How a wrong logic could affect mathematics?

[Angra Mainyu]

I already told you I understand your argument. Your logic is not faulty here. It's your assumptions. As I already told you. And all of the argument mathematicians use to support the validity of their method of logic, those I've been able to find anyway, are similarly based on faulty assumptions. Good logic, though. Ain't it ironic? A good logic to infer a wrong logic? Yeah, can happen. Mathematicians did it.
EB

No. Let me establish once again, beyond any reasonable doubt (also again), that some of your key claims are false. I will further show that your logic is faulty, and that you have failed to understand some of my main arguments (of course, given our exchange in this and other threads, I predict you will fail to understand that you are in error).
First, our premises.

I think all statements are either true or false.

Alright, let us go with that hypothesis. In particular, then, all mathematical statements are either true or false.

Let us now consider another one:
https://talkfreethought.org/showthr...gical-validity&p=668145&viewfull=1#post668145

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:

Validity
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
Internet Encyclopedia of Philosophy - https://www.iep.utm.edu/val-snd/

Thanks for your answers.
EB

Alright, so a deductive argument is CML-valid (i.e., valid according to classical mathematical logic, CML for short) if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.

So, let us go with that. Are you following so far?
I have granted for the sake of the argument one of your beliefs (namely, that all statements are either true or false), and adopted your definition of validity according to CML. So far, so good, right?


Let us now consider another one of your claims:

No. Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic.

That is false. However, let us assume for the sake of the argument that that is true. Each implication I that is valid according to Aristotelian logic and not valid according to mathematical logic, does not take a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false (by definition of CML-validity). Hence, its form is such that it is possible for the premises to be true and the conclusion nevertheless to be false . Hence, Aristotelian logic fails to be truth-preserving, so obviously CML is a far better tool for finding mathematical truth. Aristotelian logic is a disaster (not in reality, though; your claim that " Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic." is simply false.

Let us now consider more of your claims:

Now, an interesting point is that under CML, an argument is valid if it is impossible for the premises to be true but the conclusion to be false. So, as long as the premises are true, CML guarantees that so is the conclusion. Given this and the above, it turns out that one consequence of having the wrong logic is that mathematicians are able to find many truths that they would never be able to find if they had the correct logic.

What you call truths here are in fact invalid conclusions. I'm not sure there's anything interesting in doing that.

Also, you say

Truths that are not truths

You have denied that CML-valid arguments always lead from true premises to true conclusions. You are mistaken, obviously, for the following reason: Suppose a CML-valid argument has true premises P1,..,Pn, and conclusion C. Now, by assumption, C is either true, or it is false. However, since the argument is CML-valid, by definition it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Therefore, given that the premises are true, so is the conclusion.

That debunks two of your key claims. But there is more, of course. In this thread, I have given a thorough conclusive (i.e., beyond a reasonable doubt) debunking of much of your position. You may fail to see that, but here you do not only have wrong premises: your logic is also faulty. For example, your premise that "Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic." is false. But your logic is faulty, because you fail to ascertain that that premise, together with the definition of CML-validity you accept, has the devastating consequence that Aristotelian logic is not truth-preserving. And you fail to reach that conclusion even after I have shown this to be so beyond a reasonable doubt, and repeatedly.

So, no, it is not the case that you understand my arguments. You fail to follow some of my main lines of argumentation, because your logic is faulty.

 

[Speakpigeon]

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:

Validity
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
Internet Encyclopedia of Philosophy - https://www.iep.utm.edu/val-snd/

Thanks for your answers.
EB

Alright, so a deductive argument is CML-valid (i.e., valid according to classical mathematical logic, CML for short) if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.

So, let us go with that. Are you following so far?
I have granted for the sake of the argument one of your beliefs (namely, that all statements are either true or false), and adopted your definition of validity according to CML. So far, so good, right?


Let us now consider another one of your claims:

No. Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic.

That is false.

You are talking from ignorance.

However, let us assume for the sake of the argument that that is true. Each implication I that is valid according to Aristotelian logic and not valid according to mathematical logic, does not take a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false (by definition of CML-validity). Hence, its form is such that it is possible for the premises to be true and the conclusion nevertheless to be false . Hence, Aristotelian logic fails to be truth-preserving, so obviously CML is a far better tool for finding mathematical truth. Aristotelian logic is a disaster (not in reality, though; your claim that " Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic." is simply false.

No, again, you didn't understand what I said...

