Mathematicism

[Veritas Aequitas]

Godelian is one good example and practitioner of Mathematicism in a very fundamentalist and dogmatic sense.

Mathematicism is 'the effort to employ the formal structure and rigorous method of mathematics as a model for the conduct of philosophy'.[1] or else it is the epistemological view that reality is fundamentally mathematical.[2] The term has been applied to a number of philosophers, including Pythagoras[3] and René Descartes[4] although the term is not used by themselves.
https://en.wikipedia.org/wiki/Mathematicism

Those adopting Mathematicism indulge in the following;

Mathematical universe hypothesis
In physics and cosmology, the mathematical universe hypothesis (MUH), also known as the ultimate ensemble theory, is a speculative "theory of everything" (TOE) proposed by cosmologist Max Tegmark.[1][2] According to the hypothesis, the universe is a mathematical object in and of itself. Furthermore, Tegmark suggests that not only is the universe mathematical, but it is also computable.
https://en.wikipedia.org/wiki/Mathemati ... hypothesis

A proper discussion and debates of the Philosophy of Mathematics should contrast,
Mathematical Realism vs Mathematical antirealism.

Mathematical Realism is grounded on philosophical realism and/or metaphysical realism which basis is illusory.

Mathematical anti-realism [Kantian] is realistic as grounded on a human-based Framework and System [FSERC].

Discuss??
View??

[Veritas Aequitas]

Notes: KIV

[Veritas Aequitas]

Notes:

The uses and abuses of mathematics in early modern philosophy: introduction
https://link.springer.com/article/10.10 ... 017-1670-y

[godelian]

Godelian is one good example and practitioner of Mathematicism in a very fundamentalist and dogmatic sense.

I do not believe in mathematicism.

Mathematicism is 'the effort to employ the formal structure and rigorous method of mathematics as a model for the conduct of philosophy'

If a problem lends itself to the axiomatic or to the scientific or to the historical method -- most problems do not -- it is preferable to use one of these methods.

.[1] or else it is the epistemological view that reality is fundamentally mathematical.[2]

I do not believe that the physical universe is a mathematical object. I do believe, however, that it could be structurally similar to one.

Mathematical universe hypothesis
In physics and cosmology, the mathematical universe hypothesis (MUH), also known as the ultimate ensemble theory, is a speculative "theory of everything" (TOE) proposed by cosmologist Max Tegmark.[1][2] According to the hypothesis, the universe is a mathematical object in and of itself. Furthermore, Tegmark suggests that not only is the universe mathematical, but it is also computable.

I do not believe that the universe is a mathematical object. It could, however, be structurally similar to one. I also do not believe that the universe would be computable.

Mathematical anti-realism [Kantian] is realistic as grounded on a human-based Framework and System [FSERC].

There is nothing wrong with mathematical anti-realism. Mathematics can equally well be viewed as mere symbol manipulation. That is not wrong. In fact, that view is always correct.

Kant, however, was wrong to teach that natural numbers are not axiomatic. Less than a century later, the natural numbers were successfully axiomatized by Peano and Dedekind.

[Eodnhoj7]

Godelian is one good example and practitioner of Mathematicism in a very fundamentalist and dogmatic sense.

Mathematicism is 'the effort to employ the formal structure and rigorous method of mathematics as a model for the conduct of philosophy'.[1] or else it is the epistemological view that reality is fundamentally mathematical.[2] The term has been applied to a number of philosophers, including Pythagoras[3] and René Descartes[4] although the term is not used by themselves.
https://en.wikipedia.org/wiki/Mathematicism

Those adopting Mathematicism indulge in the following;

Mathematical universe hypothesis
In physics and cosmology, the mathematical universe hypothesis (MUH), also known as the ultimate ensemble theory, is a speculative "theory of everything" (TOE) proposed by cosmologist Max Tegmark.[1][2] According to the hypothesis, the universe is a mathematical object in and of itself. Furthermore, Tegmark suggests that not only is the universe mathematical, but it is also computable.
https://en.wikipedia.org/wiki/Mathemati ... hypothesis

A proper discussion and debates of the Philosophy of Mathematics should contrast,
Mathematical Realism vs Mathematical antirealism.

Mathematical Realism is grounded on philosophical realism and/or metaphysical realism which basis is illusory.

Mathematical anti-realism [Kantian] is realistic as grounded on a human-based Framework and System [FSERC].

Discuss??
View??

And there are irrational numbers....

[Impenitent]

Godelian is one good example and practitioner of Mathematicism in a very fundamentalist and dogmatic sense.

