Infinte Regress Timeline...

[surreptitious57]

Mathematics is a deductive discipline that uses proof to validate its conclusions. More
importantly it is the language of reality and as such is not a human construction even
though the symbols are. And so any other complex intelligence would not only be able
to under stand it but would with sufficient time have eventually discovered it also even
if all of their symbols were self constructed too and it was not automatically in base ten

 

[Juma]

More
importantly it is the language of reality

Yes. But it requires humans to execute.

 

[ryan]

More
importantly it is the language of reality

Yes. But it requires humans to execute.

By saying yes, you seem to be agreeing with me and surreptitious57.

 

[Juma]

Yes. But it requires humans to execute.

By saying yes, you seem to be agreeing with me and surreptitious57.

Just saying that the human mind, is real.
And since equations are something inside the humand mind they are also real.

 

[ryan]

By saying yes, you seem to be agreeing with me and surreptitious57.

Just saying that the human mind, is real.
And since equations are something inside the humand mind they are also real.

"In the mind" is the casual way to say it. But strictly speaking, don't you mean equations are a part of the mind or a quality of the mind? If they are in the mind, then that seems to mean that they are beyond the mind.

 

[Juma]

Just saying that the human mind, is real.
And since equations are something inside the humand mind they are also real.

"In the mind" is the casual way to say it. But strictly speaking, don't you mean equations are a part of the mind or a quality of the mind? If they are in the mind, then that seems to mean that they are beyond the mind.

Nope. But I have given up on you. Bye.

 

[Speakpigeon]

Mathematics is a deductive discipline that uses proof to validate its conclusions. More importantly it is the language of reality and as such is not a human construction even though the symbols are.

Well, I guess human beings are real so any language we use is a language of reality, i.e. it is reality itself which is "speaking", yes?

Or do you mean that beyond our idiosyncratic way of expressing our mathematical ideas there are mathematical things, independent of us, and part of the way reality is? If so, mathematical relations are truly discovered, yes?

However, in this case, you may be confusing the contingent concrete relations that exist between things like, say, when a set of three apples just happens to have a relation of "3 to 1" with each individual apple in it but if an idiot comes around (they always do) and eat one of the apples then the relation shifts to "2 to 1". So, it's one thing to claim that there are such contingent concrete relations between things and quite another thing to claim that abstract mathematical relations exist in their own right, alongside so to speak the ordinary furniture of the universe.

Can you tell which option you favour?
EB

 

[surreptitious57]

What I mean is that mathematics is independent of any interpretation. Proofs cannot be disregarded since they are from a logical
perspective infallible. For example : the ratio between the circumference of a circle and its diameter will always be pi. And likewise
the square of the hypotenuse of a right angled triangle will always be equal to the added squares of the other two sides. And these
and all other mathematical truths are absolute and so cannot be altered or modified in any way. Mathematics therefore exists within
its own realm immune to subjective interpretation. This cannot be said of any other discipline which makes mathematics like no other

 

[Juma]

What I mean is that mathematics is independent of any interpretation. Proofs cannot be disregarded since they are from a logical
perspective infallible. For example : the ratio between the circumference of a circle and its diameter will always be pi. And likewise
the square of the hypotenuse of a right angled triangle will always be equal to the added squares of the other two sides. And these
and all other mathematical truths are absolute and so cannot be altered or modified in any way. Mathematics therefore exists within
its own realm immune to subjective interpretation. This cannot be said of any other discipline which makes mathematics like no other

But there are no circles and radiuses "out there". Tvey exist only as abstractions.

 

[surreptitious57]

They may exist as abstractions but the paradox is that mathematics is the language that most accurately references
reality. So not everything that it does describe is an abstraction. Like for example : the speed of light in a vacuum or
the inverse square law of gravity. Numbers them selves are abstractions yet without them society could not function
so there are real world applications which are very dependent on the abstraction of mathematics. Furthermore it is a
language and all languages are themselves abstractions. Like numbers society could not function without them either

 

[untermensche]

They may exist as abstractions but the paradox is that mathematics is the language that most accurately references
reality. So not everything that it does describe is an abstraction. Like for example : the speed of light in a vacuum or
the inverse square law of gravity. Numbers them selves are abstractions yet without them society could not function
so there are real world applications which are very dependent on the abstraction of mathematics. Furthermore it is a
language and all languages are themselves abstractions. Like numbers society could not function without them either

The speed of light is not an abstraction. It is an approximation.