Some implications are valid in Aristotelian logic and invalid in mathematical logic because, assuming the premises true, Aristotelian logic proves the conclusion follows necessarily from the premises while mathematical logic proves the conclusion false.

So, it is mathematical logic which is not truth preserving, for some, infinitely many, implications.

And, conversely, for some (infinitely many) implications, mathematical logic finds the implication valid when it is not according to Aristotelian logic.


In effect, mathematical logic is toy logic. It's at best a first order approximation and this shows mathematicians don't understand logic. They rely on it, like we all do, including for proving theorems, yet they ended up inventing a formal model of it which is at best a miserable approximation of the real thing. The properties of their formal methods are correctly deduced from their axioms but it is their assumptions which are wrong. Hence the wrong conclusion.

Wrong assumptions are notoriously difficult to spot and reconsider because they're not explicit. You don't even realise you have them. I've seen one philosopher eloquently explain how to resolve a contradiction by reconsidering your assumptions and then fail to do what he had just explained. And mathematicians are all too human after all.
EB

 

[Speakpigeon]

Let us now consider more of your claims:

Now, an interesting point is that under CML, an argument is valid if it is impossible for the premises to be true but the conclusion to be false. So, as long as the premises are true, CML guarantees that so is the conclusion. Given this and the above, it turns out that one consequence of having the wrong logic is that mathematicians are able to find many truths that they would never be able to find if they had the correct logic.

What you call truths here are in fact invalid conclusions. I'm not sure there's anything interesting in doing that.

Also, you say

Truths that are not truths

You have denied that CML-valid arguments always lead from true premises to true conclusions. You are mistaken, obviously, for the following reason: Suppose a CML-valid argument has true premises P1,..,Pn, and conclusion C. Now, by assumption, C is either true, or it is false. However, since the argument is CML-valid, by definition it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Therefore, given that the premises are true, so is the conclusion.

No. You have on the one hand the definition (CML) and on the other the fact that the form may make it impossible for the premises to be true and the conclusion nevertheless to be false.

That's two different things but you seem to be unaware these are two different things.

The definition is what it is but it won't by itself make any implication valid. It is the method of logic used which, given the premises, decides whether the conclusion is true or false. In mathematical logic, the method is essentially truth tables. So truth tables may give the result required by the definition, and no wonder, the definition was cut to fit the truth table of the material implication, but that doesn't make the result true.

And, as it happens, for a range of implications, truth tables give the wrong result, sometimes "true" when it should be "false", sometimes "false" when it should be "true".

By the way, there is no argument to be had on that. I'm sure you can refuse to believe what I say, but it is futile to try and prove what I say is false. Methods of logic are artificial creations. Logic itself is a natural phenomenon. You're not going to prove logic wrong using any method of logic. Rather, you have to develop your method of logic to make sure it fits the facts of logic. Nobody has done that.

Mathematicians took a short cut. They don't have the right frame of mind and it was early days when they settled on one idiotic method. And then mathematicians all over the world learn the same idiotic method each new generation after after each generation and think it's the genuine article, because, hey, there's a proof. And it's impossible to even have a sensible conversation because they're not aware of the wrong assumptions they make.

Mathematicians already went through a difficult period around 1900 but they are going to go through another difficult period when someone exhibits the genuine article. Well, if ever.
EB

 

[Angra Mainyu]

Alright, so a deductive argument is CML-valid (i.e., valid according to classical mathematical logic, CML for short) if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.

So, let us go with that. Are you following so far?
I have granted for the sake of the argument one of your beliefs (namely, that all statements are either true or false), and adopted your definition of validity according to CML. So far, so good, right?


Let us now consider another one of your claims:

No. Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic.

That is false.

You are talking from ignorance.

However, let us assume for the sake of the argument that that is true. Each implication I that is valid according to Aristotelian logic and not valid according to mathematical logic, does not take a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false (by definition of CML-validity). Hence, its form is such that it is possible for the premises to be true and the conclusion nevertheless to be false . Hence, Aristotelian logic fails to be truth-preserving, so obviously CML is a far better tool for finding mathematical truth. Aristotelian logic is a disaster (not in reality, though; your claim that " Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic." is simply false.

No, again, you didn't understand what I said...

Some implications are valid in Aristotelian logic and invalid in mathematical logic because, assuming the premises true, Aristotelian logic proves the conclusion follows necessarily from the premises while mathematical logic proves the conclusion false.

