Why no science of logic?

[Jokodo]

I guess it depends on the world view of the person reading a post. Most assume that the person who wrote the post that was quoted is the person being addressed, not someone not even referred to. Those who think they are the center of the universe, assume that all comments are about them personally.

LOL. You can't even make sense of simple sentences.

You were ostensibly talking to Steve, sure. Not something you do very often; to start with. But then you were talking about some unspecified people, but in effect, me. Snide remarks.
EB

He was right: You do believe the universe revolves around you.

 

[skepticalbip]

I guess it depends on the world view of the person reading a post. Most assume that the person who wrote the post that was quoted is the person being addressed, not someone not even referred to. Those who think they are the center of the universe, assume that all comments are about them personally.

LOL. You can't even make sense of simple sentences.

You were ostensibly talking to Steve, sure. Not something you do very often; to start with. But then you were talking about some unspecified people, but in effect, me. Snide remarks.
EB

It would take someone with more than a bit of egomania to assert that they know what another is thinking.

ETA:
Yes, in this case I am referring to Speakpigeon as should be obvious since the post quotes a post written by you... So Steve shouldn't assume he is the target.

 

[Jimmy Higgins]

I guess it depends on the world view of the person reading a post. Most assume that the person who wrote the post that was quoted is the person being addressed, not someone not even referred to. Those who think they are the center of the universe, assume that all comments are about them personally.

LOL. You can't even make sense of simple sentences.

You were ostensibly talking to Steve, sure. Not something you do very often; to start with. But then you were talking about some unspecified people, but in effect, me. Snide remarks.
EB

He was right: You do believe the universe revolves around you.

Not the world, just this web board.

 

[Angra Mainyu]

Jokodo, if you want to see what Speakpigeon does, I suggest you take a look at our exchange in this thread (or any of the threads Speakpigeon started on the matter, but I think that one is particularly thorough).

What is the justification given by mathematicians that the notion of validity as used in mathematical logic would be correct of logic as an objective performance of humans and a capacity of the human mind?

You haven't a bloody clue.
EB

As I said repeatedly, mathematicians in general do not make claims about that. They do mathematics. And those who argue for the definition of validity that you target also do not make claims in general about whether this matches a human capacity (it does, but not what they claim). At any rate, this is beside the point. I replied to Jokodo recommending the other thread, so that he could assess by himself your behavior and argumentation in a practical case, where I showed conclusively that, under the hypothesis that every statement is either true or false (which you accept), if what you call 'mathematical logic' were wrong in the sense that it does not match human logic, it would be a tool superior to human logic as a means of finding mathematical truth. The arguments simply fly over your head, no matter how detailed: you simply misrepresent and attack.

As to the justification for the definition of validity that you mostly target (under the 'mathematical logic' tag), I already replied in this thread.

 

[Jokodo]

Speakpigeon, if people aren't getting your point, there's two logical possibilities (in any logic): people are stupid, or your point is at best poorly expressed and possibly invalid. What reason do you have (beyond maybe a belief in your infallability) to assume the former? Occam's Razor would suggest the latter, especially as it's not just a couple people but effectively everyone that'd have to be stupid

 

[Speakpigeon]

What is the justification given by mathematicians that the notion of validity as used in mathematical logic would be correct of logic as an objective performance of humans and a capacity of the human mind?

As I said repeatedly, mathematicians in general do not make claims about that. They do mathematics. And those who argue for the definition of validity that you target also do not make claims in general about whether this matches a human capacity (it does, but not what they claim).

???

George Boole: The Laws of Thought.

Frege: He hoped to develop of method of logic that would make the proof of theorems more rigorous. Obviously, this is about how mathematicians prove their theorems, but there's no reason to believe that, at the time, mathematicians themselves, as in the case of Boole himself, didn't think of the logic of mathematicians as the logic of human beings in general. This is also apparent in the fact that mathematicians presented mathematical logic as being fully in line with Aristotle's logic (although, in fact, it is contradictory to it, but never mind).

So, I don't think it would be correct at all to say that mathematicians don't present mathematical logic as if it was essentially the same as human logic. Many textbook start with Aristotle's syllogistic or some simplified presentation of it.