But numbers and equations are abstractions, as you say.

They are not the language of reality. They are a human language, an abstraction, that can be used to make approximate predictions of some situations, as long as they are not too complicated.

And yes numbers and equations are necessary for human society to work, but the real world does not use them or need them.

 

[Speakpigeon]

What I mean is that mathematics is independent of any interpretation. Proofs cannot be disregarded since they are from a logical perspective infallible. For example : the ratio between the circumference of a circle and its diameter will always be pi. And likewise the square of the hypotenuse of a right angled triangle will always be equal to the added squares of the other two sides. And these and all other mathematical truths are absolute and so cannot be altered or modified in any way. Mathematics therefore exists within its own realm immune to subjective interpretation. This cannot be said of any other discipline which makes mathematics like no other

Ok so you seem to be talking about abstractions and abstractions seems mind-dependent to me. Suppose I think of Santa Claus as a being carrying a sack containing gifts for children. It seems to follow that he is carrying those gifts that are inside his sack and no others. Yet, I guess you would agree that this Santa Claus doesn't exist at all except as an abstraction in my mind. We fancy that circles possess certain properties. Yet, there is nothing in the actual material world that we would know as possessing these properties. So it's also all in the abstract. It's true that we can repeat mental experiments whereby the ratio between the circumference of a circle and its diameter seems always to be Pi. However, Pi here is entirely definitional. Nobody can actually write down the number Pi in its entirety. This doesn't prevent us from using the concept very effectively as if we could. But as you probably know if the geometry of space is somehow curved, Pi as we usually think of it isn't even a good approximation of the actual situation. In this case, it's just plain wrong. So absolute mathematical relations like Pi only make sense as dependent on how our mind happens to work. In other words, they're not absolute at all. And indeed, we can think differently about circles. We can define circles in a different geometry where Pi as we know it doesn't apply. So in the end it seems to come down to our beliefs that abstract relations we think up somehow have a validity that extends beyond our own existence. The problem then is that since we usually accept that our brain is the product of evolution then it's not normally going to tell us that our environment doesn't make sense. It will somehow try to value its representation of the real world as essentially true of it. It will also value its logic as absolute. Yet, any logical conclusion is already contained in the premises so logic isn't going to tell us what exists in actual fact. It only tells us what exists if our premises are true.
EB

 

[surreptitious57]

Obviously there has to be some foundational basis upon which to reference the observable Universe given the natural curiosity of our
species and as far as logic is concerned the most practical methodology in that respect is mathematics. It has a beauty and simplicity
not found in other disciplines and indeed it would be next to impossible to reference anywhere else the same degree of precision that
it does and which is why it is so very useful and in so many ways too

If human beings use logic as a means of understanding then it follows that that which is not logical will be rejected. However this is
not actually true because as knowledge of the Universe increases and as phenomena appear to defy reasoning it is still nonetheless
accepted. Mammalian brains did not actually evolve with the specific purpose of comprehending the Cosmos anyway. Since the fact
that humans exist in the first place is evidence of randomness not design. So anything following from that point on can be regarded
as rather fortuitous. And indeed infinitesimally so if one takes into account the fine tuning of the Universe

Maybe mathematics is not as perfect as it appears and maybe using logic to prove logic is the absolute limitation of our capabilities
But we can only work within such parameters even if they may be restricting by default as we are not artificially intelligent. And so
cannot think in absolutely pure terms to the point where all conclusions are accepted regardless of what they are since they do not
have to be processed through another filter to see if they are psychologically or philosophically acceptable as well. And so unless or
until a better system comes along we shall carry on using the one we have as that is the most logical thing to do

 

[ryan]

They may exist as abstractions but the paradox is that mathematics is the language that most accurately references
reality. So not everything that it does describe is an abstraction. Like for example : the speed of light in a vacuum or
the inverse square law of gravity. Numbers them selves are abstractions yet without them society could not function
so there are real world applications which are very dependent on the abstraction of mathematics. Furthermore it is a
language and all languages are themselves abstractions. Like numbers society could not function without them either

The speed of light is not an abstraction. It is an approximation.

