Most predominant philosophical attitude toward mathematics

[Ahmed Abdullah]

What is the most predominant philosophical attitude toward mathematics among mathematicians?
I am talking about things like mathematical platonism, formalism, logicism etc.
In some circumstances I feel that I am a platonist (e.g when thinking about pi) in others logicist or formalist etc. Does one have to be one or other?

Thx in advance.

 

[jedishrfu]

There is a good discussion on this topic in Wikipedia.

http://en.m.wikipedia.org/wiki/Philosophy_of_mathematics

I can't say whether a poll has ever been done to determine where all mathematicians stand on this. I suspect though that most are caught in their interest to math and not its philosophical underpinnings.

 

[HallsofIvy]

While I can't speak with any degree of authority on this, I suspect that "structuralism" is most common among mathematicians, whether they think of it that way or not.

 

[Evo]

Philosophy discussions are not allowed, since the thread is not staying away from philosophy as jedishrfu suggested, it is closed.

 

[LudusRex]

I cannot speak for all mathematicians, but I can provide a general perspective on the predominant philosophical attitudes toward mathematics.

There are several different philosophical attitudes toward mathematics, including mathematical platonism, formalism, and logicism. Each of these perspectives has its own unique beliefs about the nature and existence of mathematical objects.

Mathematical platonism is the belief that mathematical objects, such as numbers and geometric shapes, exist independently of human thought and language. This perspective sees mathematics as uncovering truths about these abstract objects that already exist in some kind of transcendent realm.

Formalism, on the other hand, sees mathematics as a purely symbolic system with no inherent meaning or connection to reality. In this view, mathematical objects are simply constructs of the human mind and do not have any independent existence.

Logicism takes a more middle-ground approach, viewing mathematics as a combination of logic and language. According to this perspective, mathematical statements are true by definition and are grounded in logical reasoning.

It is important to note that these philosophical attitudes are not mutually exclusive and many mathematicians may hold a combination of these beliefs depending on the context. For example, a mathematician may view concepts like pi or infinity as existing independently of human thought (platonism), while also recognizing that mathematical proofs are constructed through logical reasoning (logicism).

Ultimately, the most predominant philosophical attitude toward mathematics among mathematicians is likely a mix of these different perspectives. Each approach offers valuable insights and can be useful in different mathematical contexts. It is not necessary for a mathematician to adhere strictly to one perspective, as the nature of mathematics is complex and multifaceted.