Philosophy Now Forum

Mathematicians make sure their theories are logically consistent but not necessarily that they are somehow true of anything in the real world.

This may be compared with scientists whose research requires that they develop a specific mathematical theory, theory which presumably they will want to be both logically consistent and applicable to the real world.

Theories will be applied whenever they are seen as applicable by those who choose to apply them. Applying a theory may be considered as the expression of the belief that the theory is somehow true of something in the real world.

Logic seems to be a special case. Most human beings seem to have some personal logical capacity, whether they use it or not. Mathematicians are perhaps the people who make the most intensive use of their own logical capacity. So, presumably, they will be acutely aware of it and therefore of the reality of it. Boole and Frege explicitly meant to develop of logical calculus somehow true of the "laws of thought", as Boole put it. In that, they were acting more like typical scientists than like typical mathematicians.

Boole seems to have been successful in his effort. I don't think anybody ever claimed Boole's algebra would somehow be unrepresentative or untrue of human logic.

However, after Boole and Frege, mathematicians working in mathematical logic seem to have moved away from the idea of a logical calculus as true somehow of the real world, and specifically true of human logic, focusing instead on the study of the formal properties of their theories.

Are there today any mathematicians, or even group of mathematicians, whose work on logic should be seen as not only mathematical but also avowedly scientific in the sense that they would try to produce a theory of logic explicitly presented as somehow true of human logic?
EB

It depends...

The closest you will get to is proof theory which attempts to unify the efforts of logicians, mathematicians and computer scientists.
The basic ideas of proof theory are covered in this introductory video.

Some of the ideas discussed above are similarly observed by Robert Harper in this article

The central dogma of computational trinitarianism holds that Logic, Languages, and Categories are but three manifestations of one divine notion of computation. There is no preferred route to enlightenment: each aspect provides insights that comprise the experience of computation in our lives.

Computational trinitarianism entails that any concept arising in one aspect should have meaning from the perspective of the other two. If you arrive at an insight that has importance for logic, languages, and categories, then you may feel sure that you have elucidated an essential concept of computation—you have made an enduring scientific discovery.

The idea of "trinitarianism" is unpacked in this presentation (from the perspective of a Mathematician): https://home.sandiego.edu/~shulman/papers/trinity.pdf

Keep in mind that logicians, mathematicians and computer scientists seem to trip over their own nomenclature when trying to communicate with each other.
Here is a Rosetta stone which maps the jargon across the three disciplines: https://ncatlab.org/nlab/show/computati ... itarianism

And a large group of collaborators who have bought into Voevodsky's ideas have been working on translating all of our Logic and Mathematical knowledge into Dependent Type Theory (working software) here: https://github.com/UniMath/UniMath

So. ...it depends on whether you accept Harper's idea that computation is an experience; and therefore - empirical/scientific.
But that may get you way too close to comfort

Speakpigeon wrote: ↑Sun May 12, 2019 6:10 pm Mathematicians make sure their theories are logically consistent.

I forgot to address this particular point.

The current definition of "inconsistency" is any logical/mathematical system in which one can prove both P and ¬P, but Voevodsky dares to go where no Mathematicians and Logician since Aristotle has dared to venture.

This video by Voevodsky is called "What if Current Foundations of Mathematics are Inconsistent?"

At 34 minutes into the video

The nature of Godel's argument shows that it is impossible to construct foundations which will be provably consistent.

What we need are foundations which can be used to construct reliable proofs despite being inconsistent

Science is empirical and logic is analytical.

PeteOlcott wrote: ↑Mon May 13, 2019 6:03 am Science is empirical and logic is analytical.

Machine learning algorithms are empirical.

Univalence wrote: ↑Sun May 12, 2019 7:11 pm It depends...

The closest you will get to is proof theory which attempts to unify the efforts of logicians, mathematicians and computer scientists.
The basic ideas of proof theory are covered in this introductory video.

