of human nature. If that is what you mean, then the answer is clearly that I do not know, because I do not have sufficient information to know whether language (the kind that is relevant here; i.e., that allows people to make arguments with premises) is part of human nature. Consider, for example, a troop of chimpanzees. They do have, in a sense, a language of sorts - they have vocalizations that allow them to communicate to some extent with each other, pass on information, etc. However, they do not have the sort of language that would allow them to make arguments with premises and a conclusion. So, it is not part of chimp nature to have the capacity to decide (or, more precisely, to ascertain) whether a conclusion follows from premises.

Of course, humans are not chimpanzees. Every human community that we are familiar with, has language. Then again, every human community that we are familiar with, has fire. But knowing how to make fire is not a part of human nature. Rather, it is a technology (or rather, many technologies) that was (were) learned many times, and passed on to other generations, etc. There might be a community without fire - an unethical but possible experiment could easily be set up -, without any sort of malfunctioning.

So, the question is:

Q: Could there be a human community without language (of the sort that is relevant here), without any (relevant; i.e., blindness is not relevant) malfunctioning?
If the answer to Q is 'yes', then the capacity to ascertain whether a conclusion follows from premises is not part of human nature.
If the answer to Q is 'no', then the capacity to ascertain whether a conclusion follows from premises might or might not be part of human nature, though I would say it very probably is (with some caveats).

Since I do not know whether the answer to Q is 'yes' or 'no', then I reckon do not know whether the answer to your question is 'yes' or 'no'...as long as my interpretation of your question (based on your statement "Please understand "inherent" to signify that it is in our nature. We have two legs because of our nature but some will be missing one or two because of the imponderables of life." and its context) is correct.

On the other hand, if my interpretation of your question is not correct, then I do not understand your question, so I do not know whether I know the answer. Moreover, in that case, thinking more about that will not help, since I do not have any further input from you. For that reason, I would ask you:

1. Is my interpretation of your question correct? Equivalently, is your question whether the capacity to ascertain whether a conclusion follows from premises, part of human nature? If so, please let me know, so that I vote "I do not know".
2. If your answer to 1. above is 'no', then if you want further input from me regarding your question, I will need further input from you regarding what you mean by that question.

Humans learned to control fir long before Aristotle or any system of logic.

 

[Speakpigeon]

For that reason, I would ask you:

1. Is my interpretation of your question correct? Equivalently, is your question whether the capacity to ascertain whether a conclusion follows from premises, part of human nature? If so, please let me know, so that I vote "I do not know".

Yes, by "inherent" here I meant that the capacity is understood to be part of human nature.
EB

 

[Speakpigeon]

Humans learned to control fir long before Aristotle or any system of logic.

And animals. Ants and bees. All sorts.
EB

 

[Angra Mainyu]

For that reason, I would ask you:

1. Is my interpretation of your question correct? Equivalently, is your question whether the capacity to ascertain whether a conclusion follows from premises, part of human nature? If so, please let me know, so that I vote "I do not know".

Yes, by "inherent" here I meant that the capacity is understood to be part of human nature.
EB

Alright. Then, for the reasons I have already stated, my answer is "I do not know". I doubt that anyone does, by the way (also, for the previously mentioned reasons).

 

[Angra Mainyu]

This is the first of a series of polls concerning logic. The overall idea is to determined whether we share a common notion of the logic of valid reasoning as done by humans.

But that is not the same as the question of whether the capacity is part of human nature.
For example, it is apparent that human nature restricts the sorts of grammars that can arise in natural languages (i.e., languages that are formed as communication means, and informally, as opposed to formal languages). It might be that logic in natural languages is even more restricted, either to a few, or even to only one single logic. The capacity to tell whether a conclusion follows from premises would still not be a part of human nature as long as language isn't, since (if language isn't) there could be a human community that has no language (of the relevant sort; see my previous post on the matter), so they would not have the capacity to tell whether a conclusion follows from premises (indeed, they would not even understand the idea of a premise), but that does not mean that there isn't a single object of study.