And I had several debates with mathematicians who insisted, against my suggestion, that mathematical logic what not contradictory to Aristotelian logic.

Also, mathematicians will usually explain the discrepancies between mathematical logic and human logic by arguing that the if-then linguistic conditional is a mixture of deductive and non-deductive inferences. This is true as to actual practice, but it is also true that it is perfectly possible for each of us to use the conditional in a strictly deductive way. Yet, even then, with this deductive subset of all uses of the conditional, mathematical logic still disagrees on some cases with the way we ordinarily use the conditional. Whatever the case, though, it is therefore apparent that mathematicians, through their discussion of the conditional, effectively argue that mathematical logic is in fact correct of human deductive logic. The discrepancies with the conditional are presented as a "defect" of the conditional, presentation which then allows mathematicians to ignore the many other cases where mathematical logic disagrees with human deductive logic. The fact that they try to hide this problem shows they are trying to present mathematical logic as correct of human logic.

There's also the names given by mathematicians to there pet method of logic. The name of intuitionistic logic certainly doesn't suggest a logic which would be somehow different from human logic, on the contrary (although, some axioms of intuitionist logic are obviously false, but apparently, they don't realise that, so much for intuition). Also, the name of the natural deduction method (Gentzen) directly suggests it is closer to, well, the natural way people argue logically. It is indeed an historial fact that Getzen himself wanted to do just that, against the more formalistic, "axiomatic", methods, in particular that of Hilbert.

And there is the name "logic" to begin with. The term "mathematical logic" only appeared as the mathematical methods of logic were becoming more formal and contrived, for example with various axiomatisations and the work on 2nd order logic.Why did they call it "logic" if they thought if was not logic?

Also, mathematicians argue among themselves which is the correct method, sometimes using ad hominem comments on the opposite side. Correct of what if not of human logic?! If you don't insist on being correct of human logic, then no method is correct because they are all arbitrary. But in this case, why do different mathematicians even argue that it is their method which is correct?

And then, read logic textbooks and find me a quote that supports your claim. A quote saying explicitly that mathematical logic doesn't try to be correct of human logic.

Mathematicians in actual fact behave in every way as if the believed mathematical logic was correct of human logic. They sure can't prove it, though, which explain why there's no justification available despite the fact that they think it is correct of human logic.
EB

 

[Speakpigeon]

Speakpigeon, if people aren't getting your point, there's two logical possibilities (in any logic): people are stupid, or your point is at best poorly expressed and possibly invalid. What reason do you have (beyond maybe a belief in your infallability) to assume the former? Occam's Razor would suggest the latter, especially as it's not just a couple people but effectively everyone that'd have to be stupid

I'm not decided on this. Maybe people are just stupid.

Or, it is just a matter that they are not motivated to think about logic.

Or, they haven't been lucky like me to find good reasons to believe differently.

Also, you are making the wrong assumption about my point being "poorly expressed". First of all, I express myself in good English. Second, I often take the time to go into the details of the point. But, sure, I'm not writing a book each time I make a reply. And, if I'm not good enough, what are you? Who on this board is anyway near being very articulate? Most people here can't even bring themselves to read properly the post they comment on.

Occam's Razor is good. We just don't have the same information to begin with so we're going to disagree which side it cuts.
EB

 

[Speakpigeon]

He was right: You do believe the universe revolves around you.

Not the world, just this web board.

Not at all. The centre of this board is Untermensche. When he's here, at least.

Maybe I should try to comment of your threads.
EB

EDIT
Fat chance. No Jimmy Higgins threads in philosophy, metaphysics or logic.

 

[Jokodo]

Speakpigeon, if people aren't getting your point, there's two logical possibilities (in any logic): people are stupid, or your point is at best poorly expressed and possibly invalid. What reason do you have (beyond maybe a belief in your infallability) to assume the former? Occam's Razor would suggest the latter, especially as it's not just a couple people but effectively everyone that'd have to be stupid

I'm not decided on this. Maybe people are just stupid.

Or, it is just a matter that they are not motivated to think about logic.

Or, they haven't been lucky like me to find good reasons to believe differently.