Some of the ideas discussed above are similarly observed by Robert Harper in this article

The central dogma of computational trinitarianism holds that Logic, Languages, and Categories are but three manifestations of one divine notion of computation. There is no preferred route to enlightenment: each aspect provides insights that comprise the experience of computation in our lives.

Computational trinitarianism entails that any concept arising in one aspect should have meaning from the perspective of the other two. If you arrive at an insight that has importance for logic, languages, and categories, then you may feel sure that you have elucidated an essential concept of computation—you have made an enduring scientific discovery.

The idea of "trinitarianism" is unpacked in this presentation (from the perspective of a Mathematician): https://home.sandiego.edu/~shulman/papers/trinity.pdf

Keep in mind that logicians, mathematicians and computer scientists seem to trip over their own nomenclature when trying to communicate with each other.
Here is a Rosetta stone which maps the jargon across the three disciplines: https://ncatlab.org/nlab/show/computati ... itarianism

And a large group of collaborators who have bought into Voevodsky's ideas have been working on translating all of our Logic and Mathematical knowledge into Dependent Type Theory (working software) here: https://github.com/UniMath/UniMath

So. ...it depends on whether you accept Harper's idea that computation is an experience; and therefore - empirical/scientific.
But that may get you way too close to comfort

That's probably all very interesting but I don't see where your reply connects with the crucial point in my post, that of logic as a human capacity. I'm sure there's a logic to computers, but there's also a logic to a fridge and to a toaster so computers sound like a derail.
What your trinity seems to miss is that logic itself is understood, certainly by most logicians, philosophers and mathematicians, as underpinning any rational thinking whatsoever. So, sure, language, computers, but also fridges and toasters. I would go the extra mile and concede that human logic is really just the particular logic of the human brain just like there is a particular logic to fridges, toasters and computers. But I still haven't seen a toaster argue convincingly about anything except... toasts. So, computers...
So, my interest here is specifically logic as a human capacity. Boole and Frege were explicit in seeing it as the reference point. Where has it gone suddenly? I don't think we stopped having a capacity for logic. I'm sure most mathematicians today have their hands already full but, surely, someone somewhere must be trying to finish the job Boole and Frege didn't.
EB

PeteOlcott wrote: ↑Mon May 13, 2019 6:03 am Science is empirical and logic is analytical.

False dichotomy.
Any thinking is both empirical and analytical. Science too. Logic too.
The only way not to be analytical is to not reason at all. And if a logician doesn't do empirical, how does he know anything about logic?
What's not empirical in the empirical fact that most logicians since Aristotle agreed (mostly) on the same formulas as logical truths, starting with Aristotle's 2,500-year old syllogisms, Theophrastus' 2,400-year old modus ponens, the reductio etc.?
It's useful to make distinctions, but it's also good to see the sameness in things.
EB

Speakpigeon wrote: ↑Mon May 13, 2019 3:52 pm That's probably all very interesting but I don't see where your reply connects with the crucial point in my post, that of logic as a human capacity.

I am not sure I see the disconnect you see.

Are Frege, Boole, Russel and Voyevodsky not human? In what capacity (if not human) would you say they were conducting their work?

The implication of Harper's observation (and computational trinitarianism in general) is that 'computation' is a human capacity and logic itself is but one aspect of it.

It quite literally means that all three fields have been working on the same problem since Aristotle.

Univalence wrote: ↑Mon May 13, 2019 4:31 pm

Speakpigeon wrote: ↑Mon May 13, 2019 3:52 pm That's probably all very interesting but I don't see where your reply connects with the crucial point in my post, that of logic as a human capacity.

I am not sure I see the disconnect you see. Are Frege, Boole, Russel and Voyevodsky not human? In what capacity (if not human) would you say they were conducting their work?

Being human is irrelevant to my point, though. Rather, it is whether you work on logic explicitly as a human capacity or on logic as the logic of some toaster you like.

