Any science of logic?

What is the basis for reason? And mathematics?

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Univalence
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Re: Any science of logic?

Post by Univalence » Thu May 23, 2019 7:03 am

wtf wrote:
Thu May 23, 2019 12:00 am
When you said the world is a computer. That's a metaphysical claim. A claim of absolute truth about the world. It's something that's unknown and possibly unknowable yet you insist on it.
Do you understand that the metaphysical claim 'the world is a computer' is a not a claim about the world, but a claim about metaphysics?
My metaphysic is the way I THINK about the world. Obviously the world is unknowable! But we must talk ABOUT the world, least we shut up and say nothing. Ever.

Did you further understand the implication when I said (and pointed you to the paper which discusses it in detail) that "logic is metaphysics"?
Did you understand the two fundamental claims of model-dependent realists?

Model-dependent realism is a view of scientific inquiry that focuses on the role of scientific models of phenomena It claims reality should be interpreted based upon these models, and where several models overlap in describing a particular subject, multiple, equally valid, realities exist. It claims that it is meaningless to talk about the "true reality" of a model as we can never be absolutely certain of anything. The only meaningful thing is the usefulness of the model

The above ties directly to your axiom of choice. The metaphysical CHOICES you make have direct consequence upon the way you VIEW the world and the way you SPEAK about it.

What you are doing is arguing (in practice) is arguing that Pi*r^2 is a better LANGUAGE for describing a circle than x^2 + y^2 = 1
You are just using DIFFERENT LANGUAGE to DESCRIBE the same phenomenon.

And if you haven't made any choices about metaphysics, then you have never engaged in any metacognition.

The same problem applies. If I am going to be talking ABOUT thinking, I need a language to describe thinking. If there are 10 different ways to describe a circle, how many different ways are there to describe thinking?

Where could I possibly find such a language?
More choices:
1. I can invent one ( which would suffer from Wittgenstein's private Language problem)
2. I can adopt one ( the language of computer science ). Bonus points - computation is empirical, so it's grounded in reality. Yay!

Do you not understand that by saying "the world is a computer" or "my mind is a computer". I am simply saying "lets interpret everything from the lens/models/language of computer science and see if it works?". And guess what? It does. So that's useful then!

It's a pragmatic choice.
wtf wrote:
Thu May 23, 2019 12:00 am
I could be misunderstanding you. Perhaps when you say the world is computer you DON'T mean to be making a claim that your statement is true about the world? Now you have me totally confused.
Nobody is, and can ever make "claims about reality". Not even physicists. Hence the standard MODEL of physics.
Which is unlikely to be called "standard" in 200 years.

We accept that. Which is why I keep saying ALL MODELS ARE WRONG. But you can't parse what that means to an empiricist while you are stuck in the dreamworld of Mathematics.
wtf wrote:
Thu May 23, 2019 12:00 am
Yes you are correct that I regard interestingness and mathematical beauty as the only criteria for worthwhile math.
OK, but while you have been taking that stance, and working in your tower - a whole huge section of the population has been participating in an activity that is rather similar. And empirical. Computer scientists.

So similar, in fact that what mathematicians call theorem-proving is the same kind of activity as "software writing".
Different models (VIEWS) produce different language, but same output. Same in the sense - IT DOES the same thing.

So, here is me attempting to (metaphorically translate) my perspective in your language (something which you fail to even attempt).
Think of the Curry-Howard-Lambek correspondence as you would think about any fixed point theorem. A bridge between two "distinct fields".

There is a view-point, from which Mathematics and Computation are equivalent. That view-point is "the observer" in physics.
wtf wrote:
Thu May 23, 2019 12:00 am
So are you now admitting that your idea that the world is a computer is only a model and not metaphysical truth?
Perhaps I've been misunderstanding you. Can you please clarify this point once and for all?
It is a metaphysical truth. I have CHOSEN my metaphysical axioms.
You are asking me to prove the axiom of choice? (look! I have learned your language!)

Having conversed with you enough, I am betting money that you can't even connect the dots between AC and the Halting problem.
Univalence wrote:
Wed May 22, 2019 7:16 am
So you don't claim the world is a computer? Please advise.
"The world is a computer" means nothing more than "I am going to INTERPRET it as one".

