## 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?

wtf wrote: Thu May 23, 2019 10:35 pm 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.
Have you heard of Wittgenstein's ruler?
Unless you have confidence in the ruler’s reliability, if you use a ruler to measure a table you may also be using the table to measure the ruler.

In this scenario you aren't the ruler. You are the table. You are as dumb as a doorknob.
wtf wrote: Thu May 23, 2019 10:35 pm Anyone with an Internet connection can learn that the axiom of choice is a set-theoretic principle
Any non-idiot who actually understands how formal systems work knows that AC is not an exclusive set-theoretic principle.
Every formal system has an AC-equivalent.

Here is the Univalent version

But I shouldn't even have to give you any links because it is on the same fucking wiki page YOU told ME to read. Oops?

I thought you said you are studying Category theory? And you've probably been at this way longer than I have. So how come you don't know this?

Some of the references here go as far back as 1974.
I guess you didn't do your homework before calling me out, huh?

Of all the variations of AC, my most favourite is the intuitionistic/constructivist one (could you have guessed?). It is so human. So to-the-point!
It's simply the function F that was desired. In plain English: Tell me what you want this function TO DO and I will construct it for you!

In intuitionistic theories of type theory (especially higher-type arithmetic), many forms of the axiom of choice are permitted. For example, the axiom AC11 can be paraphrased to say that for any relation R on the set of real numbers, if you have proved that for each real number x there is a real number y such that R(x,y) holds, then there is actually a function F such that R(x,F(x)) holds for all real numbers. Similar choice principles are accepted for all finite types. The motivation for accepting these seemingly nonconstructive principles is the intuitionistic understanding of the proof that "for each real number x there is a real number y such that R(x,y) holds". According to the BHK interpretation, this proof itself is essentially the function F that is desired.
wtf wrote: Thu May 23, 2019 10:35 pm that says that we can simultaneously choose an element from each of a collection of nonempty sets.
Could you perhaps tell us a little bit more about those sets. What do they contain?
What TYPES of elements are you choosing out of these non-empty sets? Axioms? Integers? Inference rules? Reals? Strings? Booleans? Monads? All of the above?

What you call "choosing an element from a collection of nonempty sets" (such convoluted language!), a statistician simply calls "random sampling".

And a human simply calls it "choosing stuff". You have a bunch of baskets full of things - you stick your hand and grab ANYTHING.

wtf wrote: Thu May 23, 2019 10:35 pm 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.

Its importance in my responses to Pete are that it's known to be independent of the other axioms of set theory. So 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.
I am not talking about set theory. I am talking about the set of ALL FORMAL SYSTEMS, of which ZFC is just one particular example.
ALL formal systems have axioms.
And in every formal system a different set of foundational axioms would produce a different set of theorems (you know this, right?).

Which should be obvious as fuck because that's how the butterfly effect works!

So. How did you CHOOSE your axioms?

From the bins full of AXIOM-Types which ones did you pull out?
wtf wrote: Thu May 23, 2019 10:35 pm 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.
When you encounter somebody who seems to be speaking "bullshit". Never forget the alternative hypothesis

Because from where I am looking, other than Mathematics you actually know nothing about formal systems.

You have mistaken yourself for an expert. Like most academics.
wtf wrote: Thu May 23, 2019 10:35 pm Rather, you make up your own definition and go on a rant about how clever you are while spouting off about something entirely different.
My own definitions?

I am using the standard English dictionary definition of "choice" and I am demonstrating to you that when a person undertakes to construct any formal system from first principles, they are faced with CHOOSING their foundational axioms.

That you have CHOSEN to apply this principle exclusively to the narrow world of ZFC is well. Your problem.

wtf wrote: Thu May 23, 2019 10:35 pm Well buddy you are a bullshit artist. You know it and I know it. And now everyone knows it.
Yep. You sure put your foot in your mouth on that one

I am going to repeat myself, and make it clear that this time I mean it as an insult.

You think you know Mathematics, but you don't even know how to USE it.
wtf
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### Re: Any science of logic?

Univalence wrote: Thu May 23, 2019 11:50 pm Have you heard of Wittgenstein's ruler?
Why, are we going to have a dick measuring contest?

I have no interest in continuing this back and forth. You can have the last word if you like.

I just would like to know what on earth you were thinking when you spouted off that crap about the axiom of choice having something to do with how you express the formula for the area of a circle. what on earth are you thinking?

As far as your other remarks they're completely off topic. Of course I'm aware of how the axiom of choice is represented in alternative foundational systems. For example it's often stated as, "Every surjection has a section," since that's equivalent to the axiom of choice but doesn't mention elements of sets, but only properties of functions. So it fits category- or homotopy-theoretic formulations nicely.

But still. What does that have to do with anything? I mentioned AC as an example of an independent axiom whose truth value, if it even meaningfully has one, is not determined simply by assuming an axiom.