Mathematicism is 'the effort to employ the formal structure and rigorous method of mathematics as a model for the conduct of philosophy'.[1] or else it is the epistemological view that reality is fundamentally mathematical.[2] The term has been applied to a number of philosophers, including Pythagoras[3] and René Descartes[4] although the term is not used by themselves.
https://en.wikipedia.org/wiki/Mathematicism

Those adopting Mathematicism indulge in the following;

Mathematical universe hypothesis
In physics and cosmology, the mathematical universe hypothesis (MUH), also known as the ultimate ensemble theory, is a speculative "theory of everything" (TOE) proposed by cosmologist Max Tegmark.[1][2] According to the hypothesis, the universe is a mathematical object in and of itself. Furthermore, Tegmark suggests that not only is the universe mathematical, but it is also computable.
https://en.wikipedia.org/wiki/Mathemati ... hypothesis

A proper discussion and debates of the Philosophy of Mathematics should contrast,
Mathematical Realism vs Mathematical antirealism.

Mathematical Realism is grounded on philosophical realism and/or metaphysical realism which basis is illusory.

Mathematical anti-realism [Kantian] is realistic as grounded on a human-based Framework and System [FSERC].

Discuss??
View??

And there are irrational numbers....

and imaginary numbers...

-Imp

[Eodnhoj7]

Godelian is one good example and practitioner of Mathematicism in a very fundamentalist and dogmatic sense.



Those adopting Mathematicism indulge in the following;




A proper discussion and debates of the Philosophy of Mathematics should contrast,
Mathematical Realism vs Mathematical antirealism.

Mathematical Realism is grounded on philosophical realism and/or metaphysical realism which basis is illusory.

Mathematical anti-realism [Kantian] is realistic as grounded on a human-based Framework and System [FSERC].

Discuss??
View??

And there are irrational numbers....

and imaginary numbers...

-Imp

And imaginary irrational numbers....

[Noax]

Tegmark suggests that not only is the universe mathematical, but it is also computable.
...
A proper discussion and debates of the Philosophy of Mathematics should contrast,
Mathematical Realism vs Mathematical antirealism.

The realism part seems unnecessary to me, but most others seem to feel otherwise.
The MUH suffers from positing that all mathematical objects are real, meaning not just the rare interesting ones, but also the far more numerous utterly random mathematical objects.
From that, it can be shown that there are far more mathematical objects that contain observers in a state of having observed a universe like our than there are observers in the same state that have actually observed an ordered universe like ours. This problem was pointed out by Carroll in his paper about why Boltzmann Brains are a bad thing.

And imaginary irrational numbers....

You seem to imply that mathematics would have a problem with these.
You've barely covered how complex numbers can be. Imaginary numbers have but two components. Octonians have four. It doesn't seem to get more complete than that.

I do not believe in mathematicism.

Is this just an opinion, or is there any justification behind this disbelief?

[Eodnhoj7]

Tegmark suggests that not only is the universe mathematical, but it is also computable.
...
A proper discussion and debates of the Philosophy of Mathematics should contrast,
Mathematical Realism vs Mathematical antirealism.

The realism part seems unnecessary to me, but most others seem to feel otherwise.
The MUH suffers from positing that all mathematical objects are real, meaning not just the rare interesting ones, but also the far more numerous utterly random mathematical objects.
From that, it can be shown that there are far more mathematical objects that contain observers in a state of having observed a universe like our than there are observers in the same state that have actually observed an ordered universe like ours. This problem was pointed out by Carroll in his paper about why Boltzmann Brains are a bad thing.

And imaginary irrational numbers....

You seem to imply that mathematics would have a problem with these.
You've barely covered how complex numbers can be. Imaginary numbers have but two components. Octonians have four. It doesn't seem to get more complete than that.

I do not believe in mathematicism.

Is this just an opinion, or is there any justification behind this disbelief?

All I am saying is that given irrational numbers exist in math that mathematizing reality, to gain a coherent purely rational perspective, effectively doesn't change much.

[Noax]

All I am saying is that given irrational numbers exist in math that mathematizing reality, to gain a coherent purely rational perspective, effectively doesn't change much.

I think you are using two utterly different definitions of 'rational' in the same sentence, and somehow thinking they mean the same thing.

[Eodnhoj7]

All I am saying is that given irrational numbers exist in math that mathematizing reality, to gain a coherent purely rational perspective, effectively doesn't change much.

I think you are using two utterly different definitions of 'rational' in the same sentence, and somehow thinking they mean the same thing.

Rationality is the observation of ratios, relations. An irrational number that has no fixed ratio, no boundaries or limits so to speak does little to provide coherent order to existence and in many respects justifies imbalance. Mathematics can justify the chaotic nature of the universe and in doing so defeats it's own purpose.

[godelian]

I do not believe in mathematicism.

Is this just an opinion, or is there any justification behind this disbelief?

Philosophy is not a subdivision of mathematics, if only because philosophy is not axiomatic.

Well, the parts of philosophy that are axiomatic, have been absorbed by mathematics already.

For example, propositional calculus has successfully been axiomatized. Logic used to be a subdivision of philosophy but is nowadays a subdivision of mathematics.

On the other hand, general epistemology for example, is not axiomatic at all.