While I do not know whether language (and thus, the capacity you mention) is part of human nature (and I think probably neither do you or anyone else; there is insufficient information about human psychology as far as I can tell), I think there is a high probability that there is a single human logic for naturally arising languages, and if there is not a single one, there are a few and their common points can still be studied. If there is one, I think that classical mathematical logic does capture it (at least, better than Aristotle's logic), but that is a matter for one of the other threads, so I will leave it for later.

 

[Angra Mainyu]

This view isn't a foregone conclusion. The practice of Mathematical logic today suggests on the contrary that logic is arbitrary. Mathematical logic itself is a branch of mathematics, not a method or a theory of logic. As a branch of mathematics, it brings together a very large number of theories and methods (calculus) which are all different from each other and in effect mutually contradictory.

Could you give an example of those contradictions?

This in turns falsifies the idea that mathematicians all talk about the same thing when they use the word "logic", and this makes it impossible to decide whether anyone of these theories or methods is really about the logic of valid arguments as used by humans and as first described by Aristotle.

You would have to consider how the word 'logic' is used in each context, and then analyze the logics in question.

It is even unclear at the moment whether any mathematical logic is meant to describe the logic of valid arguments.

Some are (in some contexts), some aren't. For example, when some mathematicians argue in support of intuitionistic logic and argue against ¬¬P->P, whereas others disagree and argue for classical mathematical logic (which accepts ¬¬P->P), then you have a disagreement about the correct logic. By the way, both accept P&¬P->Q for any Q, so you disagree with both of them. But that is a disagreement. There are also philosophers and mathematicians who support other logics. Perhaps, you would like relevance logic

On the other hand, a mathematician might choose to restrict their work to only finitistic arguments because that sort of proof might be useful for some applications, but they're not claiming infinite arguments are not part of human logic. So, it depends on the case. One should take a careful look at what people are saying if one wants to understand them.

 

[Speakpigeon]

This view isn't a foregone conclusion. The practice of Mathematical logic today suggests on the contrary that logic is arbitrary. Mathematical logic itself is a branch of mathematics, not a method or a theory of logic. As a branch of mathematics, it brings together a very large number of theories and methods (calculus) which are all different from each other and in effect mutually contradictory.

Could you give an example of those contradictions?

Sure. For example, "when some mathematicians argue in support of intuitionistic logic and argue against ¬¬P->P, whereas others disagree and argue for classical mathematical logic (which accepts ¬¬P->P), then you have a disagreement about the correct logic" (Angra Mainyu, 05-31-2019, 04:07 AM).

You would have to consider how the word 'logic' is used in each context, and then analyze the logics in question.

Why should I do that. My point is that mathematicians either don't use the word "logic" to mean logic or they do but they are wrong.

It is even unclear at the moment whether any mathematical logic is meant to describe the logic of valid arguments.

Some are (in some contexts), some aren't. For example, when some mathematicians argue in support of intuitionistic logic and argue against ¬¬P->P, whereas others disagree and argue for classical mathematical logic (which accepts ¬¬P->P), then you have a disagreement about the correct logic. By the way, both accept P&¬P->Q for any Q, so you disagree with both of them. But that is a disagreement. There are also philosophers and mathematicians who support other logics. Perhaps, you would like relevance logic

On the other hand, a mathematician might choose to restrict their work to only finitistic arguments because that sort of proof might be useful for some applications, but they're not claiming infinite arguments are not part of human logic. So, it depends on the case. One should take a careful look at what people are saying if one wants to understand them.

I don't want or need to understand them. The topic of this thread is whether you think humans have an inherent capacity to decide that a conclusion follows necessarily from premises. Follows necessarily from premises. I am in no doubt that this is the case, and that it is pretty obvious, too.