That is impossible. By definition, in mathematical logic, it is not possible for the conclusion to be false and the premises be true. That's the definition you provided in the other thread.

 

[Angra Mainyu]

Let us now consider more of your claims:

Also, you say

Truths that are not truths

You have denied that CML-valid arguments always lead from true premises to true conclusions. You are mistaken, obviously, for the following reason: Suppose a CML-valid argument has true premises P1,..,Pn, and conclusion C. Now, by assumption, C is either true, or it is false. However, since the argument is CML-valid, by definition it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Therefore, given that the premises are true, so is the conclusion.

No. You have on the one hand the definition (CML) and on the other the fact that the form may make it impossible for the premises to be true and the conclusion nevertheless to be false.

That's two different things but you seem to be unaware these are two different things.

The definition is what it is but it won't by itself make any implication valid. It is the method of logic used which, given the premises, decides whether the conclusion is true or false. In mathematical logic, the method is essentially truth tables. So truth tables may give the result required by the definition, and no wonder, the definition was cut to fit the truth table of the material implication, but that doesn't make the result true.

And, as it happens, for a range of implications, truth tables give the wrong result, sometimes "true" when it should be "false", sometimes "false" when it should be "true".

By the way, there is no argument to be had on that. I'm sure you can refuse to believe what I say, but it is futile to try and prove what I say is false. Methods of logic are artificial creations. Logic itself is a natural phenomenon. You're not going to prove logic wrong using any method of logic. Rather, you have to develop your method of logic to make sure it fits the facts of logic. Nobody has done that.

Mathematicians took a short cut. They don't have the right frame of mind and it was early days when they settled on one idiotic method. And then mathematicians all over the world learn the same idiotic method each new generation after after each generation and think it's the genuine article, because, hey, there's a proof. And it's impossible to even have a sensible conversation because they're not aware of the wrong assumptions they make.

Mathematicians already went through a difficult period around 1900 but they are going to go through another difficult period when someone exhibits the genuine article. Well, if ever.
EB

Now you are equivocating. The definition of validity in mathematical logic was provided by you in the other thread. You were against that definition. Under that definition, clearly everything that follows from true premises is not false, so it is true (under your hypothesis that every statement is either true or false). Thus, mathematical logic is truth-preserving. And it is stronger of course than Aristotelian logic, since there are implications that are CML-valid, but not Aristotelian-valid.

If you think the problem is truth-tables, then the problem would not be with the concept of validity (as per the other thread), but rather, truth tables would fail to be in accordance to the concept of validity in question. But let us distinguish two different ideas of validity, to address this new issue you raise. By "CML-valid" I mean "valid in accordance to the definition of validity you provided in the other thread", and by "TT-valid" I mean "valid according to truth-tables". Show me a single example of a mathematical proof that is TT-valid but not CML-valid (of course, you cannot find any, because there aren't any).

 

[Speakpigeon]

Now you are equivocating. The definition of validity in mathematical logic was provided by you in the other thread. You were against that definition. Under that definition, clearly everything that follows from true premises is not false, so it is true (under your hypothesis that every statement is either true or false). Thus, mathematical logic is truth-preserving. And it is stronger of course than Aristotelian logic, since there are implications that are CML-valid, but not Aristotelian-valid.

???

You're not making sense. Let me repeat: Some implications are valid in Aristotelian logic and invalid in mathematical logic because, assuming the premises true, Aristotelian logic proves the conclusion follows necessarily from the premises while mathematical logic proves the conclusion false.

If you think the problem is truth-tables, then the problem would not be with the concept of validity (as per the other thread), but rather, truth tables would fail to be in accordance to the concept of validity in question. But let us distinguish two different ideas of validity, to address this new issue you raise. By "CML-valid" I mean "valid in accordance to the definition of validity you provided in the other thread", and by "TT-valid" I mean "valid according to truth-tables". Show me a single example of a mathematical proof that is TT-valid but not CML-valid (of course, you cannot find any, because there aren't any).

Sure, and I already pointed out why:

So truth tables may give the result required by the definition, and no wonder, the definition was cut to fit the truth table of the material implication, but that doesn't make the result true.

I think you've run out of things to say. It all comes down to what you ignore and that you claim is false without evidence. I suspect most of mathematics is safe from wrong mathematical logic merely because mostly mathematicians don't use formal logic and instead rely on their own logical intuition, much as Euclid had. In other words, they are voting with their feet and using Aristotelian logic, by choice or accident. The question remains of whether there is any important mathematical results based on mathematical logic. I haven't taken the time to look at that yet, but prime candidates may be Gödel's and Tarski's theorems, but I'm not even clear that those really matter. I guess I'll have to find out by myself.
EB

 

[Angra Mainyu]

???

