Theists Equivocating the Empirical with the Transcendental

Is there a God? If so, what is She like?

Moderators: AMod, iMod

Skepdick
Posts: 9319
Joined: Fri Jun 14, 2019 11:16 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by Skepdick »

godelian wrote: Thu Jun 23, 2022 3:39 am If you switch to prefix notation, such as in Lisp, the compiler has a much simpler core. If you switch to postfix, such as in assembler, there is not even a need for a real compiler front end.
This has nothing to do with the notation or your compiler, it's simply a matter of how your underlying architecture handles data input.

Example: Is the string "4 5 +" in prefix or postfix notation?
Answer: It's in whichever notation you want.

It's prefix if you read it right-to-left; and postfix if you read it left-to-right, as I am sure you would agree ReverseString() is a function.

And, of course, I am assuming that the underlying architecture treats the string "4 5 +" as an atomic entity, and not as a stream of symbols.

This is lexical analysis and tokenization 101 stuff.
User avatar
Immanuel Can
Posts: 15538
Joined: Wed Sep 25, 2013 4:42 pm

Re: Theists Equivocating the Empirical with the Transcendental

Post by Immanuel Can »

godelian wrote: Thu Jun 23, 2022 3:39 am
Immanuel Can wrote: Thu Jun 23, 2022 2:36 am That's again only half the story. The idea of a totally inapplicable mathematics is futile. Mathematics is vindicated not merely by its formal elegance, but also by its efficacy and accuracy in representing empirical situations.
Yes, but this efficacy is a concern only for scientists, engineers, and anybody else who desires to apply it to real-world situations. It is not a concern for mathematics.
But that's the point: maths isn't a thing that "just exists" somewhere out in an imaginary Platonic realm. It was always a product of empirical situations in the first place. It's a tool we use in order to get a handle on the empirical, and in any matter in which it remains only self-relevant, it's not actually relevant at all.
Science and engineering seek to be meaningful and even seek to be useful. Mathematics does not.
Mathematics does not "seek." It's not a person. It has no teleology of its own.

But what's interesting, and most remarkable, is that we live in a universe that can be rationally described through the tool, mathematics. That's really astonishing, if we suppose the universe is nothing but the product of a cosmic accident. Why shoulld we be in a universe that was amenable to rational analyses at all? And why should we human beings be capable of utilizing that tool, mathematics, to unpack the universe as we do?
...mathematics itself...strives to be meaningless and useless
You're anthropomorphizing again. Maths do not "strive" for anything. Nor do they aspire, intend, aim, labour, try, or long. If mathematics has any ultimate purpose, any teleology, it is not anything that the mathematics themselves tell us anything about. It has to be some sort of purpose external to the equations. And this is what makes maths seem "meaningless": that the meaning of the equations and symbols is not at all available from within that system of equations and symbols itself.

It comes from beyond them, if it comes at all.
mathematics...is purposely..
Another anthropomorphism, surely. Maths do not "purpose" anything, anymore than they "strive."
After proper axiomatization, this source of inspiration became completely irrelevant.
Irrelevant to what? :shock:

You mean "irrelevant to whether or not the maths can perform operations with their closed symbol system"? That might be true. But that's just a further indication that the teleology or purpose of mathematics does not come from within mathematics itself.
The correspondence theory of truth is therefore inapplicable to mathematics.
I think you misunderstand me. I'm not plugging for a "correspondence theory." I'm pointing out that the lack of a purpose or meaning for maths is a product of the fact that mathematics has no teleology discernable within the system itself.

The same could be said of any symbol system. They are tools employed by conscious entities, not self-justified, Platonic realities. Their purpose has to be discerned from outside the symbol system itself.

Maths has no internal claims about its own purpose, goal or outcome. That does not mean maths has none.
Operator precedence is an issue that only exists in the infix notation, which is indeed ambiguous. It does not exist in the postfix or prefix notations, because these alternative notations are not ambiguous.

Infix notation along with the Eulerian notation for function application are costly conventions, because they are so ambiguous. These things tremendously complicate the construction of compiler front ends. If you switch to prefix notation, such as in Lisp, the compiler has a much simpler core. If you switch to postfix, such as in assembler, there is not even a need for a real compiler front end.
Sorry...you've lost me.

