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Is Mathematics Real? (2020)

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Re: Is Mathematics Real? (2020)

#51

Post by ukj »

myWindoonn wrote: post #27
ukj wrote: post #10

Category theorist: What is the universal property for “realness”? https://en.wikipedia.org/wiki/Universal_property

The abstract objects which aren't self-defeating [0] are real in this sense. Of course, note that we can't simply quantify over such objects since there is no universal way to decide whether objects are self-defeating, but it is nonetheless a simple criterion. [0] https://terrytao.wordpress.com/2009/11/05/the-no-self-defeat...

This is but an error in interpretation. An object that can contradict itself is not self-defeating - it is self-affirming!

I do not exist.

Re: Is Mathematics Real? (2020)

#52

Post by teucris »

smokel wrote: post #20
teucris wrote: post #11

Earlier quoted context omitted.

That’s exactly what I’m saying. I’m glad you like it!

I have been entertaining this idea for years. First time I hear someone else voice it. Do you have an idea what the philosophical term for this idea is? It seems related to connectionism. One might assume that abstraction and pattern matching in the brain are required to determine that two "things" are the same. It is perhaps a small step to go from comparing things to comparing integers. Unfortunately, this line of…

I don’t. I’ll do some research. The origin of this concept comes from discussions I had on identity, specifically the ability to separate the “self” from the rest of the universe, or to isolate some quantity of stuff and claim it’s an apple. Ultimately the universe has no concept of such boundaries.

[update] the study of this concept seems to be semiotics, which examines the creation and use of symbols. I don’t know what branch of semiotics examines the creation of the concepts of unity and succession.

Re: Is Mathematics Real? (2020)

#53

Post by teucris »

pcwelder wrote: post #43
teucris wrote: post #2

“God made the integers, all else is the work of man” I’m not sure if even that is true. Integer counts and succession seem like human constructs to me. An apple isn’t fundamentally a single unit. If I take a bite out of it, is it still one apple?

Your conclusion doesn't follow your premise. Whether it's still an apple is a question of categorisation and a human construct (1). But once it's established it is indeed an Apple you can count the number of such Apples. Counting is real and the number you count is "true" because it leads to real predictions. This tale of magic bucket is enlightening. (2) (1): https://www.lesswrong.com/posts/aMHq4mA2PHSM2TMoH/the-cat…

It seems you may have misunderstood my conclusion. All I meant to posit was exactly as you state:

> Whether it’s still an apple is a question of categorisation and a human construct

Re: Is Mathematics Real? (2020)

#54

Post by teucris »

ralfd wrote: post #49
beebmam wrote: post #30

Earlier quoted context omitted.

An apple is an abstraction. It's a combination of chemicals bonded together. Those chemicals are composed of atoms which are bonded together, each of which are composed of electrons, protons, and neutrons. Those particles are composed of quarks, and so on. An apple is a singular thing because it is useful for us to think of an apple as a singular thing in most contexts. It is not a singular thing when it is more usef…

Then take quarks. They are a fundamental particle with no known substructure. They are a single unit and they are countable.

Sure, but metaphysically, I’m positing that the whole concept of a unit or particle is a human thing.

Re: Is Mathematics Real? (2020)

#55

Post by teucris »

unabst wrote: post #37

One-ness is a physical property and that's why we can see it. The magic happens when we call them all one, give it a symbol, and make them all equal. Now "one" has a unique existence of its own on a piece of paper on a mathematicians desk, scribbled alongside other unique symbols, whose relationships come complete with proofs. And the only question then is whether what was scribbled says something true, as in, someth…

> One-ness is a physical property and that's why we can see it.

We can see it, but does that make it a physical property or something that we impose upon the universe?

For the rest of your statement, I don’t know if we can easily define “true” or “useful”. Epistemology has been working on those concepts for a long, long time, and I don’t know if they’ve made much progress recently.

Re: Is Mathematics Real? (2020)

#56

Post by unabst »

unabst wrote: post #37

One-ness is a physical property and that's why we can see it. The magic happens when we call them all one, give it a symbol, and make them all equal. Now "one" has a unique existence of its own on a piece of paper on a mathematicians desk, scribbled alongside other unique symbols, whose relationships come complete with proofs. And the only question then is whether what was scribbled says something true, as in, someth…

(con't) An abstraction is the smallest unit of reason, and logic creates the desired cause and effect as each truth flows through the system.