And then you went off on that complete non sequitur shaggy dog story about the area of a circle. That made a certain impression on me. At my end I prefer not to continue.

So anyway please friend, have the last word. It's been interesting. All the best.
Univalence
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### Re: Any science of logic?

wtf wrote: Fri May 24, 2019 5:05 am I just would like to know what on earth you were thinking when you spouted off that crap about the axiom of choice having something to do with how you express the formula for the area of a circle. what on earth are you thinking?
I was thinking Chomsky Type 1 grammar

I was using it as an example of linguistic expressions (because Mathematics is just a language we invented, you know this - right?) that say the same thing using different words.

I was thinking. Those words have no meaning until the Linear-bounded non-deterministic Turing machine(a.k.a time-bound Mathematician) CHOOSES the context in which to interpret them in.

And I was thinking, what would the choice-function in the automaton's memory look like and how does it select the interpretation function so as to allows the automaton to recognize both formulas as the same TYPE of thing. An n-sphere(1). Otherwise known as a 'circle'.

And THEN I was thinking. Could we construct an algorithm which recognises both formulas as being different representations of the same TYPE of object? e.g the N-Sphere TYPE.

And LASTLY I was thinking: Could we construct a Polyglot-function of some kind that can recognize and categorize the equivalences across all the different dialects Mathematicians seem to be speaking to describe the same TYPES of things?

That would be the Univalence axiom. I guess?

What Mathematics is undergoing right now (transitioning from ZFC to Univalence) is nothing new to software engineers. We call it Code refactoring.

Come talk to us if you need help.
Last edited by Univalence on Fri May 24, 2019 11:24 am, edited 1 time in total.
Speakpigeon
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### Re: Any science of logic?

Univalence wrote: 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.
Logic has been understood from the start as an incomplete representation of human thought. That was 2,500 years ago and the situation hasn't changed I don't believe.
Logic is about making inferences. This is in fact a rather belated realisation from logicians. They sort of decided fairly recently that logic was fundamentally about the question of consequence.Yeah, you bet. Still, it doesn't say therefore anything, anything at all, as to whether premises are true. If you make an argument, you have to take responsibility for claiming your premises are true. If you decide to infer from experiments that light always travel at c, then you take responsibility for claiming your premises are true. Me, I don't have any problem with that. So, where's the problem already? Incompleteness? What's that?
Univalence wrote: Thu May 23, 2019 5:41 pm WHO does it is moot. SOMEBODY has to!
???
Nobody has to do anything. You do it if you want to. Whatever you do, that's your responsibility. We have 6 billion decision-makers on the planet already. There's no shortage and global warming won't change that fact.
Formal logic is a small aspect of what the human mind does. We all know that and it's never been any problem at all. The word "tree" doesn't describe the whole of reality either. Who cares? Are you going to not use the word "tree"?
Personally, I believe the brain is, like computers, essentially a physical process, probably something like a quantum mechanical one. I don't really care. I also think the brain, like computers, could be usefully described almost entirely through formal logic. We're not there. We won't be there for maybe 1000 years still. I don't care because I don't need that and I don't think anybody does. What's needed, possibly urgently, is a proper formal description of human logic. It doesn't exist at the moment and nobody seems to care. That's a shitload of wankers around there. There are something like millions of higher-education, formal-logic-trained, "intellectual" workers around the globe. What do they do? They pee face to the wind. Whoa. Impressive.
EB
Univalence
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### Re: Any science of logic?

Speakpigeon wrote: Fri May 24, 2019 10:50 am Logic has been understood from the start as an incomplete representation of human thought.
We can't even get off the conceptual ground here. That is not how I think about logic.
For starters - it hasn't been 'understood' since we are still busy trying to understand it.

For me, logic is about externalising the internal structure off my mind.
It's producing a concise language representing my mental models
Logic is language.
Mathematics is language.
Python is language.

They are ALL formal languages. And all formal languages have been classified into four conceptual categories.

One thing to be aware of is Linguistic relativity. You could go ahead and internalize a formal language.

As it is pertinently obvious - the "Mathematician" in this thread hasn't studied linguistics and so when I bend the meaning of the external language (Mathematics) which he has internalised, he gets triggered (despite his claims that words have no meaning).

We probably compute the same consequences. We just describe the process differently. So from his position of self-assigned authority - I am 'talking bullshit'.