Perhaps you're into refined technical concepts here with which I lack familiarity.
godelian
Posts: 90
Joined: Wed May 04, 2022 4:21 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by godelian »

Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm But that's the point: maths isn't a thing that "just exists" somewhere out in an imaginary Platonic realm. It was always a product of empirical situations in the first place.
The divorce from physical reality happened 2500 years ago already. This divorce is a logical consequence of Aristotle's foundationalist concern. Aristotle did not want empirical mathematics. Euclid did not want that either. We simply continued on that path.
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm It's a tool we use in order to get a handle on the empirical
It is not a tool to get a handle on the empirical. Science is. Engineering is. Mathematics is not.
Mathematics is a tool to get a handle on language that deals with quantities, sets, and other mathematical abstractions.
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm and in any matter in which it remains only self-relevant, it's not actually relevant at all.
As Hardy wrote, "real mathematics is on the whole not useful". This is by design.
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm
Mathematics does not "seek." It's not a person. It has no teleology of its own.
Mathematics reflects the ideas that come from its grandees, starting with people such as Pythagoras, Aristotle, and Euclid. These people did "seek". In fact, everybody mentioned in mathematical publications has been "seeking".
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm Why shoulld we be in a universe that was amenable to rational analyses at all? And why should we human beings be capable of utilizing that tool, mathematics, to unpack the universe as we do?
Mathematics strives to maintain consistency in the language about quantity. The universe is mostly deemed consistent and often also readily quantified. Hence, there seems to be some equiconsistency between mathematics and our quantifiable observations of the physical universe.

For me the link is about: quantifiability and equiconsistency. Besides that, I do not believe that there is a link.
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm
You're anthropomorphizing again. Maths do not "strive" for anything. Nor do they aspire, intend, aim, labour, try, or long.
Mathematics is nothing else than the thoughts and conversations of the mathematicians of the past. They all strove, aspired, intended, aimed, laboured, tried and longed.
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm
Irrelevant to what? :shock:
Irrelevant to the work of the mathematicians of the past, who produced our theories and theorems. More contemporary mathematicians do not care about empiricism either. I have never read anything by Gödel, Tarski, Hilbert, Frege, Zermelo, or Von Neumann in which they were interested in empirical reality. Did Cantor care about empirical reality? I don't think so.

So, another reason why empirical reality is irrelevant in mathematics, is because pretty much no published mathematician ever seemed to care.
User avatar
Immanuel Can
Posts: 15538
Joined: Wed Sep 25, 2013 4:42 pm

Re: Theists Equivocating the Empirical with the Transcendental

Post by Immanuel Can »

godelian wrote: Thu Jun 23, 2022 4:19 pm
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm But that's the point: maths isn't a thing that "just exists" somewhere out in an imaginary Platonic realm. It was always a product of empirical situations in the first place.
The divorce from physical reality happened 2500 years ago already.
When did facts start getting "divorces"?

Another anthropomorphism, I'm guessing?
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm It's a tool we use in order to get a handle on the empirical
It is not a tool to get a handle on the empirical.
Mathematics is a tool to get a handle on language that deals with quantities.
Right. Because the empirical has no quantities in it... :wink:
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm Mathematics does not "seek." It's not a person. It has no teleology of its own.
Mathematics reflects the ideas that come from its grandees, starting with people such as Pythagoras, Aristotle, and Euclid. These people did "seek". In fact, everybody mentioned in mathematical publications has been "seeking".
These people were also empirical.
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm Why shoulld we be in a universe that was amenable to rational analyses at all? And why should we human beings be capable of utilizing that tool, mathematics, to unpack the universe as we do?
The universe is mostly deemed consistent
"Consistent?" In what regard? And who is doing this "deeming"? On what basis?

Not entropically, for certain. And we know it's not eternal, for both empirical and mathematical reasons. But what I'm pointing out is how amazing the existence of regularities in the universe, especially those permitting things like life, cognition and mathematics itself, really are. They are nothing we should have expected: and the mathematical improbability of them is literally "astronomical."
Immanuel Can wrote: Thu Jun 23, 2022 2:07 pm You're anthropomorphizing again. Maths do not "strive" for anything. Nor do they aspire, intend, aim, labour, try, or long.
Mathematics is nothing else than the thoughts and conversations of the mathematicians of the past.