Like the current trend in physics to INTERPRET it from the CHOSEN axioms that are the 7 SI units.

It means the same thing a physicist would mean if a physicist were to say "the world is energy".
Because there's no particle that doesn't have some FORM of energy. Which begs the (ontological) question "What is energy?"

So what kind of LANGUAGE would you use to talk about energy? Could you even understand energy via any other means except Mathematical models?

Your confusion stems from your lack of understanding of how to APPLY modeling to the problem of "understanding reality".

You lack teleology.
Last edited by Univalence on Thu May 23, 2019 11:03 am, edited 9 times in total.

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Speakpigeon
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Re: Any science of logic?

Post by Speakpigeon » Thu May 23, 2019 7:27 am

Univalence wrote:
Wed May 22, 2019 6:18 pm
Speakpigeon wrote:
Wed May 22, 2019 6:15 pm
That's a re-definition of logic, hence, it's equivocation.
You can't re-define something you never defined to begin with.
Speakpigeon wrote:
Wed May 22, 2019 6:15 pm
Here is Aristotle's definition of a syllogism and hence of logical validity and of deductive logic itself
https://en.wikipedia.org/wiki/Argument_from_authority
So, you think Aristotle's definition of a syllogism doesn't amount to a foundational definition of logic?
Or that the Organon isn't really about logic?
Or that somebody else coined the term logic?
See, we really have nothing to talk about.
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Re: Any science of logic?

Post by Univalence » Thu May 23, 2019 7:29 am

wtf wrote:
Thu May 23, 2019 12:17 am
Earlier you claimed to be studying Homotopy Type Theory, or HOTT. I found that interesting since I'm studying a related discipline, category theory.
Here's the problem. Metaphysically - the notion of "studying" means two entirely different things to you and me.
You have already made it clear that to you "studying mathematics" means nothing more than "amusing yourself". So perhaps maximum amusement means maximum understanding?
To me it means something like "constructing useful mental models". USEFUL being key here. Working back from a real-world problem to derive a Mathematical solution. Because empirical validation of my models means that I have a selection criterion that's a little more stringent than my own amusement.

Quite literally you have no way to confirm or falsify the epistemic claim "I understand mathematics". Your notion of "understanding" lacks contact with the ground. It's a castle in the sky - it means anything you want it to mean. At best - you are calibrated to some notion of "understanding" that is accepted amongst Mathematicians (e.g it's social acceptance), yet the moment you ask a mathematician about N-th order side-effects (or anything non-deterministic really) they start babbling some nonsense about "purity" and "beauty".

And if that's what mathematicians optimise for - great, but it's really difficult to setup any objective system of determining whether you actually "understand mathematics". You have read mathematics? You have adopted the language of Mathematicians? You can say things about abstract objects that don't upset other members of your tribe?

From where I am standing, Mathematicians produce useful algorithms from time to time and entirely by accident. Is just - luck is not a strategy in my game.

You have certainly admitted that you don't want to APPLY mathematics outside of the abstract, so it's really difficult to arbitrate your knowledge-claims. But that's not even the worst systemic issue at play.

If you don't know how to test/falsify your own claim of "understanding", how are you going to test somebody else's?
And if you aren't testing another's "understanding" (because you don't know what "understanding" means) then what are you testing for?

When you use a ruler to measure the table, you are also using the table to measure the ruler...
wtf wrote:
Thu May 23, 2019 12:17 am
I asked you if you knew about category theory and you claimed you did. I probed that by asking you what a universal property was. Your completely off-topic response convinced me that not only don't you know any category theory, but you are someone who claims to understand things rather than simply admit they don't.
What you were testing is whether I SPEAK the language a category theorist USE to talk about "category theory'.
Which is pretty weird, considering you know that:
1. I am more familiar with Type theory
2. Type theory is equivalent to Category Theory

And when the response that I gave you didn't arrive in the language that you expected it to arrive in, you concluded what you concluded.
So yeah. You aren't very bright when you keep missing the point: our INTUITIONS are the same. Our LANGUAGE is different.