I prefer to keep thought separate from language. This way I don't risk having my thinking influenced by other people's language.
Speakpigeon wrote: Fri May 24, 2019 10:50 am Logic is about making inferences.
This is incomplete. Thinking is more than just inferences.
Speakpigeon wrote: Fri May 24, 2019 10:50 am They sort of decided fairly recently that logic was fundamentally about the question of consequence.
I can agree with that, however, a simple consequence could have very complex causal factors. Many inputs - one output.
This is the principle of Equifinality

Another way to describe this is to say 'humans value determinism'. We want to examine a set of stochastic variables and arrive at a deterministic conclusion. Reduction of uncertainty if you will.
Speakpigeon wrote: Fri May 24, 2019 10:50 am If you decide to infer from experiments that light always travel at c, then you take responsibility for claiming your premises are true.
Me, I don't have any problem with that. So, where's the problem already? Incompleteness? What's that?
The problem is any argument which leads you to the conclusion: All parachutes open.
The argument is not true or false.

Last edited by Univalence on Fri May 24, 2019 12:10 pm, edited 2 times in total.
Univalence
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### Re: Any science of logic?

It's producing a concise language representing my mental models
In the above sentence really lies the actual problem.

How do I know that the formal language I have produced is a concise representation of my mental state?
Empirically. Can the meaning of the symbols be interpreted deterministically?