I also think that this is the view shared by most people outside mathematical logic (and possibly outside computer sciences). And this poll seems to confirm.

Mathematical logic has made itself irrelevant here since contrary to what it says, the conjunction "It's true Jack is blue and it's false Jack is blue" doesn't imply anything since nothing follows necessarily from it.
EB

 

[Angra Mainyu]

Sure. For example, "when some mathematicians argue in support of intuitionistic logic and argue against ¬¬P->P, whereas others disagree and argue for classical mathematical logic (which accepts ¬¬P->P), then you have a disagreement about the correct logic" (Angra Mainyu, 05-31-2019, 04:07 AM).

That is not a contradiction between different areas of math. That is a philosophical disagreement between mathematicians. It is not the same. Moreover, those who argue against ¬¬P->P do not argue that it is false. They argue that it is not proper to use it, for philosophical reasons. Depending on the person, they might say it's neither true nor false.

Still, now that I see what you have in mind when you say that " The practice of Mathematical logic today suggests on the contrary that logic is arbitrary. Mathematical logic itself is a branch of mathematics, not a method or a theory of logic. As a branch of mathematics, it brings together a very large number of theories and methods (calculus) which are all different from each other and in effect mutually contradictory.", I would say that philosophical disagreement and debate about what the correct logic is is more common among philosophers than it is among mathematicians. Would you agree also that the practice of philosophy today suggests that logic is arbitrary?

Why should I do that. My point is that mathematicians either don't use the word "logic" to mean logic or they do but they are wrong.

You should do that because you said " this makes it impossible to decide whether anyone of these theories or methods is really about the logic of valid arguments as used by humans and as first described by Aristotle.", but it does not make it impossible. Even if the word "logic" is used in more than one sense, it is possible to listen to what people say, in order to ascertain what sense that is, etc. There is no impossibility to decide (or, more precisely, ascertain) whether any of those theories or methods is about the logic of valid arguments, in general. It depends on the available information.

By the way, when mathematicians do debate about the correct logic (e.g., intuitionists vs. classical logic mathematicians), then that is about the logic of valid arguments. But it's not about the logic as applied in languages such as English, French or Spanish, but about as logic applied to mathematical language. Mathematical language is much more restrictive than colloquial languages (to give them a name), and not all usages of the words and connectives in colloquial language are in use in mathematics. As a result, the correct logic for mathematics may well be (and I think it is) a proper part of the full correct logic for colloquial languages. This is not to say that it's in any way in conflict with it, but rather, that it is a part of it - not all.

To give you an example, there is a use of the conditional in colloquial languages that involves causality, and which cannot be properly modeled by truth-tables, whereas there is also a use that is like that of math, and is properly modeled by truth tables. In mathematical language, I would say that the former use is not present. Of course, trying to apply truth-tables to the causal use of the conditional will give the wrong results, but that is not a problem with truth-tables in mathematics.

I don't want or need to understand them.

That is a difficulty, because you are raising disparaging accusations against "them", in the context of your argumentation.

The topic of this thread is whether you think humans have an inherent capacity to decide that a conclusion follows necessarily from premises.

That is the thread title. However, I have only addressed points you made about mathematicians and their use of the words.

Follows necessarily from premises. I am in no doubt that this is the case, and that it is pretty obvious, too.

I already addressed that point. I do not believe you know that. I understand "inherent capacity" as a question about human nature, because you explained that that is what you meant. On the basis of that, I say that I do not have sufficient information to tell whether humans have such inherent capacity. Very probably, no one has sufficient information.

I also think that this is the view shared by most people outside mathematical logic (and possibly outside computer sciences). And this poll seems to confirm.

It would be unwarranted, though. We do not know whether there can be a human society without language. Is language like, say, morality? (so, the anwswer is negative). Or is it a technology, like fire? (so, it is positive).
I gave more details in my reply here.
Still, you are not asking the right question (see here).