You're not making sense. Let me repeat: Some implications are valid in Aristotelian logic and invalid in mathematical logic because, assuming the premises true, Aristotelian logic proves the conclusion follows necessarily from the premises while mathematical logic proves the conclusion false.

I am making sense. The fact that you fail to follow does not change that. I already pointed out that the point you repeat is false. Moreover, I showed that if it were true, Aristotelian logic would fail to be truth-preserving.
But you are changing the subject because now you bring up truth-tables, whereas when we discuss CML-validity, we are talking about the definition you provided in the other thread. Let me remind you:


https://talkfreethought.org/showthr...gical-validity&p=668145&viewfull=1#post668145

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:

Validity
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
Internet Encyclopedia of Philosophy - https://www.iep.utm.edu/val-snd/

Thanks for your answers.
EB

Let me repeat:

Let me repeat: Some implications are valid in Aristotelian logic and invalid in mathematical logic because, assuming the premises true, Aristotelian logic proves the conclusion follows necessarily from the premises while mathematical logic proves the conclusion false.

What you repeat is false.

However, let us assume for the sake of the argument that that is true. Each implication I that is valid according to Aristotelian logic and not valid according to mathematical logic, does not take a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false (by definition of CML-validity). Hence, its form is such that it is possible for the premises to be true and the conclusion nevertheless to be false . Hence, Aristotelian logic fails to be truth-preserving, so obviously CML is a far better tool for finding mathematical truth. Aristotelian logic is a disaster (not in reality, though; your claim that " Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic." is simply false.

But I challenge you to show one single example of an implication that is valid in Aristotelian logic and invalid in mathematical logic. Surely, if you know there are infinitely many, you would be able to find at least one.

I think you've run out of things to say. It all comes down to what you ignore and that you claim is false without evidence.

First, you claim without evidence that "Some implications are valid in Aristotelian logic and invalid in mathematical logic because, assuming the premises true, Aristotelian logic proves the conclusion follows necessarily from the premises while mathematical logic proves the conclusion false."
You have provided exactly zero evidence in support of your false claim. I challenge you to show a single example of an implication that is Aristotelian-valid but not CML-valid. I claim you will fail to do so.

Second, I already proved that if your claim happened to be true, then Aristotelian logic would fail to be truth-preserving, which is a devastating result. Your failure to follow my proof is a problem because I can't persuade you to concede, but the proof is there - repeated even.

I suspect most of mathematics is safe from wrong mathematical logic merely because mostly mathematicians don't use formal logic and instead rely on their own logical intuition, much as Euclid had.

Of course most mathematicians do not use formal logic. Instead, they use CML intuitively! Remember, by definition (the definition you provided in the other thread), CML-validity is not tied to a formal system. We use that intuitively all the time.

The question remains of whether there is any important mathematical results based on mathematical logic.

It's all over the place. It's our logical intuition! (maybe not your untrained intuition).

 

[fromderinside]

It's all over the place. It's our logical intuition! (maybe not your untrained intuition).

Wow. So optimizing and maximizing are just logical intuitions. And they're not untrained intuitions? Guess we need to rewrite all our intro psych books.

 

[Speakpigeon]

But I challenge you to show one single example of an implication that is valid in Aristotelian logic and invalid in mathematical logic. Surely, if you know there are infinitely many, you would be able to find at least one.

There are many examples, including on Wikipedia. But feel free to ignore them.

Second, I already proved that if your claim happened to be true, then Aristotelian logic would fail to be truth-preserving, which is a devastating result. Your failure to follow my proof is a problem because I can't persuade you to concede, but the proof is there - repeated even.

No, you just misunderstand my point.

Of course most mathematicians do not use formal logic. Instead, they use CML intuitively! Remember, by definition (the definition you provided in the other thread), CML-validity is not tied to a formal system. We use that intuitively all the time.

But you took the pain to explain that any problem resulting from that would be removed because mathematicians know what they're doing. Maybe you should decide which is your position here.

It's all over the place. It's our logical intuition! (maybe not your untrained intuition).