Karl Popper's seminal publication, "Science as falsification", points out a stubborn pattern in the practice of science. It is by observing the abstract world of scientific work, publications, and even conversations that Popper came to propose his famous epistemic findings, the nature of which are not axiomatic at all.

Concerning metaphysics, parts of it may be somewhat shifting to mathematics.

For example, Tarski's semantic theory of truth is a mathematical theory that currently seems to be the most effective correspondence theory of truth. But then again, there is more to metaphysics than just the analysis of the nature of truth.

There is indeed an ongoing process of mathematical conquest, annexation and infiltration, not just in philosophy, but also in other knowledge fields, assisted by relentless progress in software development, but I do not believe that all knowledge can be axiomatized.

In fact, it is mathematics itself that guarantees the impossibility to axiomatize all truth.

There is the provable existence of true but unprovable statements (Godel) and the provable undefinability of the truth (Tarski).

These two theorems would almost surely infect any axiomatic Theory of Everything, which we do not even have, but even if we did, would therefore fail to explain or predict most truth.

We cannot even know the full truth of true arithmetic. We cannot discover most of it:

https://en.m.wikipedia.org/wiki/True_arithmetic

In mathematical logic, true arithmetic is the set of all true first-order statements about the arithmetic of natural numbers.[1] This is the theory associated with the standard model of the Peano axioms in the language of the first-order Peano axioms.

This structure is known as the standard model or intended interpretation of first-order arithmetic. We cannot discover most of it:

The central result on true arithmetic is the undefinability theorem of Alfred Tarski (1936). It states that the set Th(N) is not arithmetically definable.

[Eodnhoj7]

I do not believe in mathematicism.

Is this just an opinion, or is there any justification behind this disbelief?

Philosophy is not a subdivision of mathematics, if only because philosophy is not axiomatic.

Well, the parts of philosophy that are axiomatic, have been absorbed by mathematics already.

For example, propositional calculus has successfully been axiomatized. Logic used to be a subdivision of philosophy but is nowadays a subdivision of mathematics.

On the other hand, general epistemology for example, is not axiomatic at all.

Karl Popper's seminal publication, "Science as falsification", points out a stubborn pattern in the practice of science. It is by observing the abstract world of scientific work, publications, and even conversations that Popper came to propose his famous epistemic findings, the nature of which are not axiomatic at all.

Concerning metaphysics, parts of it may be somewhat shifting to mathematics.

For example, Tarski's semantic theory of truth is a mathematical theory that currently seems to be the most effective correspondence theory of truth. But then again, there is more to metaphysics than just the analysis of the nature of truth.

There is indeed an ongoing process of mathematical conquest, annexation and infiltration, not just in philosophy, but also in other knowledge fields, assisted by relentless progress in software development, but I do not believe that all knowledge can be axiomatized.

In fact, it is mathematics itself that guarantees the impossibility to axiomatize all truth.

There is the provable existence of true but unprovable statements (Godel) and the provable undefinability of the truth (Tarski).

These two theorems would almost surely infect any axiomatic Theory of Everything, which we do not even have, but even if we did, would therefore fail to explain or predict most truth.

We cannot even know the full truth of true arithmetic:

https://en.m.wikipedia.org/wiki/True_arithmetic

In mathematical logic, true arithmetic is the set of all true first-order statements about the arithmetic of natural numbers.[1] This is the theory associated with the standard model of the Peano axioms in the language of the first-order Peano axioms.

This structure is known as the standard model or intended interpretation of first-order arithmetic.

The central result on true arithmetic is the undefinability theorem of Alfred Tarski (1936). It states that the set Th(N) is not arithmetically definable.

To argue what an axiom is takes it outside of mathematics into philosophy as an axiom in mathematics is not argued in pure mathematics, it can't be as pure mathematics is pure number, but "philosophy of mathematics".

_________

Scratch what I said, I misread your post...

[Veritas Aequitas]

Philosophy is not a subdivision of mathematics, if only because philosophy is not axiomatic.
Well, the parts of philosophy that are axiomatic, have been absorbed by mathematics already.
......
There is indeed an ongoing process of mathematical conquest, annexation and infiltration, not just in philosophy, but also in other knowledge fields, assisted by relentless progress in software development, but I do not believe that all knowledge can be axiomatized.
.......
In fact, it is mathematics itself that guarantees the impossibility to axiomatize all truth.

That you think Mathematics is 'King' and that philosophy is subservient to Mathematics is the sort of narrow thinking that underlies why all your philosophical views are bankrupt.

See:
What are Mathematical Axioms?
viewtopic.php?t=43481

Mathematics is the Servant of Philosophy
viewtopic.php?t=43482

in justifying why your above views are false and bankrupt.

[godelian]

That you think Mathematics is 'King' and that philosophy is subservient to Mathematics

"You think that ..." followed by your own invention, is not a valid quote. You are not even good at creating a strawman. Seriously, I am not going to respond to your bullshit.