Wait...I thought you were advocating that it was a Platonic reality? :? Now you're arguing it's a social construct?

Let's keep our langauge clear, then. Maths do not have opinions, teleology, strivings, etc. Mathematics itself has no view of what it "should" be. And if any human beings do, then that is an empirical claim, not a mathematical one.
godelian
Posts: 90
Joined: Wed May 04, 2022 4:21 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by godelian »

Immanuel Can wrote: Thu Jun 23, 2022 4:46 pm These people were also empirical.
Take for example Lowenheim-Skolem theorem. What empirical element do you detect in the following explanation:
Wikipedia on "Lowenheim-Skolem" wrote: [The theorem] implies that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ, and that no first-order theory with an infinite model can have a unique model up to isomorphism. As a consequence, first-order theories are unable to control the cardinality of their infinite models.

The (downward) Löwenheim–Skolem theorem is one of the two key properties, along with the compactness theorem, that are used in Lindström's theorem to characterize first-order logic. In general, the Löwenheim–Skolem theorem does not hold in stronger logics such as second-order logic.
Please, explain what empirical elements the explanation above would be about.
User avatar
Immanuel Can
Posts: 15538
Joined: Wed Sep 25, 2013 4:42 pm

Re: Theists Equivocating the Empirical with the Transcendental

Post by Immanuel Can »

godelian wrote: Thu Jun 23, 2022 6:06 pm
Immanuel Can wrote: Thu Jun 23, 2022 4:46 pm These people were also empirical.
Take for example Lowenheim-Skolem theorem.
I'm sorry...you're outside my field of familiarity. I can't speak to that, at least not with any degree of accuracy.
bobmax
Posts: 129
Joined: Fri Jun 03, 2022 7:38 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by bobmax »

godelian wrote: Thu Jun 23, 2022 4:19 pm The divorce from physical reality happened 2500 years ago already.
It was then that humanity embarked on the Parmenidean path of the night.

In my opinion, an inevitable choice.

Because rationality had to necessarily take over.
And with it, by now understood as the source of Truth, nihilism could only make its way.

Be faithful to the earth!
Nietzsche warned.
But we betrayed the earth. We could only betray it. Following rationality.

But since nihilism is the other side of the coin of rationality, we have also fed nihilism.
Up to having to face it.
godelian
Posts: 90
Joined: Wed May 04, 2022 4:21 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by godelian »

bobmax wrote: Thu Jun 23, 2022 7:04 pm But since nihilism is the other side of the coin of rationality, we have also fed nihilism.
Pure Reason requires blind faith in first principles. You can choose first principles in whichever way you want, but Pure Reason is impossible without them.

Nihilism is about having no such first principles.

How can choosing first principles for the purpose of Pure Reason be compatible with nihilism which advocates not choosing any at all?
bobmax
Posts: 129
Joined: Fri Jun 03, 2022 7:38 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by bobmax »

godelian wrote: Fri Jun 24, 2022 1:26 am
bobmax wrote: Thu Jun 23, 2022 7:04 pm But since nihilism is the other side of the coin of rationality, we have also fed nihilism.
Pure Reason requires blind faith in first principles. You can choose first principles in whichever way you want, but Pure Reason is impossible without them.

Nihilism is about having no such first principles.

How can choosing first principles for the purpose of Pure Reason be compatible with nihilism which advocates not choosing any at all?
Nihilism is the certainty that there is no value.

Where does this certainty come from?

From the rational interpretation of the world.

I use the term "rationality" to mean the intellect, that is, the logical processing capacity of the brain.
While by "Reason" I mean the faculty that includes rationality but is not exhausted in it, it surpasses it.

Reason uses rationality but perceives its limits.
However, when rationality is understood to coincide with reason, that is, reason is lost in it, here is nihilism!

Because logic in itself has no value.

Rationality is based on the interpretation of the world as multiple.
I would say that his heart is the same principle of identity.
Without respecting this principle, no rational thought would be possible.

And it is possible precisely through separation.
Which is a denial. A = A
A is not B, C, D...

However, when this principle becomes absolute Truth ... here is nihilism!