Univalence wrote: ↑Mon May 13, 2019 4:31 pm The implication of Harper's observation (and computational trinitarianism in general) is that 'computation' is a human capacity and logic itself is but one aspect of it. It quite literally means that all three fields have been working on the same problem since Aristotle.

Well, I see human logic as an emergent property of our neuronal processes and so I'm sure there's a lot of computation going on except it's not computation. The brain is a physical thing, not a computer. Computers themselves are not logical things. They are physical things with physical processes. The logic of a computer is like the logic of a toaster, something that results from the way we designed the thing. Humans were not designed, I don't believe. Their logic is all natural. To understand how human logic works, you can't rely on the manual like we do with toasters and computers. The only way is to do empirical science. Observe human logic. That's what we've been doing since Aristotle and even before him. But, it seems mathematicians got bored doing that.
Working on computation might help. Working on language might help. But, let's not mix up everything. So my question is: Any mathematician still working on human logic, like Aristotle did?
EB

Speakpigeon wrote: ↑Mon May 13, 2019 5:17 pm Being human is irrelevant to my point, though. Rather, it is whether you work on logic explicitly as a human capacity or on logic as the logic of some toaster you like.

Would you say that working on the foundations of Logic meets your criterion for "working on logic as a human capacity"?

Every one of the names I mentioned above worked on foundations.

Speakpigeon wrote: ↑Mon May 13, 2019 5:17 pm Well, I see human logic as an emergent property of our neuronal processes

Speakpigeon wrote: ↑Mon May 13, 2019 5:17 pm They are physical things with physical processes.

Observe that you are currently busy talking about physical processes. You are trying to describe logic in terms of physical processes.

One ought to ask at least the following questions:
* When was the concept of a "physical process" first born?
* What kind of concepts/logic/language would humans have to develop in order to speak ABOUT physical processes?

Allow me to draw your attention to the Church-Turing-Deutsch principle

The principle states that a universal computing device can simulate every physical process.

If you follow the link for a "universal computing device" from the Wikipedia link above you will end up at the page titled Turing machine. You are welcome to draw your own conclusions.

So to answer your question directly...

Speakpigeon wrote: ↑Mon May 13, 2019 5:17 pm So my question is: Any mathematician still working on human logic, like Aristotle did?

Yes! Everybody working in the field of logic, mathematics, linguistics and computer science today is working on human logic.

We have learned much in the 2300 years since Aristotle. And where we have arrived is simply this claim: Computation is human logic and the Turing machine is at its foundation.

And I shall leave you with this gem from John von Neumann:

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work - that is correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain esthetic criteria - that is, in relation to how much it describes, it must be rather simple.

Mathematics/logic is a modelling tool. It is instrumental, not ontological in nature.

Univalence wrote: ↑Tue May 14, 2019 8:42 am Would you say that working on the foundations of Logic meets your criterion for "working on logic as a human capacity"?
Every one of the names I mentioned above worked on foundations.

Nah. Doesn't carry any water. Clearly, whatever the name of a theory, some people at some point have to work on the foundation of it. That doesn't mean they mean to work on human logic.
I guess the criterion is rather simple: Do these people make any explicit and unambiguous claim to be working on human logic? It is very easy to read a book on logic thinking it's about human logic. The guy will talk of Aristotle's syllogisms, the Modus Ponens blah-blah-blah but without ever claiming explicitly he is talking about logic as per the logic of human reasoning. Check any book on logic you have...
Boole and Frege, and everybody at the time, were explicit. But people today don't even seem to be aware that it may be an issue.

Univalence wrote: ↑Tue May 14, 2019 8:42 am

Speakpigeon wrote: ↑Mon May 13, 2019 5:17 pm Well, I see human logic as an emergent property of our neuronal processes
They are physical things with physical processes.

Observe that you are currently busy talking about physical processes. You are trying to describe logic in terms of physical processes.

