Bertrand Russell's logic and math?

[Jim_Baur]

If I have understood and remember correctly, Russell bases math on logic.

In his system, on what is logic based?

Thanks!

 

[AntiTheist]

If I have understood and remember correctly, Russell bases math on logic.

In his system, on what is logic based?

Thanks!

I’m not familiar enough with Russell to answer this specific question, but I am familiar enough with theist arguments to sense where this one is going, so let’s nip it in the bud.

Logic is based on the logical absolutes, such as the law of identity, which appear to be properties of the universe. The logical absolutes aren’t “based on anything” – they just are just the way things are.

If you are trying to argue that “logic must be based on god!” then the next question is “what is god based on”? If you claim that god can just be, then you’ve shot yourself in the foot because you’ve just admitted something doesn’t need to be “based on” something else. Ergo, “god” is an unnecessary assumption.

 

[Jim_Baur]

My intentions are to find out whether math is extramental.

In better words, did human beings create math?

 

[JohnDamian]

My intentions are to find out whether math is extramental.

In better words, did human beings create math?

Math is purely mental. We only have to look at functions such as infinity and division by zero to see that Mathematics translates poorly to the real world.

An argument could be made for “basic” mathematics to have an existence in the real world; but objects and facts about the universe are not intrinsically numerical – thus maths is not a study of the real world.

 

[Just_Lurking]

Russell and others like him have invented abstract systems that purport to model some or all of mathematics and its underlying logic. Once such an abstract system is defined, others can discover proofs of various theorems or results in that abstract system.

There is no single abstract system that has enough philosophical (or other) justification that all mathematicians are convinced that it is the “one” correct system for mathematical reasoning. Many mathematicians are adept at proving results in multiple different abstract systems. I personally do a lot of work in constructive mathematics.

I’m a tyro as far as philosophy is concerned, but I believe my position is known as plenitudinous platonism.

 

[Jim_Baur]

Thanks for the help thus far

If math does exist outside of the mind, what kind of demonstrations are used?

Are the demonstrations from simple math?

I kind of hold the position that math is based on human logic. Human logic is a product of the ability of human reason.

I do not wish to argue or tie this to other threads.

I am perplexed in this area, but I enjoy it.

 

[Charlemagne_II]

*An argument could be made for “basic” mathematics to have an existence in the real world; but objects and facts about the universe are not intrinsically numerical – thus maths is not a study of the real world. *

E=MC2

Albert Einstein was able to see where an understanding of this formula would lead. Although peaceful by nature and politics, he helped write a letter to the President of the United States, urging him to fund research into the development of an atomic bomb … before the Nazis or Japan developed their own first. The result was the Manhatten Project, which did in fact produce the first tangible evidence of … the atomic bomb!

The mathematical formula is the basis of nuclear energy and nuclear bomb research. From this it would seem that math is a study of the real world. If we didn’t have math, how much of the real world would we understand. Almost all laws of physics and chemistry are based on mathematical computations. Even hydrogen, the most common element in the universe, has a mathematical formula. H20

 

[Just_Lurking]

I suppose I view modern mathematics as kind of a well-defined language, where all mathematicians know the rules for the language. From that point of view, mathematics has the same ontological status as a computer language, such as Java or C++.

So, does the Java programming language exist outside the mind? Well, it was created / invented by the human mind, but when all the people who defined it are long gone, it will still make sense to ask the question of whether a given piece of text is a valid Java program.

Pre-modern mathematics was different in that it was not so well defined. For example, compare Euclid’s Elements with Hilbert’s Foundations of Geometry. I often wonder if Euclid would appreciate the development.

 

[awatkins69]

If I have understood and remember correctly, Russell bases math on logic.

In his system, on what is logic based?

Thanks!

Hi. First of all, Russell was a big guy in terms of mathematical logic. He was one of the big pioneers of symbolic and formal logic, which is real good. He also applied the area of set theory to logic. As for the bases of logic, he believed in what is called “logical atomism”.