Do Mathematical Truths Depend on the Existence of Mathematical Objects?

[poverlord]

Hey guys, I have been thinking about the problem of mathematical truths. We simply do not know if the things that mathematics deals with really exist or not, yet people still believe that its statements are true and indubitable. Unfortunately, the only truly well-respected theory of truth in the sciences requires some notion of sentences "corresponding" to the real world. If it turns out that mathematical "objects" don't exist then what can we say about mathematical truths. In short, how can we say true things about stuff that does not exist?

 

[waht]

The concept of a 'mathematical truth' ,like any other concept, is generated by billions of interconnected neurons in the brain that are physical, and follow laws of physics, and chemistry. So in a sense, a 'mathematical truth' is encoded in a physical medium which allowed it to be so.

 

[Greg Bernhardt]

Please read this thread and repost accordingly
https://www.physicsforums.com/showthread.php?t=459350

 

[HallsofIvy]

Hey guys, I have been thinking about the problem of mathematical truths. We simply do not know if the things that mathematics deals with really exist or not, yet people still believe that its statements are true and indubitable. Unfortunately, the only truly well-respected theory of truth in the sciences requires some notion of sentences "corresponding" to the real world. If it turns out that mathematical "objects" don't exist then what can we say about mathematical truths. In short, how can we say true things about stuff that does not exist?

All mathematical statements are of the form "If ... then ..." (even if the "if" part is not explicitely stated). That is, mathematics is about "structure", not "content". Think of mathematics as "templates" where you enter the specific content into the "blanks".

It is true, from the meanings of the words "or" and "if ... then", that "if a is true, then "a or b is true", is a true statement. The "content"- what "a" and "b" mean and whether a is true or not, is not part of that statement and the truth of the statement does not depend on the truth of a and b separately.