No. I'm saying logic is not a physical process. Logic is emergent. Broadly, brains tend to behave in a logical way, but not necessarily, because it's a probabilistic matter. Just like a computer tends to behave in a certain way, obviously because it's been designed this way, but still it is a probabilistic matter. Sometimes, both a brain and a computer won't do their logical thing. So, essentially, we invent the notion of logic because it's convenient to describe a computer our the human mind as logical, even though we know full well sometimes it doesn't work and it doesn't work in some unexpected way. That's why I used the word "emergent", to signify it's an abstraction, a mental construct, an approximation.
And again, brains haven't been designed. Computers have. Why should computers somehow have essentially the same logic as humans? A toaster doesn't.

Univalence wrote: ↑Tue May 14, 2019 8:42 am One ought to ask at least the following questions:
* When was the concept of a "physical process" first born?
* What kind of concepts/logic/language would humans have to develop in order to speak ABOUT physical processes?

I don't really know. It might be with computing, if that's your point, although I would expect it came sooner, at the time of the industrial revolution. when people first started to work out some abstract model of the production process to try and optimise costs and production. Most likely with Taylorism. And I wouldn't be too surprised if the notion had already been discussed before that, in particular by scientists, although I doubt that.
Still, the point is irrelevant. That human logic comes out as broadly a physical process, just like a river is broadly a physical process, is only relevant in that it helps to understand human logic. But it doesn't say what is human logic.

Univalence wrote: ↑Tue May 14, 2019 8:42 am Allow me to draw your attention to the Church-Turing-Deutsch principle

The principle states that a universal computing device can simulate every physical process.

You understand it's a "principle", yes?
I'm very well aware of it but I have zero reason to believe it's true.

Univalence wrote: ↑Tue May 14, 2019 8:42 am If you follow the link for a "universal computing device" from the Wikipedia link above you will end up at the page titled Turing machine. You are welcome to draw your own conclusions.

Ah, see, right here, you're doing it! This is your typical salesman. Get a bonus.
I asked for mathematicians who have been explicit. All we have here is a "principle" and the principle only says that a Turing could do the job, not that anybody is doing it.
My question is whether anybody is actually claiming to be working on human logic. We don't need Turing. Logic is broadly a physical process, so according to your infomercial here, any scientists would be working on human logic...

Univalence wrote: ↑Tue May 14, 2019 8:42 am So to answer your question directly...

Speakpigeon wrote: ↑Mon May 13, 2019 5:17 pm So my question is: Any mathematician still working on human logic, like Aristotle did?

Yes! Everybody working in the field of logic, mathematics, linguistics and computer science today is working on human logic.

Good, but the actual question is a bit more demanding:

Speakpigeon wrote: Are there today any mathematicians, or even group of mathematicians, whose work on logic should be seen as not only mathematical but also avowedly scientific in the sense that they would try to produce a theory of logic explicitly presented as somehow true of human logic?

Explicitly presented as somehow true of human logic...
I expect quotes, you know, not just vacuous claims...

Univalence wrote: ↑Tue May 14, 2019 8:42 am We have learned much in the 2300 years since Aristotle.

No, we haven't, not about logic.
You are confusing mathematical logic with human logic but mathematical logic is not logic proper, it's an extension of logic. It's mathematics, not logic. It's applied logic if you like. Mathematicians assume they have the foundation squared so they work on building more storeys. All the progress you're talking about is more storeys. Mathematics.

Univalence wrote: ↑Tue May 14, 2019 8:42 am And where we have arrived is simply this claim: Computation is human logic and the Turing machine is at its foundation.

If that's true, you'll have no difficulty quoting some of the great mind of the computing world... saying it explicitly?

Univalence wrote: ↑Tue May 14, 2019 8:42 am And I shall leave you with this gem from John von Neumann:
The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work - that is correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain esthetic criteria - that is, in relation to how much it describes, it must be rather simple.
Mathematics/logic is a modelling tool. It is instrumental, not ontological in nature.

