What is the Nature of Mathematics?

[Alexander]

Originally posted by Mentat


[From] An empirical pattern of behavior that one observes in the Universe.

Not exactly. I would say, from empirical property "being able to exist" and "being able not to exist".

The origin of fundamental logical/mathematical entities "0" and "1" (false/true, no/yes, etc) - as I pointed many times over - comes simply from labeling (nicknaming) existence as "1" ( or "true", or "yes", etc) and labeling lack of it as "0" (or "false", "no", etc).

Therefore, anything existing obeys logic (and math which is just a complex form of logic) just by definition of logic.

Existence is logic, so to speak.

 

[Alexander]

Originally posted by Sting
Mathematics - Description

Also an artform but my head is hurting so I won't go into any philosophical discussion

Description can't predict. Math can.

 

[Sting]

Description can't predict. Math can.

True, a description can't predict but I can see where mathematics both describes and predicts.

 

[Sting]

Wait, giving slightly more thought as not exacerbate my headache, isn't there a connection between description and prediction?

 

[Alexander]

Not much. Unless you use logic (=math).

 

[Hurkyl]

logic (=math)

Just curious how you justify the '=' in your statement, not to mention how logic alone can take you from description to prediction.

 

[Mentat]

Originally posted by Alexander
Not exactly. I would say, from empirical property "being able to exist" and "being able not to exist".

The origin of fundamental logical/mathematical entities "0" and "1" (false/true, no/yes, etc) - as I pointed many times over - comes simply from labeling (nicknaming) existence as "1" ( or "true", or "yes", etc) and labeling lack of it as "0" (or "false", "no", etc).

Therefore, anything existing obeys logic (and math which is just a complex form of logic) just by definition of logic.

Existence is logic, so to speak.

You are contradicting yourself. When will you see the contradiction. Let me spell it out for you:

First you said that the origin of logic is the labeling of the states of phenomena (which I agree with), then you said that everything existing obeys logic. This is a contradiction.[/color]

 

[Mentat]

Originally posted by Alexander
Description can't predict. Math can.

Math is a description.

 

[Mentat]

Originally posted by Sting
True, a description can't predict but I can see where mathematics both describes and predicts.

Prediction is just a form of description (particularly, the one that pertains to things that haven't happened yet).

 

[quantumdude]

The multiplicity of these threads is getting troublesome. I have already addressed the following comment, but not even I can find where!

Originally posted by Alexander
Description can't predict. Math can.

That is false. With mathematics, we can describe:

1. Physical states.
2. Time evolution of physical systems.

If we can accurately describe a physical state at one spacetime point, and if we can accurately describe the time evolution, then we can accurately describe the physical state at any spacetime point, including those in the future.

That sort of description is called a prediction[/color].

 

[wimms]

Originally posted by Alexander
The origin of fundamental logical/mathematical entities "0" and "1" (false/true, no/yes, etc) - as I pointed many times over - comes simply from labeling (nicknaming) existence as "1" ( or "true", or "yes", etc) and labeling lack of it as "0" (or "false", "no", etc).

Therefore, anything existing obeys logic (and math which is just a complex form of logic) just by definition of logic.

You are talking about presence and absence. How can you label something that does not exist?? And then use as justification to fundamentals of logic itself? Absence or lack 'of it' presupposes existence of it and thus at least imaginable presence. And what does my absence from a party has to do with fundamentals and 'obeying logic'?
Where is the glue between 'existence' and 'obeying logic'??

Besides, what makes "0" fundamental logic/math entity? What makes "false" entity at all? Fundamental to math and logic is equivalence, '=' sign, validation operator. All else is endless crusade to get that '=' sign somewhere with maximum bang effect. Shuffling nicknames left and right doesn't make a reality, its just tailoring a suit to a shape of it. You are saying that suit makes a Man. Most say that suit fits a Man, and many suits fit.

 

[Sting]

Prediction is just a form of description (particularly, the one that pertains to things that haven't happened yet).

Yes, as soon as I posted that, I realized the ambigious nature of that statement (but the headache is gone and I can at least think logically )

 

[Mentat]

Originally posted by Tom
The multiplicity of these threads is getting troublesome. I have already addressed the following comment, but not even I can find where!

Imagine how that would be compounded if you and one other member were engaged in back-and-forth debate on two threads (at the same time) that had started to be about exactly the same thing. This is the situation that drag and I found ourselves in (on the "Purpose" thread and the "Cause-and-effect" thread).

 

[Mentat]

Originally posted by Sting
Yes, as soon as I posted that, I realized the ambigious nature of that statement (but the headache is gone and I can at least think logically )

It happens to the best of us (which is why it has yet to happen to me ).