OK, that's a good point and a rather worrying idea, that mathematicians allowed their natural logical intuition to be overwritten by mathematical logic. I guess it's not entirely impossible. This would need to be empirically verified, though. But that's another reason to call for stopping today's mathematicians from mutilating their students. Sounds like abusing parents who have been abused themselves.

Anyway, I was looking for specific examples of mathematical theorems directly resulting from mathematical logic, not some general considerations about the issue.
EB

 

[Angra Mainyu]

It's all over the place. It's our logical intuition! (maybe not your untrained intuition).

Wow. So optimizing and maximizing are just logical intuitions. And they're not untrained intuitions? Guess we need to rewrite all our intro psych books.

That does not seem related to my post. Are you following the exchange?

 

[Angra Mainyu]

But I challenge you to show one single example of an implication that is valid in Aristotelian logic and invalid in mathematical logic. Surely, if you know there are infinitely many, you would be able to find at least one.

There are many examples, including on Wikipedia. But feel free to ignore them.

Where on Wikipedia? On which pages? Could you provide a single one of those examples? If you do not want to take the trouble of copying and pasting, a single link will do.

Second, I already proved that if your claim happened to be true, then Aristotelian logic would fail to be truth-preserving, which is a devastating result. Your failure to follow my proof is a problem because I can't persuade you to concede, but the proof is there - repeated even.

No, you just misunderstand my point.

No, I already provided a proof - repeatedly. Your failure to understand it is beside the point.

But you took the pain to explain that any problem resulting from that would be removed because mathematicians know what they're doing. Maybe you should decide which is your position here.

I explained it in detail. My position is clear to a reader being rational and paying attention, who has sufficient intelligence to understand. I explained why the chances of CML-invalid proofs getting into papers and remaining there without correction was extremely low. Again, those proofs are checked, and rechecked, and checked again, etc.

OK, that's a good point and a rather worrying idea, that mathematicians allowed their natural logical intuition to be overwritten by mathematical logic. I guess it's not entirely impossible. This would need to be empirically verified, though.

First, as I explained to you in the other thread, mathematicians who have never taken a course in mathematical logic and find it for the first time find it very, very intuitive. Well, most mathematicians at least. There is the question of whether those who instead support intuitionistic logic (a minority, but not a minuscule one) find the latter more intuitive, or are instead motivated by a philosophical argument. At any rate, intuitionists also accept explosion. And while a few mathematicians do not find it intuitive, those are a minuscule minority. Again, this is the general intuition of mathematicians, not that of those who have taken a course in mathematical logic previously.

But that's another reason to call for stopping today's mathematicians from mutilating their students. Sounds like abusing parents who have been abused themselves.

That is just considerably worse slander than before. You accuse people teaching math to their students of abuse and mutilation. It is a false and unwarranted accusation. There are different degrees of immorality. Your behavior is getting increasingly unethical.

Anyway, I was looking for specific examples of mathematical theorems directly resulting from mathematical logic, not some general considerations about the issue.

That is simply pointless, for the following reason: When Bomb#20 gave you an example of an easy derivation you couldn't do in Aristotelian logic and challenged you to use Aristotle's syllogisms to prove it, you failed. But you declared his example faulty. If one were to provide other examples in math papers, you could simply say the examples fail, and continue to engage in increasingly unethical slander against us.

You want me to give you specific examples? First show me why Bomb#20's example fails. Derive the conclusion in Aristotelian logic. If you manage to do that, I promise I will do my best to provide specific examples (of course, you cannot do that).

 

[Speakpigeon]

Where on Wikipedia? On which pages? Could you provide a single one of those examples? If you do not want to take the trouble of copying and pasting, a single link will do.

You know, I discovered by myself such a flawed inference in mathematical logic, something really, really bad. I thought it was a discovery I made. I thought nobody knew of it, stupid me. Then, more recently, I stumbled on it on a Wiki page. It was there for all to see and apparently nobody cares! It wasn't in the list of paradoxes of the material implication, though, and I wonder why because it should be there. So, yes, it's for all to see but, possibly, you need to understand what you're looking at.

There's is something else I found on the internet that mathematicians have discovered, but something they don't understand the significance of. So, yes, possibly you need to understand what you're looking at. I'm in no doubt you know your stuff and I'm really impressed. Yet, it's clear to me there are a few things, a few crucial facts, that either you really don't know, or that, just possibly, you know but fail to understand. It's on Wikipedia. For all to see. Why haven't you seen it?