Also, you are making the wrong assumption about my point being "poorly expressed". First of all, I express myself in good English. Second, I often take the time to go into the details of the point. But, sure, I'm not writing a book each time I make a reply. And, if I'm not good enough, what are you? Who on this board is anyway near being very articulate? Most people here can't even bring themselves to read properly the post they comment on.

Occam's Razor is good. We just don't have the same information to begin with so we're going to disagree which side it cuts.
EB

It's not an assumption, it's an observation. What are you doing in a science forum if you can't distinguish the two?

 

[Angra Mainyu]

Frege: He hoped to develop of method of logic that would make the proof of theorems more rigorous. Obviously, this is about how mathematicians prove their theorems, but there's no reason to believe that, at the time, mathematicians themselves, as in the case of Boole himself, didn't think of the logic of mathematicians as the logic of human beings in general. This is also apparent in the fact that mathematicians presented mathematical logic as being fully in line with Aristotle's logic (although, in fact, it is contradictory to it, but never mind).

And you keep misrepresenting.
First, you made a claim about "mathematicians", not about a minuscule percentage of mathematicians. Now, mathematicians in general do not make claims about that. They do mathematics.

And most of the minuscule minority of mathematicians who argue for the definition of validity that you target also do not make claims in general about whether this matches a human capacity (it does, but not what they claim). Of course, I'm not claiming they believed it was different from human logic. My point is that they don't generally make claims about whether that is a species-wide or species-specific capacity. They just talk about logic.

Yet, even then, with this deductive subset of all uses of the conditional, mathematical logic still disagrees on some cases with the way we ordinarily use the conditional.

No, what you call "mathematical logic" captures the use of the conditional in some cases, including all cases of mathematics.

And there is the name "logic" to begin with. The term "mathematical logic" only appeared as the mathematical methods of logic were becoming more formal and contrived, for example with various axiomatisations and the work on 2nd order logic.Why did they call it "logic" if they thought if was not logic?

As if I had even suggested that mathematicians thought it was not logic. Given that you continue to misrepresent what I say, here's another debunking of part of your position as a fair retaliation (you just ignore the debunkings and continue to misrepresent, but there are other readers too, so here's the deal: you misrepresent, then I debunk again).

Let us begin:

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

Okay, so let us say that that is the definition in mathematical logic.

Now let us see:
https://talkfreethought.org/showthr...ct-mathematics&p=683824&viewfull=1#post683824

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. But you insist.

https://talkfreethought.org/showthr...ct-mathematics&p=684760&viewfull=1#post684760

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.

Let us consider this for a moment. Assuming your claims, there are implications that are valid in Arisotelian logic, but not in mathematical logic. Now, since they are not valid in mathematical logic, they do not take "a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false." So, what form do they take? The only alternative (as they have some form) is that they take a form that makes it possible for the premises to be true but the conclusion nevertheless to be false. So, Aristotelian logic is not truth-preserving. That shows that pretty much shows (from your assmption) that Aristotelian logic is a disaster: it doesn't even preserve truth.


But there is more:

https://talkfreethought.org/showthr...ct-mathematics&p=687751&viewfull=1#post687751

Aristotle's logic is the same as that of any human being and it is intuitively clear that these implications are invalid. What Aristotle himself said also confirm this.

So, it follows that human logic is a disaster: it doesn't even preserve truth. Mathematical logic does, so for that reason alone it is far superior to human logic.

Now, before you start misrepresenting away, I'm saying that that would be the rational assessment assuming some of your main claims.

 

[A Toy Windmill]

One minor nitpick. This was traditionally taken as valid in Aristotelian logic:

1) All X are Y.
2) All Y are Z.
3) Some X are Z.

It's not valid when interpreted in terms of Boolean sets. Aristotle's logic assumes that all terms hold of at least one thing, whereas in modern logic, we allow that sets may be empty and that quantifiers can range over empty domains.

This point was used in a popular article some time ago, highlighting a controversy in popular understandings of logic.

 

[Angra Mainyu]

One minor nitpick. This was traditionally taken as valid in Aristotelian logic:

1) All X are Y.
2) All Y are Z.
3) Some X are Z.