Code: Select all

``````express(mental-model) = language
interpret(language) = mental-moddel
interpret(express(mental-model)) = mental-model``````
We have languages that can do that.
Speakpigeon
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### Re: Any science of logic?

Univalence wrote: Fri May 24, 2019 11:34 am
Speakpigeon wrote: Fri May 24, 2019 10:50 am Logic has been understood from the start as an incomplete representation of human thought.
We can't even get off the conceptual ground here. That is not how I think about logic.
For starters - it hasn't been 'understood' since we are still busy trying to understand it.
Then you're using the word "logic" to mean not logic but thinking, possibly rational thinking I wouldn't know. Therefore, equivocation.
So the question is: Why are you using the wrong word? You're wasting your time!
Univalence wrote: Fri May 24, 2019 11:34 am For me, logic is about externalising the internal structure off my mind.
But then, you'd need to clarify the means to do that. I'm looking at a different but similar problem and I'm approaching it as an empirical enquiry. I look at the evidence: What people have said since and even before Aristotle. And what is my own logical intuition. I only looked at what mathematicians were saying about Aristotelian logic to sink each of their silly claims. I understand what I am doing. It's quite simple and transparent. What you're doing doesn't look like it's transparent. You can't even articulate your methodology as I did my own. The vocabulary is wrong (not "logic"), the stated objective seems way too ambitious. As I said, there have been megabucks invested in the same quest for a long time now with really little result. You're on your own? Logic is simple and I know I can do it. Thinking is a very different beast. The amount of data processed by just one brain every second beats all the computers that are running now and I think the picture will remain the same for quite some time still. I'm sure you understand that even the smallest of any realistic inference would already require absolutely massive computing power to solve. I believe myself that there's no existing computer that could replicate what the brain really does when it solves even simple problems, like deciding what the Cogito means. So, good luck.
Univalence wrote: Fri May 24, 2019 11:34 am
Speakpigeon wrote: Fri May 24, 2019 10:50 am Logic is about making inferences.
This is incomplete. Thinking is more than just inferences.
So we agree, I limit myself to logic, you are talking about something else, thinking, which is magnitudes more complex.
Univalence wrote: Fri May 24, 2019 11:34 am
Speakpigeon wrote: Fri May 24, 2019 10:50 am They sort of decided fairly recently that logic was fundamentally about the question of consequence.
I can agree with that, however, a simple consequence could have very complex causal factors. Many inputs - one output.
This is the principle of Equifinality
Yes, but because I limit myself to logic I don't care. You are going into the complexity of human thought and I'm not. Learn enough language to understand that the word "logic" doesn't mean, and never meant, "thought". This is a really very basic mistake.
EB
Univalence
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### Re: Any science of logic?

Speakpigeon wrote: Fri May 24, 2019 4:35 pm Then you're using the word "logic" to mean not logic but thinking, possibly rational thinking I wouldn't know. Therefore, equivocation.
Distinction without a difference.
Speakpigeon wrote: Fri May 24, 2019 4:35 pm So the question is: Why are you using the wrong word? You're wasting your time!
How did we get into the morality of language all of a sudden?

I use the word the way I see appropriate. If you don't like my use of the word... tough shit
Speakpigeon wrote: Fri May 24, 2019 4:35 pm So we agree, I limit myself to logic, you are talking about something else, thinking, which is magnitudes more complex.
Begging the question. What is logic?
Speakpigeon wrote: Fri May 24, 2019 4:35 pm Yes, but because I limit myself to logic I don't care. You are going into the complexity of human thought and I'm not. Learn enough language to understand that the word "logic" doesn't mean, and never meant, "thought". This is a really very basic mistake.
So you understand logic but you can't describe it and provide us with an empirical/scientific model? Great.

RCSaunders
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### Re: Any science of logic?

Univalence wrote: 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
It's nice to know someone knows who Shannon was, since his work was so important to modern digital transmission and storage. It is unfortunate that it was called, "information," theory. He was wrong about knowing the past, except imperfectly and incompletely, but he was right about not knowing (or being able to predict) the future.

But knowledge certainly is not, "history." While the future cannot be predicted, in fact, it can be predicted in principle, which is why science is successful. Every scientific principle of physics, electronics, and chemistry makes it possible to say, if this is done, this will be the consequence. It is why Shannon's rule of error detection and correction works just as predicted.
Univalence wrote: Thu May 23, 2019 2:50 pm 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.
You cannot predict the future. You cannot predict what anyone will have for a meal, for example, but you can say with certainty, if they include a few rosary peas in their dinner they will die. (Rosary peas contain abrin which is 75 times more toxic than ricin). You cannot predict how many cell phones will be produced and sold next year, but every cell phone works because the principles of electronics that define the millions of events that must occur for them to work are determined by principles which are absolute, and known.
Speakpigeon
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### Re: Any science of logic?

RCSaunders wrote: Fri May 24, 2019 6:11 pmYou cannot predict how many cell phones will be produced and sold next year, but every cell phone works because the principles of electronics that define the millions of events that must occur for them to work are determined by principles which are absolute, and known.
Nobody knows all possible causes of failure of a cellphone. You don't even know that your own cellphone works properly. All you can do is feel certain that it does, possibly based on empirical evidence. Certainty doesn't entail knowledge of whatever you're certain about. I'm certain of that. Evidence doesn't amount to the truth of whatever is being evidenced. Obviously.
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Speakpigeon
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### Re: Any science of logic?

Univalence wrote: Fri May 24, 2019 6:00 pm
Speakpigeon wrote: Fri May 24, 2019 4:35 pm Then you're using the word "logic" to mean not logic but thinking, possibly rational thinking I wouldn't know. Therefore, equivocation.
Distinction without a difference.
Seems you've run out of anything rational to say.
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Univalence
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### Re: Any science of logic?

Speakpigeon wrote: Sat May 25, 2019 10:23 am Seems you've run out of anything rational to say.
'rational' is not an adjective I use to describe language. Or thought.
Univalence
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### Re: Any science of logic?

RCSaunders wrote: Fri May 24, 2019 6:11 pm He was wrong about knowing the past, except imperfectly and incompletely
Throughout the other threads you have been happy to ignore the imperfection and incompleteness of that which you call "knowledge", but you are happy to critique Shannon on the same point. Why the double-standard?
RCSaunders wrote: Fri May 24, 2019 6:11 pm But knowledge certainly is not, "history."
All that which you call "knowledge" is a model of reality based on historical information. a.k.a evidence.
All models work. Until they don't. Some models work better than other models.

Past behaviour needs not be an indication of future behaviour.
RCSaunders wrote: Fri May 24, 2019 6:11 pm While the future cannot be predicted, in fact, it can be predicted in principle, which is why science is successful.
All scientific models work within their domain of applicability. Using a model outside of its operational limits is not what I would call "successful".
RCSaunders wrote: Fri May 24, 2019 6:11 pm Every scientific principle of physics, electronics, and chemistry makes it possible to say, if this is done, this will be the consequence.
Boring truism. There is always consequence. There is consequence for doing, and consequence for not-doing.
RCSaunders wrote: Fri May 24, 2019 6:11 pm You cannot predict the future.
And yet, in the paragraph above you predicted that IF one follows Shannon's guidelines and IF the communication channel is not too noisy then they will be able to detect errors. And you have predicted that errors that are detected can be corrected.

You are using models to make predictive claims while arguing that you can't make predictions.
RCSaunders wrote: Fri May 24, 2019 6:11 pm You cannot predict what anyone will have for a meal, for example, but you can say with certainty, if they include a few rosary peas in their dinner they will die. (Rosary peas contain abrin which is 75 times more toxic than ricin). You cannot predict how many cell phones will be produced and sold next year, but every cell phone works because the principles of electronics that define the millions of events that must occur for them to work are determined by principles which are absolute, and known.
It depends on your criteria for "successful prediction". Predictive models have all sorts of metrics associated with them. Fidelity, confidence intervals, sensitivity, specificity, recall.

Is all relative. I know what my father is going to have for dinner on Sunday. The same damn thing he has eaten every Sunday for 10 years. He's a creature of habit.
RCSaunders
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### Re: Any science of logic?

Speakpigeon wrote: Sat May 25, 2019 10:22 am Nobody knows all possible causes of failure of a cellphone.
They do know the reason they work when they do not fail, which was my only point.
RCSaunders
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### Re: Any science of logic?

I'm sorry, Univalence, I have apparently not made myself understood, but I have enjoyed the conversation. Hope your father enjoys his dinner.