Mathematical logic has made itself irrelevant here since contrary to what it says, the conjunction "It's true Jack is blue and it's false Jack is blue" doesn't imply anything since nothing follows necessarily from it.

If you were right about the lack of implication, mathematical logic would not be irrelevant. It would fail to capture human logic in that particular case (though it was meant to capture logic as used in math, but anyway). But it would still remain a (much) better tool for finding mathematical truths than Aristotelian logic (see my post in the other thread), or (if human logic truly lacks the Principle of Explosion) than human logic.

 

[Speakpigeon]

Sure. For example, "when some mathematicians argue in support of intuitionistic logic and argue against ¬¬P->P, whereas others disagree and argue for classical mathematical logic (which accepts ¬¬P->P), then you have a disagreement about the correct logic" (Angra Mainyu, 05-31-2019, 04:07 AM).

That is not a contradiction between different areas of math. That is a philosophical disagreement between mathematicians. It is not the same. Moreover, those who argue against ¬¬P->P do not argue that it is false. They argue that it is not proper to use it, for philosophical reasons. Depending on the person, they might say it's neither true nor false.

Still, now that I see what you have in mind when you say that " The practice of Mathematical logic today suggests on the contrary that logic is arbitrary. Mathematical logic itself is a branch of mathematics, not a method or a theory of logic. As a branch of mathematics, it brings together a very large number of theories and methods (calculus) which are all different from each other and in effect mutually contradictory.", I would say that philosophical disagreement and debate about what the correct logic is is more common among philosophers than it is among mathematicians. Would you agree also that the practice of philosophy today suggests that logic is arbitrary?

By contradiction, I mean just that. One theory will say something is true, the other will say something is false.

Intuitionistic logic
Intuitionistic logic can be understood as a weakening of classical logic, meaning that it is more conservative in what it allows a reasoner to infer, while not permitting any new inferences that could not be made under classical logic. Each theorem of intuitionistic logic is a theorem in classical logic, but not conversely. Many tautologies in classical logic are not theorems in intuitionistic logic (...)
https://en.wikipedia.org/wiki/Intuitionistic_logic

So here, Wiki says intuitionistic logic will say formula A is not a valid inference whereas classical logic will say formula A is a valid inference. Contradiction.
EB

 

[Speakpigeon]

By the way, when mathematicians do debate about the correct logic (e.g., intuitionists vs. classical logic mathematicians), then that is about the logic of valid arguments.

How could they decide which logic is correct?! I have asked you for a justification that the definition of validity used in mathematical logic was correct, to no avail. There is no such justification. So, they may have arguments about which is correct, but none of them can support their respective claim.

But it's not about the logic as applied in languages such as English, French or Spanish, but about as logic applied to mathematical language. Mathematical language is much more restrictive than colloquial languages (to give them a name), and not all usages of the words and connectives in colloquial language are in use in mathematics.

There is just one deductive logic. We all use the same. Whether in our linguistic utterances, our thoughts, in writing, colloquial or formal. What is not deductive logic is mathematical logic. What is funny is that mathematicians use deductive logic like everybody else and somewhat with more rigour, yet they keep up the fiction that mathematical logic is "correct". It's not. They know it's not but they keep pretending. One is reminded of the tremendous capability of human beings for dissembling. That's toeing the party line and nothing else.

As a result, the correct logic for mathematics may well be (and I think it is) a proper part of the full correct logic for colloquial languages. This is not to say that it's in any way in conflict with it, but rather, that it is a part of it - not all.

No it's not. Human logic and mathematical logic are mutually contradictory.

To give you an example, there is a use of the conditional in colloquial languages that involves causality, and which cannot be properly modeled by truth-tables, whereas there is also a use that is like that of math, and is properly modeled by truth tables. In mathematical language, I would say that the former use is not present. Of course, trying to apply truth-tables to the causal use of the conditional will give the wrong results, but that is not a problem with truth-tables in mathematics.