What Feynman said rings true. If you can't explain it to somebody else - you don't understand it.
If you want to convince me that you 'understand category theory'. Translate your understanding of 'universal properties' into Type theory and see if you arrive at identity types

Similarly - if you asked me if I know anything about "proof theory" It would be a lie if I told you that I don't.
Because I have written more proofs than you have.

Only, I don't call them "proofs". I call them programs. So when you keep using your language to test my understanding - you are setting yourself up for failure.

You might find some truly useful insights about this problem in the first chapter of a book called "The Mathematical theory of Communication" by one, Claude E. Shannon. That is - if you actually care about applied Mathematics.

wtf wrote:
Thu May 23, 2019 12:17 am
And now I ask you what's a homotopy, and you have no idea. So you're not actually studying HOTT.
So are you claiming that my concrete example of APPLIED homotopy (parallel computation) in the real world is "me having no idea"?

Tell us all about how HOTT is a pure discipline, reserved only for the higher echelons of the Mathematical elite, and how my empirical intuitions and practical understanding of distributed systems is not transferable knowledge.

I can understand how it's upsetting to you. That a 22 year old DOING real-world computer science can develop the same intuitions about homotopy which takes 30+ years to acquire through the usual scholastic methods.
wtf wrote:
Thu May 23, 2019 12:17 am
And YOU are the one who chose Univalence as your handle, and you don't even know what the word means or what is its significance in modern alternative approaches to math foundations.
Sounds to me like you got triggered. Few weeks back you claimed that words have no meaning, and look at you now - defending the meaning of a word!

Observe how you are interpreting the significance of Univalence to the sub-culture of Mathematics. Still refusing to step outside that box and attempt to compute the consequences from a broader perspective.

Further observe, that despite the significance of the Curry-Howard-Lembek isomorphism, you insist on talking about Mathematics as if it has absolutely no relevance to Computation, or as if my empirical knowledge about large-scale computation is somehow not transferable into the world of Mathematics. That's just tribal thinking.

And you continue to repeat the tribal error of most humans "If you don't speak my language - you aren't one of us".
That's one way of refusing to acknowledge that all of your precious Mathematics boils down to a computational system that is less than 200000 lines of code. For some perspective. The Linux kernel alone is +- 20 million.

All you "understand" is Mathematics. If you can even call that "understanding".
wtf wrote:
Thu May 23, 2019 12:17 am
I'm perfectly justified in calling you out on your bluster. If you clearly don't know what you're talking about regarding subjects I'm familiar with
Yep... there it is. Because you spend time reading books about it, you have deemed yourself an expert.
Your ability to measure others understanding ends with your ability to measure your own.

Because your understanding is only scholastic you only know how to test for LANGUAGE. Somebody who TALKS about category theory.
Not somebody who BUILDS SYSTEMS that USE category theory.

Pretend you and I don't share a conversational language, then come up with an experiment to "test my understanding" of your field.
You can't? Because it's entirely abstract? Sucks to be you.

So, I guess I am going to continue "not know what I am talking about" when I point out that relational databases are the analog equivalent of your abstract area of expertise.

This is yet another example as to how and why my understanding is calibrated by reality. If you want to prove any sort of "familiarity" about category theory you should have absolutely no problem pointing us to the Mathematical equivalent of the CAP theorem?
wtf wrote:
Thu May 23, 2019 12:17 am
, then that causes me to doubt that you know what you're talking about on subjects I don't know anything about but that you claim to.
Because your ONLY test for asserting one's "knowledge" and "understanding" boils down to "Can you talk about X the way I talk about X"?
Your very own notion of "understanding" (or how to test for it) is. Well. Absent.

The way I test for "understanding" is if people can apply their knowledge to the real world.
If you can't - it's not knowledge.
wtf wrote:
Thu May 23, 2019 12:17 am
Yes I do see you managed to regurgitate some stuff you just hurriedly looked up. You simply have not convinced me.
Then come back to me when you have convinced yourself that relational databases are applied category theory.
wtf wrote:
Thu May 23, 2019 12:17 am
As an example, when I pointed out that I learned that the lambda calculus is an example of a Cartesian closed category, I expected that you might say something like, "Cool, can you tell me more about what that means?" Or, "Thanks but I'm not interested in that." What I did NOT expect was for you to pretend to understand the remark when it's so painfully obvious that you don't. That's where I'm losing my enthusiasm for this conversation.
Q.E.D What you are TESTING is whether I SPEAK your language.