Sometimes, people who live from the book will rebuke other people for not reading the books where the science is all explained. Well, why didn't you read the Wiki page where the thing is? It is for all to see (and unlike books, it's just one page long and free).

Anyway, I was looking for specific examples of mathematical theorems directly resulting from mathematical logic, not some general considerations about the issue.

That is simply pointless, for the following reason: When Bomb#20 gave you an example of an easy derivation you couldn't do in Aristotelian logic and challenged you to use Aristotle's syllogisms to prove it, you failed. But you declared his example faulty.

This is another example of something you don't understand. I was certain you were confused about this but you just confirmed the fact. You're just making an assumption, all by yourself, and it's wrong. Essentially I guess because you don't have the proper picture of Aristotle's logic so you misunderstand what I say.

If one were to provide other examples in math papers, you could simply say the examples fail, and continue to engage in increasingly unethical slander against us.

That's not what I meant. I would be interested in possible examples of important mathematical theorems based on mathematical logic. Obviously, if mathematical logic is wrong, some of these theorems could be in fact invalid, and obviously it would be better if someone at least could realise that.

You want me to give you specific examples?

Yes, badly.

First show me why Bomb#20's example fails. Derive the conclusion in Aristotelian logic. If you manage to do that, I promise I will do my best to provide specific examples (of course, you cannot do that).

Oh, I think this is in fact rather easy. I haven't had the time to really look at the details of Bomb#20's argument but I'm sure it's very easy. I even look forward to doing it. My intuition tells me it's easy in Aristotelian logic and it can't wait to do it. Still, sometimes, even simple things make you realise there was something you didn't quite understand.

No, I won't provide the proof. Just tell me where I could publish it (because of course, such a proof would be complete news to mathematicians). That would be the only way for you to see it. Do you think a respected journal of logic, or even a journal of philosophy, with a reputation to preserve, would publish something like this? Coming from a retired old fart who dropped out of university many decades ago? I don't think so. Too bad, hey? But seeing how academics are invariably so certain of their expertise, I'm not sure I wouldn't have the heart to break the news to them of their own utter ignorance of the subject.
EB

 

[steve_bank]

I recently stumbled on a wiki page o how the Earth is really flat and the sun goes round the Erath.

On the History show there is a series called Ancient Aliens. It is amazing revelation. The pyramids were actualy built by ET and Jesus was an ET sent to Earth to change the coarse of humanity.

In the words attributed to PT Barnum, 'there is a sucker born every minute'.

 

[Speakpigeon]

I'm not alone in some of what I say...

material "implication" is not an implication connective. -- Alan Ross Anderson & Nuel D. Belnap jr. Princeton University Press (1975)

Although even these people don't realise how bad it really is.

And their book contains ad hominem jokes about "mainstream" mathematicians...
EB

 

[steve_bank]

I'm not alone in some of what I say...

material "implication" is not an implication connective. -- Alan Ross Anderson & Nuel D. Belnap jr. Princeton University Press (1975)

Although even these people don't realise how bad it really is.

And their book contains ad hominem jokes about "mainstream" mathematicians...
EB

I have a PHD in net references.

'Philosopher l\know thyself'' It applies here.

https://en.wikipedia.org/wiki/Know_thyself

On the okd Johny Carson show he would say to the audience that something was realy bad, and the ausdince would say 'How bad is it?' afer which Carson would lanch into a joke.

So EB 'How bad is it?' Bad as in the looming collapse of human civilization because of bad logic?

 

[Angra Mainyu]

You know, I discovered by myself such a flawed inference in mathematical logic, something really, really bad.

I challenge you to provide any evidence of that. At all. Any link will do. Or an argument. Or anything, but the bare claims.

I thought it was a discovery I made. I thought nobody knew of it, stupid me. Then, more recently, I stumbled on it on a Wiki page. It was there for all to see and apparently nobody cares!

Well, it's not that nobody cares. I would be very interested in the example if I only knew which one of the gazillion Wikipidia pages you are talking about. But you will not say. And you think it's reasonable to reckon that no one cares?

It wasn't in the list of paradoxes of the material implication, though, and I wonder why because it should be there. So, yes, it's for all to see but, possibly, you need to understand what you're looking at.

It's not for all to see. It's for all who stumble upon it, or have a link. I cannot read your mind. There are a zillion Wikipedia pages. Do you actually believe that you are behaving in a reasonable manner?