It's not valid when interpreted in terms of Boolean sets. Aristotle's logic assumes that all terms hold of at least one thing, whereas in modern logic, we allow that sets may be empty and that quantifiers can range over empty domains.

This got used in a popular article about ten years back as an example to highlight a controversy in popular understandings of logic.

However, that is valid under the definition of validity in mathematical logic provided by Speakpigeon, and it is valid precisely because there is an implicit hypothesis that there are no empty terms in the premises. If, on the other hand, one does not include that hypothesis, it is not valid under the definition of validity in mathematical logic provided by Speakpigeon, but is not valid in Aristotelian logic, either (else, Aristotelian's logic would indeed not be truth-preserving).

 

[skepticalbip]

nm

 

[Angra Mainyu]

The SEP gives an example.

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

Using it we can get Some monsters are chimeras from the apparently true All chimeras are monsters; but the former is often construed as implying in turn There is something which is a monster and a chimera, and thus that there are monsters and there are chimeras. In fact, this simply points up something about Aristotle’s system: Aristotle in effect supposes that all terms in syllogisms are non-empty.

Under the non-empty hypothesis, there is no problem with validity.

At any rate, if Speakpigeon's claim were true, then Aristotelian logic would fail to be truth-preserving, and so would human logic. That's a pretty good reason to abandon it for the better logic Speakpigeon calls 'mathematical logic', which is truth-preserving.

 

[Jokodo]

One minor nitpick. This was traditionally taken as valid in Aristotelian logic:

1) All X are Y.
2) All Y are Z.
3) Some X are Z.

It's not valid when interpreted in terms of Boolean sets. Aristotle's logic assumes that all terms hold of at least one thing, whereas in modern logic, we allow that sets may be empty and that quantifiers can range over empty domains.

This got used in a popular article about ten years back as an example to highlight a controversy in popular understandings of logic.

However, that is valid under the definition of validity in mathematical logic provided by Speakpigeon, and it is valid precisely because there is an implicit hypothesis that there are no empty terms in the premises. If, on the other hand, one does not include that hypothesis, it is not valid under the definition of validity in mathematical logic provided by Speakpigeon, but is not valid in Aristotelian logic, either (else, Aristotelian's logic would indeed not be truth-preserving).

Doesn't presupposing non empty terms nullify the equivalence between "ALL NOT" and "NOT ANY" (or ALL and NOT ANY NOT). It's intuitively clear that "there exist no unicorns that are not green", and under this equivalence it naturally follows that "all unicorns are green" is (vacuously) true, or at least not false.

 

[Angra Mainyu]

One minor nitpick. This was traditionally taken as valid in Aristotelian logic:

1) All X are Y.
2) All Y are Z.
3) Some X are Z.

It's not valid when interpreted in terms of Boolean sets. Aristotle's logic assumes that all terms hold of at least one thing, whereas in modern logic, we allow that sets may be empty and that quantifiers can range over empty domains.

This got used in a popular article about ten years back as an example to highlight a controversy in popular understandings of logic.

However, that is valid under the definition of validity in mathematical logic provided by Speakpigeon, and it is valid precisely because there is an implicit hypothesis that there are no empty terms in the premises. If, on the other hand, one does not include that hypothesis, it is not valid under the definition of validity in mathematical logic provided by Speakpigeon, but is not valid in Aristotelian logic, either (else, Aristotelian's logic would indeed not be truth-preserving).

Doesn't presupposing non empty terms nullify the equivalence between "ALL NOT" and "NOT ANY" (or ALL and NOT ANY NOT). It's intuitively clear that "there exist no unicorns that are not green", and under this equivalence it naturally follows that "all unicorns are green" is (vacuously) true, or at least not false.

Yes, that seems to be the case. The same goes for the SEP example I posted above.

However, in order to make the inference truth-preserving, you need the following hypothesis:

1') There is at least one X.
1) All X are Y.
2) All Y are Z.
3) Some X are Z (i.e., there is at least one X that is Z).

But the question of whether the terms had to be empty seems disputed, with a translation making the Aristotelian inference valid, but saying something else (see https://plato.stanford.edu/entries/square/#AriForOFor ). I have to admit I'm no expert in the translations of Aristotle, so I do not know.