Sure, and that's all irrelevant here.
EB

Speakpigeon wrote: ↑Tue May 14, 2019 12:16 pm I guess the criterion is rather simple: Do these people make any explicit and unambiguous claim to be working on human logic?

Why do they have to be explicit about it? Logic (studying or applying) is a profoundly human activity and so I cannot think of any other kinds of logic.
Could you give me an example of something which you consider to fall outside of the category of 'human logic'?

Speakpigeon wrote: ↑Tue May 14, 2019 12:16 pm No. I'm saying logic is not a physical process. Logic is emergent.

Then I will simply restate my question:
* When was the concept of a "emergence" first born?
* What kind of concepts/logic/language would humans have to develop in order to speak ABOUT emergent phenomena?

No matter how you frame it, when you choose to speak about X, you require nomenclature/language.

What language do you propose we ought use when formalising our knowledge of emergent phenomena?

Speakpigeon wrote: ↑Tue May 14, 2019 12:16 pm You are confusing mathematical logic with human logic but mathematical logic is not logic proper, it's an extension of logic. It's mathematics, not logic.

You don't get to append the adjective 'proper' to a word and pretend as if it somehow different.

I am not confusing logic with mathematics. I explicitly stated that they are three different-but-similar aspects of the computational trinitarianism.
I gave you plenty of references and almost 3+ hours of video content. I really doubt you have gone over (and understood) all of it for you to be making the counter-arguments you are making.

Speakpigeon wrote: ↑Tue May 14, 2019 12:16 pm If that's true, you'll have no difficulty quoting some of the great mind of the computing world... saying it explicitly?

This is a rather strange request. You are appealing to an authority. Why?

Whatever your reasons for committing this logical fallacy, I am happy to oblige.

Quote from Scott Aronson who won the Alan T. Waterman Award

The Alan T. Waterman Award is the United States's highest honorary award for scientists no older than 40, or no more than 10 years past receipt of their Ph.D. It is awarded on a yearly basis by the National Science Foundation. In addition to the medal, the awardee receives a grant of $1,000,000 to be used at the institution of their choice over a period of five years for advanced scientific research.

In his own blog he makes this statement:

The moral order of the universe is restored, and the Turing machine’s exalted position at the base of all human thought reaffirmed.

Speakpigeon wrote: ↑Tue May 14, 2019 12:16 pm Sure, and that's all irrelevant here.
EB

It is not irrelevant. If science is the process of describing observed phenomena then it begs a question:

What concepts/language/nomenclature would you use to describe the phenomenon of 'human logic'?

But I already asked that question...

Univalence wrote: ↑Tue May 14, 2019 12:29 pm

Speakpigeon wrote: ↑Tue May 14, 2019 12:16 pm I guess the criterion is rather simple: Do these people make any explicit and unambiguous claim to be working on human logic?

Why do they have to be explicit about it?

They don't have to. It was just the sense of my question.

Univalence wrote: ↑Tue May 14, 2019 12:29 pm Logic (studying or applying) is a profoundly human activity and so I cannot think of any other kinds of logic.

Computer logic? Mathematical logic?
Mathematicians who work on geometry don't necessarily try to describe the actual geometry of space.

Univalence wrote: ↑Tue May 14, 2019 12:29 pm Could you give me an example of something which you consider to fall outside of the category of 'human logic'?

That's easy. All of mathematical logic since broadly Boole. And now apparently just about any work done in logic, whether by mathematicians, computer scientists or even philosophers.

Univalence wrote: ↑Tue May 14, 2019 12:29 pm

Speakpigeon wrote: ↑Tue May 14, 2019 12:16 pm No. I'm saying logic is not a physical process. Logic is emergent.

