Fun with logic, Peano and Constructivism!

[Skepdick]

https://philosophy.stackexchange.com/qu ... tructivism

One of the Peano axioms says:

For ALL natural numbers x and y, if x = y then y = x

And it got me curious. That’s a bit-flip - a mutation! The state of the system has changed: x and y have switched places! That is how learning works - arrival of new information!

And then I got even more curious. The Mathematical universe is (apparently ) immutable. I don't have a source for this view - it's just a feeling I've developed through interacting with Mathematicians - they abhor side-effects and insist on pure functions and referential transparency, so how does learning happen?

If the Mathematical universe was truly immutable, no information could ever leave it under observation. No Mathematician could ever learn anything about Mathematics.
(...continued...)

[TheVisionofEr]

That’s a bit-flip

I would say Kant agrees with you. After all, the Brits are a bit batty on their pretend world of pure absolute safe deductions from idealized axioms.

[RCSaunders]

If the Mathematical universe was truly immutable, no information could ever leave it under observation. No Mathematician could ever learn anything about Mathematics.
(...continued...)

There is no such thing as a, "mathematical universe." "Mathematics is a human invention for dealing with those aspects of existence which can be counted and measured. Outside human minds, mathematics does not exist at all.

[surreptitious57]

If the Mathematical universe was truly immutable no information could ever leave it under observation

While it is a deductive discipline that deals in proof it is also a body of knowledge that has increased over time
It creates new axioms when there are gaps that have to be filled and so in that sense it is not immutable at all
Such as for example the invention of the complex plane for a solution for the square roots of negative integers
There are also problems such as the Riemann Hypothesis which has remained unsolved for over a hundred years

[Skepdick]

There is no such thing as a, "mathematical universe." "Mathematics is a human invention for dealing with those aspects of existence which can be counted and measured. Outside human minds, mathematics does not exist at all.

You don't even know what the word "exist" means.

Mathematics is language. Like English is a language. In so far as languages are used for description - they both serve the same purpose.

[RCSaunders]

There is no such thing as a, "mathematical universe." "Mathematics is a human invention for dealing with those aspects of existence which can be counted and measured. Outside human minds, mathematics does not exist at all.

You don't even know what the word "exist" means.

Mathematics is language. Like English is a language. In so far as languages are used for description - they both serve the same purpose.

I didn't say mathematics does not exist, I said it does not exist outside human minds.

Mathematics, like the other knowledge methods, language, logic, geometry, and all knowledge desciplines, the sciences, history, geography, and the content of all literature are the creation of human minds. The all exist but only exist epistemologically, not materially or ontologically. If there were no human beings, there would be no language, mathematics, logic, geometry, science, history, geography, or literature.

[Skepdick]

I didn't say mathematics does not exist, I said it does not exist outside human minds.

Distinction without a difference. Your mind exists - it's part of broader existence.

Mathematics, like the other knowledge methods, language, logic, geometry, and all knowledge desciplines, the sciences, history, geography, and the content of all literature are the creation of human minds. The all exist but only exist epistemologically, not materially or ontologically. If there were no human beings, there would be no language, mathematics, logic, geometry, science, history, geography, or literature.

Everything that "exists ontologically" is described in Math - all of physics.

The software that runs your computer - it exists outside of human minds. It's math. It exists ontologically in the memory of your computer.
If all human beings vanished today - our math would remain.

Human knowledge neither describes, nor prescribes how the world is. it inscribes it.

[RCSaunders]

I didn't say mathematics does not exist, I said it does not exist outside human minds.

Distinction without a difference. Your mind exists - it's part of broader existence.

Mathematics, like the other knowledge methods, language, logic, geometry, and all knowledge desciplines, the sciences, history, geography, and the content of all literature are the creation of human minds. The all exist but only exist epistemologically, not materially or ontologically. If there were no human beings, there would be no language, mathematics, logic, geometry, science, history, geography, or literature.

Everything that "exists ontologically" is described in Math - all of physics.

Do you mean, "described by Math?" Surely existents aren't described in Math.

The software that runs your computer - it exists outside of human minds. It's math. It exists ontologically in the memory of your computer.

The "software" in any computer is nothing but physical states and has no more meaning than a bank of switches, some tuned on and some turned off. There is no knowledge or, "math," in a computer. We computer engineers use math to design computers and write software, but in a computer they are just states with no meaning whatsoever.

If all human beings vanished today - our math would remain.

Where would it be and in what form?

Human knowledge neither describes, nor prescribes how the world is. it inscribes it.

Well, I cannot argue with that, since I have no idea what you are talking about.

[Scott Mayers]

If the Mathematical universe was truly immutable, no information could ever leave it under observation. No Mathematician could ever learn anything about Mathematics.
(...continued...)

There is no such thing as a, "mathematical universe." "Mathematics is a human invention for dealing with those aspects of existence which can be counted and measured. Outside human minds, mathematics does not exist at all.