If you are looking to speak about category theory in the abstract then you should probably look for other people who aspire to Mathematical purism/idealism. I am not one of those people.
If you want to talk about the APPLICATION of Mathematics ( e.g real-world problems!) Talk to me.

Because I have made it quite clear (and you keep proving my point). The patterns from your field are the patterns from my field.

And you have failed to convince me that you have anything remotely resembling of "understanding" when you can't even see how a relational database are APPLIED category theory.

You are the epitome of the pet-peeve I have with academics. You aren't interested in understanding the world. You are interested in abstract ideas.
So how about the abstract idea of "understanding what it means to understand the world"?
Last edited by Univalence on Thu May 23, 2019 12:39 pm, edited 30 times in total.

Univalence
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Re: Any science of logic?

Post by Univalence » Thu May 23, 2019 8:54 am

Speakpigeon wrote:
Thu May 23, 2019 7:27 am
So, you think Aristotle's definition of a syllogism doesn't amount to a foundational definition of logic?
It is one foundational definition of logic. There are many foundational definitions possible.
How would you go about deciding which one is the "correct" foundation?
Speakpigeon wrote:
Thu May 23, 2019 7:27 am
Or that the Organon isn't really about logic?
It's about one kind of logic. There are many different logics possible.
Speakpigeon wrote:
Thu May 23, 2019 7:27 am
Or that somebody else coined the term logic?
Why is that even relevant?

Can you even determine whether "logic" means the same thing to you as it does to the person who coined it?
Speakpigeon wrote:
Thu May 23, 2019 7:27 am
See, we really have nothing to talk about.
See. You were making an appeal to purity all along! You are convinced that your conception of "logic" is the only conception.

That's just your tribalism kicking in. "If you don't think like me - you aren't one of us".

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Re: Any science of logic?

Post by Speakpigeon » Thu May 23, 2019 10:24 am

Univalence wrote:
Thu May 23, 2019 8:54 am
Speakpigeon wrote:
Thu May 23, 2019 7:27 am
So, you think Aristotle's definition of a syllogism doesn't amount to a foundational definition of logic?
It is one foundational definition of logic. There are many foundational definitions possible.
How would you go about deciding which one is the "correct" foundation?
Like how I decide what the taxman really, really means when he says I have to pay. It's functional equivalency all along. I don't want to go to jail, you know.
Univalence wrote:
Thu May 23, 2019 8:54 am
Speakpigeon wrote:
Thu May 23, 2019 7:27 am
Or that the Organon isn't really about logic?
It's about one kind of logic. There are many different logics possible.
No. There are different models but there's just one logic. Those people who work on different models still use the same logic. To believe all these models are true of human logic is to live in La La Land.
Univalence wrote:
Thu May 23, 2019 8:54 am
Can you even determine whether "logic" means the same thing to you as it does to the person who coined it?
I certainly believe I can. If I'm wrong, then I am wrong precisely because there's just one human logic.
Univalence wrote:
Thu May 23, 2019 8:54 am
See. You were making an appeal to purity all along! You are convinced that your conception of "logic" is the only conception.
That's just your tribalism kicking in. "If you don't think like me - you aren't one of us".
Not in the least. You're not listening! I said it: you cannot not think like me. At base, you have the same logic as everybody else because Quantum Physics trumps your Turing La La Land.
In fact, if anything, it's myself I want to claim as outside of your "tribe". You are a committed member of the La La Club. I'm not. There's a bunch of you guys out there who think they have it all figured out. Look at the financial investment sunk in AI R&D during the last few decades. Literally billions. And all of it on trust. On the say-so of a few illuminated bright and less-than-bright kids and divas. Some results for sure, but no way near the repeated mantra of AI research. Your "metaphysical" claim is vacuous. The whole of mathematics has come out of human logic. Give me one mathematical theory that's been worked out by an AI! Mathematicians all use human logic, even those who work on non-human mathematical logic. Tout ça c'est du flan. C'est de la daube. Why would you be wasting your precious time here peddling your nonsense if your metaphysics had any application at all outside of your little private La La Land?
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Re: Any science of logic?

