On the Philosophy of Mathemathics

In summary, the conversation discusses the concept of adding temporal intervals and its relation to physical interpretation. The initial post poses the idea that if 2+2=4 and adding 2 apples to 2 apples gives 4 apples, then adding temporal intervals should also result in a larger interval. The response agrees with this logic and adds that the result should also be the same regardless of the objects being added. However, the question is raised about what happens when adding water drops to water drops in free fall, where the result is not a larger amount but rather the same amount as the original drops. The idea of destroying numbers is also brought up in this context.
  • #1
sigurdW
27
0
Reading a locked thread a post caught my eye:

"Well...that's easy; if you have a finite temporal interval 1/2, and you add 1/4 and 1/8 and 1/16 and so on, then you get a temporal interval of 1. I really don't understand what "physical interpretation" is supposed to mean in this context. If 2+2=4, then adding 2 apples to 2 apples gives me 4 apples; if a geometric series converges to a sum, then adding up temporal intervals equal in magnitude to the terms of that series gives me a temporal interval equal to that sum."

Actually only this part of it: "If 2+2=4, then adding 2 apples to 2 apples gives me 4 apples"

I couldn't agree more...also adding 1 apple to 1 apple gives 2 apples...

But what are we doing when we in free fall adds 1 drop of water to 1 drop of water?

1+1=2 but here the result is not 2 drops of water but 1 drop of water. Its having the added mass of the original drops but the fact that it is only 1 drop of water remains in front of our eyes. We can't draw the conclusion that (in this case) 1+1 = 1, since the only solution to the equation x+x=x is zero...Does it matter what objects we add?

So again: What are we doing while "adding" water drops to water drops? Destroying numbers?
 
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  • #2
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What is the Philosophy of Mathematics?

The Philosophy of Mathematics is a branch of philosophy that focuses on the nature, foundations, and methods of mathematics. It examines the fundamental principles and concepts that underlie mathematical theories and investigates the relationship between mathematics and other areas of knowledge.

Why is the Philosophy of Mathematics important?

The Philosophy of Mathematics is important because it helps us understand the nature of mathematics and its role in our understanding of the world. It also provides a framework for evaluating the validity and reliability of mathematical theories and methods.

What are the main schools of thought in the Philosophy of Mathematics?

The main schools of thought in the Philosophy of Mathematics are logicism, formalism, and intuitionism. Logicism holds that mathematics is reducible to logic, formalism views mathematics as a purely formal system, and intuitionism emphasizes the role of human intuition in mathematical reasoning.

What are some key philosophical questions in the Philosophy of Mathematics?

Some key philosophical questions in the Philosophy of Mathematics include: What is the nature of mathematical objects? Are mathematical truths discovered or invented? Can mathematics be reduced to logic? Is mathematics a universal language? What is the relationship between mathematics and reality?

How does the Philosophy of Mathematics impact other fields of study?

The Philosophy of Mathematics has a significant impact on other fields of study, such as physics, computer science, and philosophy of science. It provides a framework for understanding the use and reliability of mathematical models in these fields and helps to clarify the relationship between mathematics and the natural world.

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