2 is the origin of all evil.

But the manifold is only the path of the night. At any time we can leave it and follow the path of the day.
Skepdick
Posts: 9319
Joined: Fri Jun 14, 2019 11:16 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by Skepdick »

bobmax wrote: Fri Jun 24, 2022 8:29 am Which is a denial. A = A
A=A is just an axiom. Like all axioms it's contingent upon the will of the axiomatiser.

You can choose to accept the axiom.

Code: Select all

In [1]: class Something: pass
In [2]: A = Something()
In [3]: A == A
Out[3]: True
Or you can choose to reject the axiom.

Code: Select all

In [1]: class Something:
   ...:     def __eq__(self, other):
   ...:         return False
   ...:
In [2]: A = Something()
In [3]: A == A
Out[3]: False
None of this has any bearing on the process of computation - nothing bad or tragic happens when A != A.
And you can be as outraged as you want about the rejection of the first "law" of thought, but is it really a law?

A != A is a perfectly coherent and meaningful thing to say in English and is in no way nihilistic.

Now is not now.
bobmax
Posts: 129
Joined: Fri Jun 03, 2022 7:38 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by bobmax »

Skepdick wrote: Fri Jun 24, 2022 9:08 am
bobmax wrote: Fri Jun 24, 2022 8:29 am Which is a denial. A = A
A=A is just an axiom. Like all axioms it's contingent upon the will of the axiomatiser.

You can choose to accept the axiom.

Code: Select all

In [1]: class Something: pass
In [2]: A = Something()
In [3]: A == A
Out[3]: True
Or you can choose to reject the axiom.

Code: Select all

In [1]: class Something:
   ...:     def __eq__(self, other):
   ...:         return False
   ...:
In [2]: A = Something()
In [3]: A == A
Out[3]: False
None of this has any bearing on the process of computation - nothing bad or tragic happens when A != A.
And you can be as outraged as you want about the rejection of the first "law" of thought, but is it really a law?

A != A is a perfectly coherent and meaningful thing to say in English and is in no way nihilistic.

Now is not now.
You cannot logically deny that A = A.

Because it is the foundation of logic.

It has nothing to do with accepting an axiom or not.

Your example is based on A = A

There is no rational construction that can establish that A != A

I have the impression that these computers are overrated ...
Skepdick
Posts: 9319
Joined: Fri Jun 14, 2019 11:16 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by Skepdick »

bobmax wrote: Fri Jun 24, 2022 10:01 am You cannot logically deny that A = A.

Because it is the foundation of logic.
It's not a foundation of any kind. It's just an axiom. There are logics which accept the axiom (e.g classical logic); and there are logics which reject the axiom e.g Schrödinger logic.

Here is the important bit:
These logics are motivated by the consideration that in quantum mechanics, elementary particles may be indistinguishable, even in principle, on the basis of any measurement. This in turn suggests that such particles cannot be considered as self-identical objects in the way that such things are usually treated within formal logic and set theory.
So you know what that means in practice? If you are committed to a logic which accepts the identity axiom while you happen to live in a quantum-mechanical universe; then you have chosen the wrong tool to reason about the universe you live in.
bobmax wrote: Fri Jun 24, 2022 10:01 am It has nothing to do with accepting an axiom or not.
Yes it does. It's just a choice.

I can choose to accept A=A as true.
I can choose to accept the negation of A=A as true.
bobmax wrote: Fri Jun 24, 2022 10:01 am Your example is based on A = A

There is no rational construction that can establish that A != A
You have confused yourself over notation/syntax. A != A is syntactically equivalent to not(A=A).
However you formulate it - it doesn't really matter in a system in which identity does not hold.

In English the expression A=A means "Is A the same as A?". It's a question, not a statement.
If A=A is true then A is the same as A.
If A=A is false then A is not the same as A.

Below is a perfectly rational construction. An abstract object which does not obey the identity axiom.
Constructively speaking - this is a valid proof for the existence of the object!