Post by Univalence » Thu May 23, 2019 10:41 am

Speakpigeon wrote:
Thu May 23, 2019 10:24 am
Like how I decide what the taxman really, really means when he says I have to pay. It's functional equivalency all along. I don't want to go to jail, you know.
False analogy.

We have ostensive definitions for a taxman, money. I can demonstrate to you the act of payment.

You are busy trying to PRODUCE an ostensive definition for "logic".
Speakpigeon wrote:
Thu May 23, 2019 10:24 am
No. There are different models but there's just one logic.
Those people who work on different models still use the same logic. To believe all these models are true of human logic is to live in La La Land.
OK. I am still waiting for you to state your epistemic criterion for deciding which model is the most accurate one then?

Or would you be willing to admit that the above is just your axiomatic assumption?

Notice you are still the one talking about "truth". Perhaps Philosophical idealism has rubbed off you you too much?
I am not making any claims about my models other than "they work".

You don't have to use them if you don't want to... but you are talking to me USING a computer.
Speakpigeon wrote:
Thu May 23, 2019 10:24 am
I certainly believe I can. If I'm wrong, then I am wrong precisely because there's just one human logic.
You are arguing for monism. I am on the same page as you. I have arrived at computation. a.k.a Digital physics.

Digital philosophy is a modern re-interpretation of Gottfried Leibniz's monist metaphysics, one that replaces Leibniz's monads with aspects of the theory of cellular automata.

In 2019 we understand Monads. As best as they can be understood theoretically and empirically: Mathematically and Programatically.
Speakpigeon wrote:
Thu May 23, 2019 10:24 am
Not in the least. You're not listening! I said it: you cannot not think like me. At base, you have the same logic as everybody else because Quantum Physics trumps your Turing La La Land.
A quantum computer can be emulated on a Turing machine. Go ahead Try it.

In fact, for most part Quantum Computers are equivalent. Only much faster.
Except for the problems which can only be solved with a quantum computer.

But this is puzzling. If you are appealing to quantum logic, then you absolutely MUST reject Aristotelian logic as being anything remotely resembling of "human logic".
Speakpigeon wrote:
Thu May 23, 2019 10:24 am
Why would you be wasting your precious time here peddling your nonsense if your metaphysics had any application at all outside of your little private La La Land?
Notice how you have setup your question in a way to perfectly agree with your confirmation bias.

You are COMMUNICATING this to me using a computer right now. Because this dude called Shannon did this cool thing.
There's even going to be a movie about him: https://thebitplayer.com/

30 seconds ago you believed that Quantum Physics is magic. Then I gave you a quantum computer to play with.
And if you want to learn more about Quantum Logic then try this: https://github.com/Qiskit/qiskit

My "little private" La La land is everywhere. In your car. in your microwave. Your TV. Your phone.

You may have heard of this thing, called The Internet? Google? It is total fucking nonsense. It all just metaphysics.
It STARTED OUT as metaphysics. But then we created it.

You have some magical thinking going on in your head. That "truth" (once you find it) will trigger off a rush of endorphins, sparkles and unicorns in your mind to signal to you that you have arrived!

Keep searching then.

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Re: Any science of logic?

Post by Univalence » Thu May 23, 2019 11:37 am

Speakpigeon wrote:
Thu May 23, 2019 10:24 am
There's a bunch of you guys out there who think they have it all figured out. Look at the financial investment sunk in AI R&D during the last few decades. Literally billions. And all of it on trust. On the say-so of a few illuminated bright and less-than-bright kids and divas. Some results for sure, but no way near the repeated mantra of AI research.
You are harping on about "human logic". YOU keep claiming that you understand 'human logic'. YOU keep claiming that you have 'figured it out'.

