Is math real? Is physics math describable?

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Discussion Overview

The discussion revolves around the nature of mathematics and its relationship to physics, questioning whether mathematics is a real entity or merely a construct of human thought. Participants explore the implications of mathematics as a language for describing physical phenomena and the philosophical perspectives on whether mathematical truths are discovered or invented.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that mathematics is an abstract game created by humans, while others argue that it represents truths that exist independently of human thought.
  • A viewpoint is presented that the efficiency of mathematics in describing physical phenomena may stem from underlying axioms shared between both fields.
  • Some participants identify as platonists, believing that mathematical entities are discovered, while others lean towards constructivism, viewing mathematics as a human invention.
  • One participant asserts that mathematics serves as a precise language for describing relationships and quantities, which explains its effectiveness in the natural sciences.
  • References to Wigner's work are made, with participants discussing its relevance to the topic and the implications of Wigner's views on mathematics and physics.
  • There is a contention regarding Wigner's characterization as a creationist, with some participants opposing this label and discussing the historical context of such terms.
  • Some participants express skepticism about the intrinsic nature of mathematics, suggesting it is a language developed over time to model reality rather than a pre-existing truth.
  • Discussion includes references to literature that explores the history and philosophy of mathematics, indicating a desire for deeper understanding of the topic.

Areas of Agreement / Disagreement

Participants express a range of views on the nature of mathematics, with no clear consensus on whether it is discovered or constructed. The discussion remains unresolved with multiple competing perspectives presented.

Contextual Notes

Some arguments depend on specific philosophical definitions of mathematics and its role in science, which may not be universally accepted. The discussion also touches on the historical context of mathematical development and the implications of labeling individuals with certain philosophical stances.

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  • #33
TheStatutoryApe said:
"Don't confuse the map with the territory."
Deep..!

PS: My thread! :D
 
  • #34
Phrak said:
Question : is mathematics discovered or invented?

Many inventions come from discoveries/accidents/refinement/improvements etc. And the methods that we have in mathematics didn't come from just one person, and didn't come overnight... it is like linux ... somebody started off with an idea and then it started to get built up/evolve ... like open source.
 
  • #35
This is my understanding of mathematics:
We state a list of axoims, use deductive logic and the variety of theorems pop out.
This collection is then called a theory.

Now, in choosing the axioms, have we not fixed any and all theorems that are derived from them? Hence it is a discovery, since those theorems exist as a result of the axioms and formal logic that operates on those axioms, even though we don't yet know what they are.

Related question: Where did formal logic come from, and how is it valid? <- This may in fact be a meaningless question since being valid is a logical state.

I would just like to know to say to someone who asks why we bother with being logical at all.
 
  • #36
Logic is just a means of non-contradictory i.e. meaningful communication.
 
  • #37
You all got it wrong about math. It is not a game, etc. Instead, math is based upon a collection of arbitrary, self-consistent statements (postulates, properties, etc.) Math is not true, but consistent. Science is the application of math to the world, and is true to the extent that it agrees (partially) with experiments and observations.
 
  • #38
Borek said:
This made me wonder - is math real? I don't mean real like a hammer - math is competely abstract, there is no doubt about it. However, is math really a game?

Maths is a discipline that has evolved, beginning from the time when somebody needed to start adding, and subtracting. Then later people discovered multiplication, division, and exotic features of working with numbers. And this discipline can be applied in conjunction with other disciplines to make our society more 'advanced'...building elaborate/sophisticated things etc.

If you're going to ask if maths is real, then you're going to have to ask 'are numbers real?'. It's up to you to choose what is real or not real.
 
  • #39
Math is not something of our own devising.

Math exists on a Platonic plane independent of man and God. If there is a God, He used math as the scaffholding to construct the universe.
 

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