Then I will simply restate my question:
* When was the concept of a "emergence" first born?
* What kind of concepts/logic/language would humans have to develop in order to speak ABOUT emergent phenomena?
No matter how you frame it, when you choose to speak about X, you require nomenclature/language.

You've lost me. How is that relevant?

Univalence wrote: ↑Tue May 14, 2019 12:29 pm What language do you propose we ought use when formalising our knowledge of emergent phenomena?

???
Whatever language would be appropriate?

Univalence wrote: ↑Tue May 14, 2019 12:29 pm

Speakpigeon wrote: ↑Tue May 14, 2019 12:16 pm You are confusing mathematical logic with human logic but mathematical logic is not logic proper, it's an extension of logic. It's mathematics, not logic.

You don't get to append the adjective 'proper' to a word and pretend as if it somehow different.

"Proper" here just means mathematical logic is not the proper description of human logic.

Univalence wrote: ↑Tue May 14, 2019 12:29 pm I am not confusing logic with mathematics. I explicitly stated that they are three different-but-similar aspects of the computational trinitarianism.
I gave you plenty of references and almost 3+ hours of video content. I really doubt you have gone over (and understood) all of it for you to be making the counter-arguments you are making.

I didn't look it up. Not interested.

Univalence wrote: ↑Tue May 14, 2019 12:29 pm

Speakpigeon wrote: ↑Tue May 14, 2019 12:16 pm If that's true, you'll have no difficulty quoting some of the great mind of the computing world... saying it explicitly?

This is a rather strange request. You are appealing to an authority. Why?

I don't think anybody will pay any attention to the claim in question i.e. that "Computation is human logic and the Turing machine is at its foundation". It's not a claim to be working on human logic, it's a claim that human logic is nothing but computation. Possibly, but then again, it is like saying the guy is working on the human mind since he is working on quantum physics.

Univalence wrote: ↑Tue May 14, 2019 12:29 pm Whatever your reasons for committing this logical fallacy, I am happy to oblige.
Quote from Scott Aronson who won the Alan T. Waterman Award
The Alan T. Waterman Award is the United States's highest honorary award for scientists no older than 40, or no more than 10 years past receipt of their Ph.D. It is awarded on a yearly basis by the National Science Foundation. In addition to the medal, the awardee receives a grant of $1,000,000 to be used at the institution of their choice over a period of five years for advanced scientific research.
In his own blog he makes this statement:

The moral order of the universe is restored, and the Turing machine’s exalted position at the base of all human thought reaffirmed.

Yes. Quantum Physics is also at the base of all human thought, presumably.
So, it's just this one guy? Nobody else?

Univalence wrote: ↑Tue May 14, 2019 12:29 pm

Speakpigeon wrote: ↑Tue May 14, 2019 12:16 pm Sure, and that's all irrelevant here.

It is not irrelevant. If science is the process of describing observed phenomena then it begs a question:
What concepts/language/nomenclature would you use to describe the phenomenon of 'human logic'? But I already asked that question...

I would use any language at all as long as it's convenient. English, C++, morse code. So, now, explain your point here.
EB

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm They don't have to. It was just the sense of my question.

Ok, but then the criteria for whether somebody is working on "human logic" are born entirely out of your own, subjective, expectations.

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm

Could you give me an example of something which you consider to fall outside of the category of 'human logic'?

That's easy. All of mathematical logic since broadly Boole. And now apparently just about any work done in logic, whether by mathematicians, computer scientists or even philosophers.

So what you mean by "human logic then" is Boolean logic and nothing else? That sounds like a No True Scotsman fallacy to me.

Is there anything that can convince you that the works of Cantor, Russel, Godel, Church, Turing, Chomsky, Frege, Curry, Howard, Brouwer, Heyting, Kolmogorov, Kleene, and so many other that I am too embarrassed to have not mentioned....

Is there anything that would convince you that what they worked on was "human logic", or are you dogmatically committed to the purity of Boole's work?

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm You've lost me. How is that relevant?