So fucking tell us how it works already!!!! What are you waiting for?

Write the book which finishes Boole's work!
Write the algorithm for your mind and publish it on GitHub - then we can all have a look and be mighty impressed how one Frenchman did what thousands of scientist have tried and failed at!
Invent a machine that does the same thing you do!
Communicate to me your understanding in a way that I could use it too!
You know? Like Shannon COMMUNICATED his understanding of communication using the LANGUAGE of Mathematics and a coin!

Choose a medium for self-expression and express yourself already! Tell us what you know!
Or are you just taunting us that you have all the answers and we don't?

Last, but not least. You are claiming that you "understand human logic". Cool. I can neither prove nor disprove your claims, but also - that's not really my job. That's your job.

It is your job to contrive some kind of experiment that allows you to verify OR falsify your own epistemic claim. The claim that you "understand human logic".

If your experiment is successful - then it could be said that you understand human logic.
If your experiment is a failure - then it can't be said that you understand human logic.

Could I suggest an experiment perhaps? Build a machine that works like your mind!

Or I can just ask you this question: Why do you even want to describe 'human logic'? Is it just a need to be understood, or do you have some other purpose/end-goal in mind?

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Re: Any science of logic?

Post by RCSaunders » Thu May 23, 2019 2:44 pm

Speakpigeon wrote:
Sun May 12, 2019 6:10 pm
I don't think anybody ever claimed Boole's algebra would somehow be unrepresentative or untrue of human logic.
Russel did, and he was right. He refers specifically to Boole's 1854 An Investigation of the Laws of Thought, pointing out that human thought involves much more than logic.
Speakpigeon wrote:
Sun May 12, 2019 6:10 pm
... a theory of logic explicitly presented as somehow true of human logic?
Whatever you mean by, "human logic," if it is logic it is only the formalization of correct human reason. Both volition and knowledge precede reason because reason is done by choice and knowledge is all there is to reason about or reason with.

Modern so-called logic is an attempt to describe reason without reference to knowledge. It is a huge floating abstraction.

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Re: Any science of logic?

Post by Univalence » Thu May 23, 2019 2:50 pm

RCSaunders wrote:
Thu May 23, 2019 2:44 pm
Modern so-called logic is an attempt to describe reason without reference to knowledge. It is a huge floating abstraction.
What you seem to call 'knowledge' I call 'history'.

We know the past but cannot control it. We control the future but cannot know it. --Claude E. Shannon

Modern "so called logic" is an attempt to describe decision-making under uncertainty.
Having knowledge of history, while being acutely aware that things could have changed since, how can I predict the future?

Bonus point for avoiding catastrophic errors in the process.

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Re: Any science of logic?

Post by Speakpigeon » Thu May 23, 2019 5:30 pm

RCSaunders wrote:
Thu May 23, 2019 2:44 pm
Speakpigeon wrote:
Sun May 12, 2019 6:10 pm
I don't think anybody ever claimed Boole's algebra would somehow be unrepresentative or untrue of human logic.
Russel did, and he was right. He refers specifically to Boole's 1854 An Investigation of the Laws of Thought, pointing out that human thought involves much more than logic.
You think Boole was so stupid as to have argued that logic was all there was to human thought?!
Russell may have remarked there was more to human thought than logic, but I doubt very much it was anything like a criticism.
This is the full title of Boole's book:
An Investigation of The Laws of Thought on which are founded the Mathematical Theories of Logic and Probabilities

So, clearly, Boole wasn't even trying to describe all the laws of thought, a task which would have appeared as obviously impossible at the time.
Speakpigeon wrote:
Sun May 12, 2019 6:10 pm
... a theory of logic explicitly presented as somehow true of human logic?
Whatever you mean by, "human logic," if it is logic it is only the formalization of correct human reason. Both volition and knowledge precede reason because reason is done by choice and knowledge is all there is to reason about or reason with.
Modern so-called logic is an attempt to describe reason without reference to knowledge. It is a huge floating abstraction.[/quote]
And?
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Re: Any science of logic?