But numbers and equations are abstractions, as you say.

They are not the language of reality. They are a human language, an abstraction, that can be used to make approximate predictions of some situations, as long as they are not too complicated.

And yes numbers and equations are necessary for human society to work, but the real world does not use them or need them.

I assume that we can agree that the symbols/abstractions represent things outside of the mind. Whatever these things are, they follow the mental models that have been course-grained into our memories/thoughts. Our thoughts are a result of what nature does.

 

[surreptitious57]

The symbols of mathematics are mental constructs but the discipline it self is not
For it could just as easily be discovered by complex intelligent life elsewhere in the
Cosmos. Their symbols would be different of course and they may not use base ten
but everything else would be the same because mathematics is a universal language

 

[untermensche]

The symbols of mathematics are mental constructs but the discipline it self is not
For it could just as easily be discovered by complex intelligent life elsewhere in the
Cosmos. Their symbols would be different of course and they may not use base ten
but everything else would be the same because mathematics is a universal language

Mathematics wasn't discovered. It is not out there to be discovered.

It was invented, like alphabets were invented. And there is no way to know if any other form of life is capable of inventing it.

We know that no other life form besides humans on this planet is capable of inventing it. It is possible that humans are the only life form to ever invent it.

 

[untermensche]

I assume that we can agree that the symbols/abstractions represent things outside of the mind. Whatever these things are, they follow the mental models that have been course-grained into our memories/thoughts. Our thoughts are a result of what nature does.

The number 1 represents nothing in the real world. There is no number 1 out there, or any number, especially infinity which really isn't a number. It is an unending process.

If so, where is it? Plainly say where numbers clearly exist.

Saying that we have equations that are able to make a few predictions is not clear evidence of numbers existing in the world. It is only evidence that human mathematics can be used to make real world predictions. It is no more than that.

 

[ryan]

I assume that we can agree that the symbols/abstractions represent things outside of the mind. Whatever these things are, they follow the mental models that have been course-grained into our memories/thoughts. Our thoughts are a result of what nature does.

The number 1 represents nothing in the real world. There is no number 1 out there, or any number, especially infinity which really isn't a number. It is an unending process.

If so, where is it? Plainly say where numbers clearly exist.

Saying that we have equations that are able to make a few predictions is not clear evidence of numbers existing in the world. It is only evidence that human mathematics can be used to make real world predictions. It is no more than that.

The number 1 represents a property of something outside of the mind. "One banana" is something specific about something that exists outside of the mind that is different than "two bananas". We use the symbol "1" to symbolize this difference.

 

[untermensche]

The number 1 represents nothing in the real world. There is no number 1 out there, or any number, especially infinity which really isn't a number. It is an unending process.

If so, where is it? Plainly say where numbers clearly exist.

Saying that we have equations that are able to make a few predictions is not clear evidence of numbers existing in the world. It is only evidence that human mathematics can be used to make real world predictions. It is no more than that.

The number 1 represents a property of something outside of the mind. "One banana" is something specific about something that exists outside of the mind that is different than "two bananas". We use the symbol "1" to symbolize this difference.

Show me the number one in the world.

Don't talk to me of imaginary things that don't exist in the world.

More than one banana exists in the world. Talking about bananas is not a clear demonstration that the number 1 exists in the world. The number 1 is not a banana. The fact that you can't tell the difference is interesting.

 

[ryan]

The number 1 represents a property of something outside of the mind. "One banana" is something specific about something that exists outside of the mind that is different than "two bananas". We use the symbol "1" to symbolize this difference.

Show me the number one in the world.

Don't talk to me of imaginary things that don't exist in the world.

More than one banana exists in the world. Talking about bananas is not a clear demonstration that the number 1 exists in the world. The number 1 is not a banana. The fact that you can't tell the difference is interesting.

There is a difference between "1 banana" and "banana". "One banana" adds information to "banana" that originally comes from outside of the mind.