However, my point regarding Aristotelian logic wasn't about what is valid in Aristotelian logic, but rather, that assuming Speakpigeon's claim that some inferences are Aristotelian-valid but not valid according to the definition of validity in mathematical logic (what she calls that, anyway) that she provided, then Aristotelian logic fails to be truth-preserving, and then, so does human logic (by Speakpigeon's claim that Aristotelian logic=human logic), so what she calls "mathematical logic" is surely superior, as it preserves truth with its inferences.

 

[Speakpigeon]

Speakpigeon, if people aren't getting your point, there's two logical possibilities (in any logic): people are stupid, or your point is at best poorly expressed and possibly invalid. What reason do you have (beyond maybe a belief in your infallability) to assume the former? Occam's Razor would suggest the latter, especially as it's not just a couple people but effectively everyone that'd have to be stupid

I'm not decided on this. Maybe people are just stupid.

Or, it is just a matter that they are not motivated to think about logic.

Or, they haven't been lucky like me to find good reasons to believe differently.

Also, you are making the wrong assumption about my point being "poorly expressed". First of all, I express myself in good English. Second, I often take the time to go into the details of the point. But, sure, I'm not writing a book each time I make a reply. And, if I'm not good enough, what are you? Who on this board is anyway near being very articulate? Most people here can't even bring themselves to read properly the post they comment on.

Occam's Razor is good. We just don't have the same information to begin with so we're going to disagree which side it cuts.
EB

It's not an assumption, it's an observation.

Yeah, yours.

What are you doing in a science forum if you can't distinguish the two?

???

You must be kidding, right?
EB

 

[Speakpigeon]

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.

Let us consider this for a moment. Assuming your claims, there are implications that are valid in Arisotelian logic, but not in mathematical logic. Now, since they are not valid in mathematical logic, they do not take "a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false." So, what form do they take? The only alternative (as they have some form) is that they take a form that makes it possible for the premises to be true but the conclusion nevertheless to be false. So, Aristotelian logic is not truth-preserving. That shows that pretty much shows (from your assmption) that Aristotelian logic is a disaster: it doesn't even preserve truth.

Your argument here shows you don't understand my question to begin with.

Basically, I was assuming mathematical logic was wrong, and therefore had an incorrect notion of validity, and asked what could be the consequences of that.

Instead of replying to my question, you assume here that the mathematical notion of validity is correct and infer from that Aristotle would be wrong. This is pathetic.

I lost interest in what you can tell a while ago. You haven't answered my questions. Not this one, not the question on validity. You won't ever, simply because, somehow, you don't understand the questions.

Even though they are really, really simple.

Have a good day.
EB

 

[Speakpigeon]

Reminder.

Why no science of logic?

By science of logic, I mean a scientific investigation of logic as objective performance and manifest capability of human beings, investigation that would try to develop a formal model of logic which would be accurate and operational.

I can't think of any important aspect of the empirical world which is similarly neglected by science.

There doesn't seem to be any practical impossibility.

Cost would not be a significant factor.

Logic seems to be a rather crucial aspect of human intelligence, which is itself at the centre of the very costly drive to produce artificial intelligence systems. The usefulness of an accurate formal model of logic seems therefore beyond question.

So, 2,400 years after Aristotle, why is there still, in the 21st century, no science of logic?
EB

If you don't have anything relevant to say on this, please abstain from posting irrelevant comments.
EB

 

[Jokodo]

Reminder.

Why no science of logic?

By science of logic, I mean a scientific investigation of logic as objective performance and manifest capability of human beings, investigation that would try to develop a formal model of logic which would be accurate and operational.

I can't think of any important aspect of the empirical world which is similarly neglected by science.

There doesn't seem to be any practical impossibility.

Cost would not be a significant factor.

Logic seems to be a rather crucial aspect of human intelligence, which is itself at the centre of the very costly drive to produce artificial intelligence systems. The usefulness of an accurate formal model of logic seems therefore beyond question.

So, 2,400 years after Aristotle, why is there still, in the 21st century, no science of logic?
EB

If you don't have anything relevant to say on this, please abstain from posting irrelevant comments.
EB

Your questions have been answered, in this thread and elsewhere.

You just don't like the answer.