There's is something else I found on the internet that mathematicians have discovered, but something they don't understand the significance of. So, yes, possibly you need to understand what you're looking at. I'm in no doubt you know your stuff and I'm really impressed. Yet, it's clear to me there are a few things, a few crucial facts, that either you really don't know, or that, just possibly, you know but fail to understand. It's on Wikipedia. For all to see. Why haven't you seen it?

There are a gazillion pages on Wikipedia. Obviously, I have seen only a small minority of them. As for philosophy, I tend to read from better sources, such as the Standford Encyclopedia of Philosophy, or Philosophy papers. But in any case, again, I challenge you to give an argument, or provide a link.

Sometimes, people who live from the book will rebuke other people for not reading the books where the science is all explained. Well, why didn't you read the Wiki page where the thing is? It is for all to see (and unlike books, it's just one page long and free).

I'm not a person who lives from a book. And certainly if I were, my book would not be Wikipedia. However, I challenge you to post a link, and offer to read a Wikipedia article if you identify it.

This is another example of something you don't understand. I was certain you were confused about this but you just confirmed the fact. You're just making an assumption, all by yourself, and it's wrong. Essentially I guess because you don't have the proper picture of Aristotle's logic so you misunderstand what I say.

You are wrong about the proper picture of Aristotle's logic, as your claims in this and other threads show. However, it is true I do not have your (mistaken) belief about what Aristotle's logic says, because you have not explained it.

As a result, it would be pointless to show you theorems that cannot be proven using only Aristotle's logic, because you can simply declare that Aristotle's logic has no problem proving them, while at the same time refusing to provide the proof, or a link, or anything at all.

Still, since you like Wikipedia so much, the following is on a Wikipedia page (which I will identify of course):

https://en.wikipedia.org/wiki/Syllogism#Terms_in_syllogism

For example, Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle".

One can find a more interesting example in the SEP (always a good philosophy resource). Relevance logics exclude the Principle of Explosion and probably other things you don't like. I do not know whether that is what you go for (your position is not known because of your unacceptable refusal to explain it while demanding that others explain theirs), but nevertheless, it is interesting to see what happens when one limits logic to that extent:

https://plato.stanford.edu/entries/logic-relevance/

Relevant logic has been used as the basis for mathematical theories other than set theory. Meyer has produced a variation of Peano arithmetic based on the logic R. Meyer gave a finitary proof that his relevant arithmetic does not have 0 = 1 as a theorem. Thus Meyer solved one of Hilbert's central problems in the context of relevant arithmetic; he showed using finitary means that relevant arithmetic is absolutely consistent. This makes relevant Peano arithmetic an extremely interesting theory. Unfortunately, as Meyer and Friedman have shown, relevant arithmetic does not contain all of the theorems of classical Peano arithmetic.

A weaker limitation is intuitionistic logic. Now, intuitionistic logic does accept explosion, so you do not like it. But still, it's interesting that even the much weaker limitations imposed by it result in a considerably different mathematics in some (many) fields. For example, when it comes to natural numbers, intuitionistic proofs are much more complicated, but that's about it. But when it comes to the continuum, things become considerably different.

For interested readers, here is a good link:

https://plato.stanford.edu/entries/intuitionism/

That's not what I meant. I would be interested in possible examples of important mathematical theorems based on mathematical logic. Obviously, if mathematical logic is wrong, some of these theorems could be in fact invalid, and obviously it would be better if someone at least could realise that.

You do not seem to understand what I'm saying. If you ask me to provide an example of a theorem that is "based on mathematical logic", I would for example look for a theorem that cannot be proven in Aristotelian logic. That is easy (see B20's example or the Wikipedia example above for easier deductions). But as soon as I provide an example, you can just claim that my example fails and that the theorem is derivable in Aristotelian logic. As usual, you would just claim that, but fail to prove it or provide any evidence of your claim. But it is pointless to provide examples, given that you can simply declare them failures, without providing a shred of evidence of your claim, or and argument, or anything at all - and have shown yourself willing to do just that.

Still, for the benefit of readers, I have provided examples above. I offer to provide more tailored examples if you show that Bomb#20's example fails (which, obviously, you will not do, since you can't).

Oh, I think this is in fact rather easy. I haven't had the time to really look at the details of Bomb#20's argument but I'm sure it's very easy. I even look forward to doing it. My intuition tells me it's easy in Aristotelian logic and it can't wait to do it. Still, sometimes, even simple things make you realise there was something you didn't quite understand.