I'm atheist. Given a reality where 'god' cannot be scientificaly rationalized, whatever we are made up of, if by 'laws', these have no foundation for being "obeyed" even by nature without some underlying LOGIC of abstract factors that lack any SPECIAL case, like our particular Universe that has laws. As such, reality HAS TO BE 'mathematical' (ie logical) with the only 'constants' possible as "absolutely nothing" or "absolutely everything" as elemental inputs.

Think of reality as merely abstract pieces or bits based upon nothing at all. OF the chaos of information, the bits can be arranged in unendingly different ways such that some form patterns while others do not. Those that form patterns are the foundation of worlds like ours. You can't presume that WE are the abitors of our own underlying existence for being able to "sense" ourselves. If math wasn't more real than our local manifestation of it, not even physics can justly USE math to prove anything. Or do you expect to prove how you yourself can build a house with an imaginary set of tools? You can't ignore nor trivialize this without begging our senses are 'gods' themselves unqualifiably.

[RCSaunders]

Think of reality as merely abstract pieces or bits based upon nothing at all.

Why would anyone think of reality in terms of a bad metaphor. Reality is not, "made up," of anything. Reality is simply all that is (exists) and has the nature it has, indepenedent of anyone's consciousness or knowledge of it.

Some aspects of reality are countable (because there are a multiplicity existents) and some aspects can be measured by the human method of applying counting to relationships as though they had parts (which factually, they do not). Counting is always exact. If there are eighteen entities, and I count them, there are exactly eighteen. But all measurement requires some arbitrary human invented unit of measure that is seldom perfectly commensurate with any actual entity's relative magnitude. If I measure something as eighteen inches long, it is very likely slightly less or more than eighteen inches long. Some relationships cannot be measured at all and are called incommensurables.

Mathematics is only a specialized form of language for describing those aspects of reality which can be described in countable or measurable terms. Reality is no more mathematical than it is
Greek or Spanish, because it can be described in those languages.

Please describe the physical properties of clockwise, left and right, above and below, inside and outside, using only numbers and mathematical symbols.

[nothing]

I'm atheist. Given a reality where 'god' cannot be scientificaly rationalized, whatever we are made up of, if by 'laws', these have no foundation for being "obeyed" even by nature without some underlying LOGIC of abstract factors that lack any SPECIAL case, like our particular Universe that has laws. As such, reality HAS TO BE 'mathematical' (ie logical) with the only 'constants' possible as "absolutely nothing" or "absolutely everything" as elemental inputs.

Excellent post - made me happy reading.

To approach this idea in another way:

wherein {alpha+/-omega} serve as a universally bestowed, locally employed null binary
which can be assumed by any (meta-)physical binary relationship:
conjugation, reciprocation, denial (ie. thesis/antithesis) etc.

If we say all-knowing is a valid state (ie. as often attributed to 'god') then
...to know {all thus not} to believe...
indefinitely approaches such an all-knowing state,
revealing that {knowledge and belief} are antithetical, thus:
all knowledge negates all belief-based ignorance(s) ad infinitum.

If Satan had a phallus, he'd have named it 'BELIEF'
would that all "believers" be incessant suckers.
-nothing

That one will sting the "believers".

[Skepdick]

Do you mean, "described by Math?" Surely existents aren't described in Math.

Existents are described in language.

The trouble is that you don't see the difference between describing "The Universe" and describing "the color red".

Both the Kolmogorov complexity and Descriptive complexity theory is Math.

They are formal frameworks that allow you to capture/quantify/understand what complexity is.

The "software" in any computer is nothing but physical states and has no more meaning than a bank of switches, some tuned on and some turned off.

Exactly! The state of the system is described in the language of Boolean Logic.

More complex systems are described by more complex logics, but they are described in logics.

Obviously. Because that is what we use logic/mathematics for - to design the things we make.

There is no knowledge or, "math," in a computer. We computer engineers use math to design computers and write software, but in a computer they are just states with no meaning whatsoever.

"We" you are no engineer if you think the state of the system has "no meaning". The state of the system which you programmed is in your control.

Control engineering

Where would it be and in what form?

The software of every man-made computer.

Well, I cannot argue with that, since I have no idea what you are talking about.

I am talking about mutability/inter-dependence.

Western Philosophy tries to study the world by pretending the observer doesn't exist; by pretending the observer doesn't matter. It's all about "mind independence" and "objectivity". To maintain this idiotic view on knowledge requires you to ignore all the technology we keep building in order to acquire knowledge.

All the technology we keep building wouldn't exist without mathematics. Neither would our knowledge.

[Scott Mayers]

Think of reality as merely abstract pieces or bits based upon nothing at all.

Why would anyone think of reality in terms of a bad metaphor. Reality is not, "made up," of anything. Reality is simply all that is (exists) and has the nature it has, indepenedent of anyone's consciousness or knowledge of it.

Some aspects of reality are countable (because there are a multiplicity existents) and some aspects can be measured by the human method of applying counting to relationships as though they had parts (which factually, they do not). Counting is always exact. If there are eighteen entities, and I count them, there are exactly eighteen. But all measurement requires some arbitrary human invented unit of measure that is seldom perfectly commensurate with any actual entity's relative magnitude. If I measure something as eighteen inches long, it is very likely slightly less or more than eighteen inches long. Some relationships cannot be measured at all and are called incommensurables.