Causality, if it exists at all, is a fixture of natural world. As such, there can't be any logical problem with causality.
EB

 

[Speakpigeon]

I also think that this is the view shared by most people outside mathematical logic (and possibly outside computer sciences). And this poll seems to confirm.

It would be unwarranted, though. We do not know whether there can be a human society without language. Is language like, say, morality? (so, the anwswer is negative). Or is it a technology, like fire? (so, it is positive).
I gave more details in my reply here.
Still, you are not asking the right question (see here).

Your point is irrelevant. Logic does not depend on any formal system and does not depend on language. You are confusing the communicating of the message with the meaning conveyed. Logic is what makes us say what we say when we speak logically but 99.999% of the time we don't even verbalise the logical inferences we make. Indeed, we are not even aware we are making them because, essentially, they remain unconscious. Aristotle pointed at logic, and like most people you're still looking at his finger.

Mathematical logic has made itself irrelevant here since contrary to what it says, the conjunction "It's true Jack is blue and it's false Jack is blue" doesn't imply anything since nothing follows necessarily from it.

If you were right about the lack of implication, mathematical logic would not be irrelevant. It would fail to capture human logic in that particular case (though it was meant to capture logic as used in math, but anyway). But it would still remain a (much) better tool for finding mathematical truths than Aristotelian logic (see my post in the other thread), or (if human logic truly lacks the Principle of Explosion) than human logic.

Mathematical theorems are understood by mathematicians using their intuition mostly. Proofs are sketchy indications of the validity of the theorem meant for other mathematicians. They understand each other mostly without using formal logic. Mathematical logic is irrelevant except probably in the few cases where it is misleading.
EB

 

[Angra Mainyu]

By contradiction, I mean just that. One theory will say something is true, the other will say something is false.

However, that is not what happens between mathematical theories. It is what happens between philosophical theories about mathematics. Some philosophers and some mathematicians adhere to some of those theories; others, adhere to other such theories.

In any case, if you think that this suggests logic is arbitrary, it seems it's not so much the practice of mathematical logic today (no contradiction there), but the philosophical practices of some mathematicians and some philosophers. However, by the same disagreement criterion, we could say the practice of, say, physics today suggest that physics is arbitrary; the practice of ethical philosophy or ethical debates today suggests ethics is arbitrary, and so on. I think it's an extremely weak case.

So here, Wiki says intuitionistic logic will say formula A is not a valid inference whereas classical logic will say formula A is a valid inference. Contradiction.

Hold on. There are different ways in which mathematicians use intuitionistic logic. When they are doing mathematics, they use it to infer things from premises. Now, when they're doing that, they are making no claims whatsoever about whether all classical inferences are valid. They might be using intuitionistic logic because they think that some classical inferences are not valid but all intuitionistic inferences are. Or they may have no objection to the validity of classical inferences, but instead they use intuitionistic logic because the sort of constructive proof they're much more likely to get is also useful for some purposes they may have, whereas classical proofs would not give them the practical tools they need in that particular case. Or they might have a different motivation. But regardless of their motivation, they're not saying (even if they believe it) anything about the validity of classical inferences.
Now, when some mathematicians and/or philosophers claim and/or argue that some classical inferences are not valid, they are engaging in philosophical argumentation. Nothing wrong with that of course, but it's something else. Similarly, for that matter, different physicists and philosophers propose competing (and mutually incompatible) theories of, say, the laws of nature, or even about time or space (sometimes, the disagreement is scientific; sometimes, it seems it's philosophic, and sometimes, it's a mixture). Different philosophers (and posters on the internet) defend competing (and mutually incompatible) metaethical theories, or first-order ethical theories, or epistemic theories, etc.

My point is that what you describe as "contradictions" are just examples of philosophical disagreement. It's not a particular feature of mathematics, but it's all over the place - and it was so in the time of Aristotle as well, even if the matters about which there was disagreement were not the same as they are in the present.