No, I won't provide the proof. Just tell me where I could publish it (because of course, such a proof would be complete news to mathematicians). That would be the only way for you to see it.

That is just libel. It is unacceptable behavior on your part. Actually, the way for me to see it would be for you to write it here, so that I can see it. You refuse to speak, and then accuse me of refusing to listen!. Do you really believe your behavior is acceptable? (Yes, of course you do. That's even more disturbing).

But no, you will not show that Bomb#20's example is wrong. You can't. You believe you can, but you are above us, so you won't. In reality, you can't. You are not even close. But as I said above, it is pointless to provide more specific examples, because you have shown with your behavior that you are willing to dismiss and attack without even making an argument or providing any evidence of your claims. Still, I provided links to the relevant SEP articles. You will not learn, but if some interested readers might like them.

 

[Speakpigeon]

That's not what I meant. I would be interested in possible examples of important mathematical theorems based on mathematical logic. Obviously, if mathematical logic is wrong, some of these theorems could be in fact invalid, and obviously it would be better if someone at least could realise that.

You do not seem to understand what I'm saying. If you ask me to provide an example of a theorem that is "based on mathematical logic", I would for example look for a theorem that cannot be proven in Aristotelian logic. That is easy (see B20's example or the Wikipedia example above for easier deductions). But as soon as I provide an example, you can just claim that my example fails and that the theorem is derivable in Aristotelian logic. As usual, you would just claim that, but fail to prove it or provide any evidence of your claim. But it is pointless to provide examples, given that you can simply declare them failures, without providing a shred of evidence of your claim, or and argument, or anything at all - and have shown yourself willing to do just that.

Thanks for your examples but, again, that's not what I meant. This thread is about the possible consequences of mathematical logic being wrong. I'm asking you for examples of important theorems based on mathematical logic, not trivial examples where I can see that the conclusion follows and therefore where nobody is wrong.
EB

 

[Angra Mainyu]

That's not what I meant. I would be interested in possible examples of important mathematical theorems based on mathematical logic. Obviously, if mathematical logic is wrong, some of these theorems could be in fact invalid, and obviously it would be better if someone at least could realise that.

You do not seem to understand what I'm saying. If you ask me to provide an example of a theorem that is "based on mathematical logic", I would for example look for a theorem that cannot be proven in Aristotelian logic. That is easy (see B20's example or the Wikipedia example above for easier deductions). But as soon as I provide an example, you can just claim that my example fails and that the theorem is derivable in Aristotelian logic. As usual, you would just claim that, but fail to prove it or provide any evidence of your claim. But it is pointless to provide examples, given that you can simply declare them failures, without providing a shred of evidence of your claim, or and argument, or anything at all - and have shown yourself willing to do just that.

Thanks for your examples but, again, that's not what I meant. This thread is about the possible consequences of mathematical logic being wrong. I'm asking you for examples of important theorems based on mathematical logic, not trivial examples where I can see that the conclusion follows and therefore where nobody is wrong.
EB

Yes, of course, I understand what you are saying. I'm talking about important theorems not derivable in Aristotelian logic. For that matter, I already provided links so that interested readers can find that important theorems are not derivable when one restricts logic in different senses. The point is that if I show examples, you can simply say that I'm wrong.

That said, I already showed the consequences of having this particular "wrong" logic, assuming it's wrong as in not matching human logic. I showed that it's a superior method of finding mathematical truth (under the assumption that you implied that all mathematical statements are either true or false). Your failure to understand my arguments is another matter.

 

[steve_bank]

Thanks for your examples but, again, that's not what I meant. This thread is about the possible consequences of mathematical logic being wrong. I'm asking you for examples of important theorems based on mathematical logic, not trivial examples where I can see that the conclusion follows and therefore where nobody is wrong.
EB

Yes, of course, I understand what you are saying. I'm talking about important theorems not derivable in Aristotelian logic. For that matter, I already provided links so that interested readers can find that important theorems are not derivable when one restricts logic in different senses. The point is that if I show examples, you can simply say that I'm wrong.

That said, I already showed the consequences of having this particular "wrong" logic, assuming it's wrong as in not matching human logic. I showed that it's a superior method of finding mathematical truth (under the assumption that you implied that all mathematical statements are either true or false). Your failure to understand my arguments is another matter.

Nicely put, I have been trying to figure out how to say that. All math truths do not necessarily decompose into Aristotelian logic.

 

[fromderinside]

After A.E. van Vogt: Not everything is logical that way.