When scientists make new discoveries, acquire new knowledge - they invent new jargon.
Since you seem convinced that 'human logic' is not yet sufficiently or accurately described in any language/nomenclature we currently possess I am merely curious as to your own expectations as to what an "accurate description of human logic" might look like and how you would recognise it for what it is.

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm Whatever language would be appropriate?

Would you say that any of the current logics (perhaps hundreds of them) are "inappropriate"?

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm "Proper" here just means mathematical logic is not the proper description of human logic.

If any of the above-mentioned logics we currently have are the "proper description of human logic" - would you be able to tell? How?

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm I didn't look it up. Not interested.

Ok then you are not pursuing insight into body of knowledge pertaining to human understanding of logic. You are pursuing your own agenda.

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm So, it's just this one guy? Nobody else?

How many do you need for an Appeal to Authority to become valid form of justification?

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm I would use any language at all as long as it's convenient. English, C++, morse code. So, now, explain your point here.

My point is that inventing logics is precisely the science you seek. It's staring you in the face.

We, humans, invented Boolean logic.
We, humans, invented Algebra.
We, humans, invented morse code.
We, humans, invented C++.
We, humans, invented type systems.
We, humans, continue to invent new Mathematics.

We, humans, continue to make discoveries which are significant to the paradigm of computation.

If that is not "human logic" and you have new insights - please, share your knowledge with us.

Univalence wrote: ↑Wed May 15, 2019 10:09 pm

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm They don't have to. It was just the sense of my question.

Ok, but then the criteria for whether somebody is working on "human logic" are born entirely out of your own, subjective, expectations.

I'm fine with that. When you choose to walk through a door rather than through the wall, it's entirely out of your subjective expectations.
And I've looked at what the so-called experts talk about and I've found what they say lacking.

Univalence wrote: ↑Wed May 15, 2019 10:09 pm

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm

Could you give me an example of something which you consider to fall outside of the category of 'human logic'?

That's easy. All of mathematical logic since broadly Boole. And now apparently just about any work done in logic, whether by mathematicians, computer scientists or even philosophers.

So what you mean by "human logic then" is Boolean logic and nothing else?

No, I mean human logic. What's even difficult to understand? How could you possibly go through life without understanding what such a simple expression as "human logic" means? The logic of the human mind? The logic of rational thinking? Do you want me to explain what I mean by human being?
And, you don't even seem to understand the word "since".

Univalence wrote: ↑Wed May 15, 2019 10:09 pm Is there anything that can convince you that the works of Cantor, Russel, Godel, Church, Turing, Chomsky, Frege, Curry, Howard, Brouwer, Heyting, Kolmogorov, Kleene, and so many other that I am too embarrassed to have not mentioned....

Sorry, I don't seem to see the end of your sentence here... What's the question?
Most humans are more concerned with other humans than with the truth of anything. Mathematicians want to be the best among their peers.
Think of games. People want to play, whatever the game. But you don't get to play if you insist on redefining the rules. Once in a while you'll have individuals who decided to upend the table, Copernicus, Kepler, Einstein. For any Einstein, you could quote thousands of experts who asserted that Newton was correct. In fact, they're still saying it today!
I mean I'm sure these people were bright minds but so what? You think a bright mind is necessarily correct?
Basically, these people didn't even look, really, at human logic. That's all there is to it.

Univalence wrote: ↑Wed May 15, 2019 10:09 pm Is there anything that would convince you that what they worked on was "human logic", or are you dogmatically committed to the purity of Boole's work?

Boole got a few things right. The more simple ones. But, basically, he was wrong, too. Look up "since" in a dictionary.
If something say the Moon is square and green, I infer they're not talking about what I call the Moon.

Univalence wrote: ↑Wed May 15, 2019 10:09 pm When scientists make new discoveries, acquire new knowledge - they invent new jargon. Since you seem convinced that 'human logic' is not yet sufficiently or accurately described in any language/nomenclature we currently possess I am merely curious as to your own expectations as to what an "accurate description of human logic" might look like and how you would recognise it for what it is.