Post by Speakpigeon » Thu May 23, 2019 5:34 pm

Univalence wrote:
Thu May 23, 2019 2:50 pm
Modern "so called logic" is an attempt to describe decision-making under uncertainty.
No. That's for maths to "describe decision-making under uncertainty".
Formal logic is an attempt to describe logic. Except of course mathematical logic isn't really formal logic at all.
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Re: Any science of logic?

Post by Univalence » Thu May 23, 2019 5:41 pm

Speakpigeon wrote:
Thu May 23, 2019 5:34 pm
No. That's for maths to "describe decision-making under uncertainty".
We are going to get nowhere with this "that's somebody else's problem" attitude.

Does your mind make decisions? Mine does. I am pretty sure yours does too.
Any description of 'logic' that doesn't describe the process of decision-making would be incomplete.

WHO does it is moot. SOMEBODY has to!
Last edited by Univalence on Thu May 23, 2019 6:01 pm, edited 4 times in total.

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Re: Any science of logic?

Post by Univalence » Thu May 23, 2019 5:51 pm

Speakpigeon wrote:
Thu May 23, 2019 5:34 pm
Formal logic is an attempt to describe logic
So formal logic describes itself in formal logic?

That seems a little recursive. Recursion is computation you know...

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Re: Any science of logic?

Post by Univalence » Thu May 23, 2019 6:09 pm

Speakpigeon wrote:
Thu May 23, 2019 5:30 pm
You think Boole was so stupid as to have argued that logic was all there was to human thought?!
Russell may have remarked there was more to human thought than logic, but I doubt very much it was anything like a criticism.
Well, that's not even close to an exhaustive list of people who have an opinion on the matter.

You may want to look into this: https://en.wikipedia.org/wiki/Mental_model
Scientific debate continues about whether human reasoning is based on mental models, versus formal rules of inference

Me? I am in the camp that says 'rules of inference' are extracted FROM mental models.

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Re: Any science of logic?

Post by wtf » Thu May 23, 2019 10:35 pm

Univalence wrote:
Thu May 23, 2019 7:03 am
Model-dependent realism is a view of scientific inquiry that focuses on the role of scientific models of phenomena It claims reality should be interpreted based upon these models, and where several models overlap in describing a particular subject, multiple, equally valid, realities exist. It claims that it is meaningless to talk about the "true reality" of a model as we can never be absolutely certain of anything. The only meaningful thing is the usefulness of the model

The above ties directly to your axiom of choice. The metaphysical CHOICES you make have direct consequence upon the way you VIEW the world and the way you SPEAK about it.

What you are doing is arguing (in practice) is arguing that Pi*r^2 is a better LANGUAGE for describing a circle than x^2 + y^2 = 1
You are just using DIFFERENT LANGUAGE to DESCRIBE the same phenomenon.
The problem isn't that you're ignorant. Ignorance can be remedied with education and study.

The problem is that you are a complete bullshit artist.

Anyone with an Internet connection can learn that the axiom of choice is a set-theoretic principle that says that we can simultaneously choose an element from each of a collection of nonempty sets.

It's equivalent to some familiar mathematical statements such as: every vector space has a basis; every surjective function has a right inverse (also called a section); and that any set can be well-ordered. It has a long history going back to Zermelo in the early 1900's. In the first half of the 20th century it was controversial because in some contexts it's perfectly obvious; and in others it's totally counterintutive and seemingly false.

Its importance in my responses to Pete is that it's known to be independent of the other axioms of set theory. We can have set theory with choice and without it. So Pete's claim that truth follows from assuming axioms is wrong. It's falsified by the very well-known example of the axiom of choice. That's the only reason I mentioned it.

When you encounter a term you don't know, you don't bother to look it up, ask questions, admit it's new to you. Rather, you make up your own definition and go on a rant about how clever you are while spouting off about something entirely different.

You claim to be studying homotopy type theory (HOTT) but have no idea what a homotopy is and claim that's a picky detail too far beneath you to learn. You claim knowledge of category theory but your responses to simple questions about it are embarrassingly wrong. You change your handle to Univalence but have no idea what the Univalence axiom is.

Well buddy you are a bullshit artist. You know it and I know it. And now everyone knows it.

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