Mathematics is only a specialized form of language for describing those aspects of reality which can be described in countable or measurable terms. Reality is no more mathematical than it is
Greek or Spanish, because it can be described in those languages.

Please describe the physical properties of clockwise, left and right, above and below, inside and outside, using only numbers and mathematical symbols.

We are stuck with using models and symbols to communicate. But these are reflecting the reality if we aren't speaking of just the symbols themselves. The reality cannot be 'special' (by being 'finitely' fixed to some particular history) on the whole or it reduces to a religious interpretation. While we may not be able to scientifically or rationally prove all of what Totality is, if you presume our own backyard IS the reality since it is "all that matters" to most, then you are biased to practical 'truths' only.

Like I said, I am not religious and can even argue against specific religious claims and its irrationality. As such, reality has to be based upon nothing and/or absolutely everything. Anything else in between can only be a subset of it only. As such, reality has to be simple on its most fundamental level.

I happen to be working on just such a theorem and contrary to your presumption of "left/right", "above/below", "clockwise/counterclockwise", etc, these CAN be expressed in language and logic. Because the language is itself NOT the reality, for someone like yourself, you may not likely ever WANT to hear such a description beyond the practical. I'm not concerned but know that the reality and the abstractions ARE the same on a fundamental level.

I gave the puzzle-pixel example because most can relate to how the pieces/pixels do not require having meaning, can have patterns, and demonstrate even more combinations that lack any pattern at all, ....like the old air channels 'off-air'. I don't know what problem you have with this example but don't think any other would matter to you given that one is very simplistic itself.

[RCSaunders]

Think of reality as merely abstract pieces or bits based upon nothing at all.

Why would anyone think of reality in terms of a bad metaphor. Reality is not, "made up," of anything. Reality is simply all that is (exists) and has the nature it has, indepenedent of anyone's consciousness or knowledge of it.

Some aspects of reality are countable (because there are a multiplicity existents) and some aspects can be measured by the human method of applying counting to relationships as though they had parts (which factually, they do not). Counting is always exact. If there are eighteen entities, and I count them, there are exactly eighteen. But all measurement requires some arbitrary human invented unit of measure that is seldom perfectly commensurate with any actual entity's relative magnitude. If I measure something as eighteen inches long, it is very likely slightly less or more than eighteen inches long. Some relationships cannot be measured at all and are called incommensurables.

Mathematics is only a specialized form of language for describing those aspects of reality which can be described in countable or measurable terms. Reality is no more mathematical than it is
Greek or Spanish, because it can be described in those languages.

Please describe the physical properties of clockwise, left and right, above and below, inside and outside, using only numbers and mathematical symbols.

We are stuck with using models and symbols to communicate. But these are reflecting the reality if we aren't speaking of just the symbols themselves. The reality cannot be 'special' (by being 'finitely' fixed to some particular history) on the whole or it reduces to a religious interpretation. While we may not be able to scientifically or rationally prove all of what Totality is, if you presume our own backyard IS the reality since it is "all that matters" to most, then you are biased to practical 'truths' only.

I have no idea what you are talking about. The use of symbols is hardly being, "stuck." It is the method human beings have discovered to from concepts by which all knowledge is held.

The rest of what you said seems totally irrelevant to the point. My original statement to which you responded was, "There is no such thing as a, 'mathematical universe.' "Mathematics is a human invention for dealing with those aspects of existence which can be counted and measured. Outside human minds, mathematics does not exist at all."

My only point was that everything cannot be explained or understood in terms of mathematics alone, because, even physical existence has attributes that mathematics alone cannot describe, like the examples I provided. My very point is, it takes language that is not mathematical to identify those attributes.

Like I said, I am not religious and can even argue against specific religious claims and its irrationality.

What has that got to do with anything. It's good that you are not superstitious and hold no mystical view. Either do I.

I happen to be working on just such a theorem and contrary to your presumption of "left/right", "above/below", "clockwise/counterclockwise", etc, these CAN be expressed in language and logic.

Well don't strain yourself on your theorem, since it's already been done. It's called epistemology and means all knowledge is made possible and is only possible by means of language, and is exactly the point I was making, that mathematics is only a subset of language, like logic and geometry are subsets of language.

[Scott Mayers]

I have no idea what you are talking about. The use of symbols is hardly being, "stuck." It is the method human beings have discovered to from concepts by which all knowledge is held.

The rest of what you said seems totally irrelevant to the point. My original statement to which you responded was, "There is no such thing as a, 'mathematical universe.' "Mathematics is a human invention for dealing with those aspects of existence which can be counted and measured. Outside human minds, mathematics does not exist at all."

My only point was that everything cannot be explained or understood in terms of mathematics alone, because, even physical existence has attributes that mathematics alone cannot describe, like the examples I provided. My very point is, it takes language that is not mathematical to identify those attributes.

Then you defined your limits. I personally don't care for those who lock the door to discussion but speak anyways as though you have any relevance to add. You stated your position and there's no more to discuss with you.