Code: Select all

In [1]: class Something:
   ...:     def __eq__(self, other):
   ...:         return False
   ...:

In [2]: A = Something()
In [3]: A == A
Out[3]: False
In [4]: A != A
Out[4]: True
In [5]: not(A == A)
Out[5]: True

bobmax wrote: Fri Jun 24, 2022 10:01 am I have the impression that these computers are overrated ...
And I have the impression that logic is a religion; and if you deem A=A as a sacred cow - then I also have the impression that you are religious.
bobmax
Posts: 129
Joined: Fri Jun 03, 2022 7:38 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by bobmax »

Skepdick wrote: Fri Jun 24, 2022 11:33 am In English the expression A=A means "Is A the same as A?". It's a question, not a statement.
If A=A is true then A is the same as A.
If A=A is false then A is not the same as A.
You are kidding me.
Beyond the signs, the concept should be clear.
In the search for Truth, A is A becomes a problem.

But ok, for you A is A and also A is not A.
At this point no speech is possible. Even without using signs.
Bye.
Skepdick
Posts: 9319
Joined: Fri Jun 14, 2019 11:16 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by Skepdick »

bobmax wrote: Fri Jun 24, 2022 3:54 pm You are kidding me.
Beyond the signs, the concept should be clear.
The concept is perfectly clear. It's just not universally applicable to all other concepts we converse about. In particular the identity axiom severely restricts our ability to talk about change over time!

A rose is a rose. ( A = A)
Now is not now. ( B ! =B)

This is a trivial distinction in any many-sorted logic.
What applies to A doesn't always apply to B and it's far closer to English than Classical logic!
bobmax wrote: Fri Jun 24, 2022 3:54 pm
In the search for Truth, A is A becomes a problem.
Why is it a "problem"?

What was True now is not True now - Truth changed!
bobmax wrote: Fri Jun 24, 2022 3:54 pm
But ok, for you A is A and also A is not A.
No! For me A=A has no truth-value a priori- it's just a proposition.

It could be true. A rose is a rose. ( A = A)
It could be false. Now is not now. (A !=A)

bobmax wrote: Fri Jun 24, 2022 3:54 pm
At this point no speech is possible. Even without using signs.
I think you are over-exaggerating. Absolutely nothing is hindering speech. Except your religious assumption that A=A is gospel.

And even that's not hindering your speech. It's only hindering my speech. Should you choose to restrict my speech to your axiom.
bobmax wrote: Fri Jun 24, 2022 3:54 pm
Bye.
Au revoir. Interacting with believers never leads to a constructive dialogue anyway. They just want to preach, not reconsider their beliefs.
godelian
Posts: 90
Joined: Wed May 04, 2022 4:21 am

Re: Theists Equivocating the Empirical with the Transcendental

Post by godelian »

bobmax wrote: Fri Jun 24, 2022 8:29 am Because logic in itself has no value.
In the formalist ontology, logic is indeed not "about" anything at all.
bobmax wrote: Fri Jun 24, 2022 8:29 am Rationality is based on the interpretation of the world as multiple.
I personally think that the intuitionist ontology is not particularly helpful. Computing devices can mechanically verify the correctness of a proof, and sometimes even discover proof. These machines do not have intuition.
bobmax wrote: Fri Jun 24, 2022 8:29 am I would say that his heart is the same principle of identity.
Without respecting this principle, no rational thought would be possible.
Restrictions to the law of identity actually do appear in certain types of logic:
Wikipedia on "Schrodinger logics" wrote: Schrödinger logics are a kind of non-classical logic in which the law of identity is restricted. These logics are motivated by the consideration that in quantum mechanics, elementary particles may be indistinguishable, even in principle, on the basis of any measurement. This in turn suggests that such particles cannot be considered as self-identical objects in the way that such things are usually treated within formal logic and set theory. [1]
The problem of indistinguishable abstract objects also occurs with nonstandard numbers:
Victoria Gitman on "nonstandard models of arithmetic" wrote: In particular, a nonstandard model of arithmetic can have indiscernible numbers that share all the same properties.
Even if the law of identity applies to the intended interpretation (universe) of the theory, we may want to consider that theories that generate a potentially infinite universe always have nonstandard interpretations (universes). The law of identity may break down in (some sectors of) such nonstandard universe.

Note that this happens in spite of the fact that the law of identity was intended to apply. Depending on their construction logic, we cannot control or prevent nonstandard interpretations of a theory from arising. They simply also exist alongside the intended one.
Post Reply