Aristotle's syllogistic would have to be a start. And then you make up the language as you go. And what you do should help explain what logicians in the past have said. Unfortunately, Boole didn't and his followers took what he had done as the new starting point. Different game. Not mine.

Univalence wrote: ↑Wed May 15, 2019 10:09 pm

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm Whatever language would be appropriate?

Would you say that any of the current logics (perhaps hundreds of them) are "inappropriate"?

I can't vouch for all of them being inappropriate but each one I took the time to look at is indeed inappropriate and I think I looked at the main ones. I thought initially Gentzen's natural deduction was likely correct but turns out it isn't.

Univalence wrote: ↑Wed May 15, 2019 10:09 pm

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm "Proper" here just means mathematical logic is not the proper description of human logic.

If any of the above-mentioned logics we currently have are the "proper description of human logic" - would you be able to tell? How?

I can only use my own intuition. That's all each of us has. Aristotle's syllogistic is faultless. A bit limited in scope but all good. The Stoics seem all good to me but I haven't looked at the details. I'm fine with all widely accepted logical truths since Aristotle. Isn't that a solid foundation? Well, not quite but that's a start. Most logicians nowadays poo-poo intuition, essentially because respected mathematicians in the past have been guilty of committing themselves to quite a few paradoxes. I disagree. We only have our intuition just as we only have our senses of perception. Logical intuition is essentially like a sense of perception. Too me, it is exactly that.

Univalence wrote: ↑Wed May 15, 2019 10:09 pm

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm I didn't look it up. Not interested.

Ok then you are not pursuing insight into body of knowledge pertaining to human understanding of logic. You are pursuing your own agenda.

Yes, I am. Were not sheep, you know.

Univalence wrote: ↑Wed May 15, 2019 10:09 pm

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm So, it's just this one guy? Nobody else?

How many do you need for an Appeal to Authority to become valid form of justification?

Quote somebody with the stature of a Boole, Frege, Russell, Tarsky, Quine etc.

Univalence wrote: ↑Wed May 15, 2019 10:09 pm

Speakpigeon wrote: ↑Wed May 15, 2019 4:53 pm I would use any language at all as long as it's convenient. English, C++, morse code. So, now, explain your point here.

My point is that inventing logics is precisely the science you seek. It's staring you in the face.
We, humans, invented Boolean logic.
We, humans, invented Algebra.
We, humans, invented morse code.
We, humans, invented C++.
We, humans, invented type systems.
We, humans, continue to invent new Mathematics.
We, humans, continue to make discoveries which are significant to the paradigm of computation.

So designing a new fridge or a new toaster is doing something like inventing a new kind of human logic?!
OK, you believe there's no logic that's intrinsic to the human brain. Me, I do. And I believe that if we didn't have that, we couldn't design any new toaster, let alone some computer. In fact, I believe we couldn't even make sense of the world around us.
Possibly, we can invent sub-par logics and, essentially, that's what the logics of today's mathematicians are.
Conceivably, we might be able to improve on Aristotle's logic, but then who is going to do that?

Univalence wrote: ↑Wed May 15, 2019 10:09 pm If that is not "human logic" and you have new insights - please, share your knowledge with us.

I only asked a simple question. I didn't mean to give a lecture. I told you the broad methodological principles that I believe we should follow. What more could you possibly need?
As to sharing my views, I realised recently there's little possibility of doing that. Who would publish unconventional logic coming from a non-specialist without any qualification? Who is even publishing today anything on human logic? Oh, well, maybe Notre Dame?
Well, I guess that was the point of my question...
You obviously know your way around the building so, tell me, what would be the three or four best academic journals to publish on human logic, or even to publish on falsifying mathematical logic?
I know somebody who could use that information.
EB