Re: Is Mathematics Real? (2020)

#57

Post by unabst »

teucris wrote: post #55
unabst wrote: post #37

One-ness is a physical property and that's why we can see it. The magic happens when we call them all one, give it a symbol, and make them all equal. Now "one" has a unique existence of its own on a piece of paper on a mathematicians desk, scribbled alongside other unique symbols, whose relationships come complete with proofs. And the only question then is whether what was scribbled says something true, as in, someth…

> One-ness is a physical property and that's why we can see it. We can see it, but does that make it a physical property or something that we impose upon the universe? For the rest of your statement, I don’t know if we can easily define “true” or “useful”. Epistemology has been working on those concepts for a long, long time, and I don’t know if they’ve made much progress recently.

One-ness is a shape of a thing, much like triangle-ness or circle-ness. Shapes are physical, but they can be copied, unlike the things themselves. And when meaning is associated with a shape, that meaning can then be copied and read. So we can take "one-ness" which is physically measurable and identifiable, associate a new shape such as "1", and now we have a shape with meaning detached from its origin that we can copy, read, and communicate. The source is still reality, and this physical mechanism is what makes communication possible. Gather enough of these symbols and you have a language. Combine these symbols and you have a statement. Have anything that reads and reacts to statements and you have consequences. From DNA to protein, from grocery list to grocery bag, from tweet to insurrection.

Any combination of words can form a statement. So someone comes along and says let's agree on grammar. Then someone comes along and says let's confirm with nature whether statements actually align with nature before we call it a fact. This is modern science and the scientific truth. Scientifically, nature is the single source of truth and is all true. False only exists in the gap between a statement and nature.

Re: Is Mathematics Real? (2020)

#58

Post by teucris »

unabst wrote: post #57
teucris wrote: post #55

Earlier quoted context omitted.

> One-ness is a physical property and that's why we can see it. We can see it, but does that make it a physical property or something that we impose upon the universe? For the rest of your statement, I don’t know if we can easily define “true” or “useful”. Epistemology has been working on those concepts for a long, long time, and I don’t know if they’ve made much progress recently.

One-ness is a shape of a thing, much like triangle-ness or circle-ness. Shapes are physical, but they can be copied, unlike the things themselves. And when meaning is associated with a shape, that meaning can then be copied and read. So we can take "one-ness" which is physically measurable and identifiable, associate a new shape such as "1", and now we have a shape with meaning detached from its origin that we can co…

I think facts, truth, unity, etc, are fundamental building blocks of our perception of reality, not reality itself. That doesn’t make truths or facts invalid. We all share some common perception of the universe, at a very low, fundamental level. I believe knowledge can be built on that foundation.

Re: Is Mathematics Real? (2020)

#59

Post by unabst »

teucris wrote: post #58
unabst wrote: post #57

Earlier quoted context omitted.

One-ness is a shape of a thing, much like triangle-ness or circle-ness. Shapes are physical, but they can be copied, unlike the things themselves. And when meaning is associated with a shape, that meaning can then be copied and read. So we can take "one-ness" which is physically measurable and identifiable, associate a new shape such as "1", and now we have a shape with meaning detached from its origin that we can co…

I think facts, truth, unity, etc, are fundamental building blocks of our perception of reality, not reality itself. That doesn’t make truths or facts invalid. We all share some common perception of the universe, at a very low, fundamental level. I believe knowledge can be built on that foundation.

Not only do we share some common perception, we're also all real. We are part of the universe. So to say people are subjective or that imagination is imaginary or that reality is an illusion for the purpose of dismissing them from reality is all wrong. You need a model that is more inclusive that describes it all with physics as the premise. For example, a dream requires a sleeping biological brain full of memories drawn from physical experiences.

Truth isn't reality itself in the physical sense. But the word "apple" isn't an actual apple either in the physical sense. Yet, for the purposes of language, it is. And that is the exact extent to which truth is reality in language. When we claim truth, we claim to be making a statement of reality. If that statement includes God, then your reality includes God. If it includes only physical evidence, then your reality is based on physical evidence. We can align our realities scientifically by aligning them with science. But again, based on your life, your work, and your beliefs, your reality will deviate. That's just part of what makes us all unique.

But as you say, our unique realities are still valuable and real. Though error prone as they may be, they are real reality drawn from a real life. It's not separate just because they contradict. That's why our ability to communicate our truths is cital, and Free Speech is sacrosanct.

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