Mathematics: A Key to Understanding Metaphysics?

In summary, Metaphysics is a strong interest of mine, as is Philosophy in general. I also enjoy Math, and more importantly, I recognize some mathematical concepts are needed for Metaphysics. A simple example is the concept of infinity (what it is). I'm asking, are there any courses, or even books on Mathematics I should look into for the sake of Metaphysics? Or even ones I might find of interest (as a Philosophy student)? What is metaphysics? I think books on logic and / or set theory come to mind. And Popper and Wittgenstein on the philosophers' side.
  • #1
VCrakeV
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Metaphysics is a strong interest of mine, as is Philosophy in general. I also enjoy Math, and more importantly, I recognize some mathematical concepts are needed for Metaphysics. A simple example is the concept of infinity (what it is).

I'm asking, are there any courses, or even books on Mathematics I should look into for the sake of Metaphysics? Or even ones I might find of interest (as a Philosophy student)?
 
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  • #2
What is metaphysics?
 
  • #3
Books on logic and / or set theory come to mind. And Popper and Wittgenstein on the philosophers' side.
 
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  • #4
Student100 said:
What is metaphysics?
Literally "before physics"; the study of the fundamental things of the Universe. Not a perfect definition, but it's okay...

Some common themes of Metaphysics are "is there a God?", "is life deterministic?", and "what is?"
 
  • #5
VCrakeV said:
Literally "before physics"; the study of the fundamental things of the Universe. Not a perfect definition, but it's okay...

Some common themes of Metaphysics are "is there a God?", "is life deterministic?", and "what is?"
Not quite sure whether it can be said in this way. It's rather an "after", than a "before".
http://www.etymonline.com/index.php?allowed_in_frame=0&search=metaphysics
Also the Wikipedia definitions and descriptions in English and in my language are not one-to-one.

I like to see it as: Physics is about the real world's constituencies. Metaphysics is about the nature of physics, i.e. about it's methods and models. One can add prefixes of meta- to indicate the next level, which is discussing the former.

To add an important hint here: We do not discuss philosophy on PF. So this thread is very much on the edge and might get closed by the administrators.
 
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  • #6
fresh_42 said:
Not quite sure whether it can be said in this way. It's rather an "after", than a "before".
http://www.etymonline.com/index.php?allowed_in_frame=0&search=metaphysics
Also the Wikipedia definitions and descriptions in English and in my language are not one-to-one.

I like to see it as: Physics is about the real world's constituencies. Metaphysics is about the nature of physics, i.e. about it's methods and models. One can add prefixes of meta- to indicate the next level, which is discussing the former.

To add an important hint here: We do not discuss philosophy on PF. So this thread is very much on the edge and might get closed by the administrators.
My bad... I always thought it was before (as in, metaphysics comes before physics; it is the basis of physics, not vice versa).

And sorry about that, I was thinking it was more a topic about Math, but I understand.
 
  • #7
VCrakeV said:
My bad... I always thought it was before (as in, metaphysics comes before physics; it is the basis of physics, not vice versa).
I guess there isn't really one unique definition and assume that different authors use it slightly differently.
And sorry about that, I was thinking it was more a topic about Math, but I understand.
Yes, it can be. As I said, e.g. in set theory and logic. Goedel (https://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems) and Russell (https://en.wikipedia.org/wiki/Russell's_paradox) count as mathematicians. It is a thin line here between them. And it's not that mathematicians or physicists weren't interested in philosophy or wouldn't discuss it. Most of them are Platonists. It's more that internet debates on philosophical questions usually lead to nowhere and can go on forever without any significant gain. That's all. I've read discussions like "Is zero real" or similar here, which I thought would have been immediately closed. I simply wanted to say it, in order to stay on the safe side.
 
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As fresh_42 said,
fresh_42 said:
We do not discuss philosophy on PF.
 
  • #11
VCrakeV said:
Literally "before physics"; the study of the fundamental things of the Universe. Not a perfect definition, but it's okay...

Some common themes of Metaphysics are "is there a God?", "is life deterministic?", and "what is?"

I thought Descartes already proved there was a God?
 
  • #12
PeroK said:
I thought Descartes already proved there was a God?
I like Hardy's version:
fresh_42 said:
It is not quite clear whether Hardy believed in God or was just superstitious. However, in any case he believed God will do everything to make his life tough and complicated. One day he was on a journey back home. (I've heard it with Harald Bohr and Copenhagen, but also found Norway in the internet.) Anyway. He had to take a ship and the boat he got didn't look very trustful. Typically, he thought, why me?
So he sent a postcard before boarding - say to Bohr - claiming he has found the proof of Riemann's hypothesis.
When afterwards asked why, he replied: "Well, if the ship sank the proof would have been lost but I would have become the most famous mathematician of my generation. God won't allow this to happen. This way I only had to write Bohr another postcard in which I stated to have made a mistake."
 
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fresh_42 said:
I like Hardy's version:

Although, I'm sure it's not beyond God's power to disrupt the postal service and make a card go missing. He does that all the time, as far as I can judge.
 
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  • #14
PeroK said:
I thought Descartes already proved there was a God?
Supposedly, but it's often not regarded as a proof. Even at the time of publishment, Antoine Arnauld criticized Descartes for his circular reasoning in God and the truth rule.
 
  • #15
Damn, we are getting off topic...
 
  • #16
VCrakeV said:
Supposedly, but it's often not regarded as a proof. Even at the time of publishment, Antoine Arnauld criticized Descartes for his circular reasoning in God and the truth rule.
This list of "proofs" reads like a who-is-who in philosophy.
 
  • #17
VCrakeV said:
Supposedly, but it's often not regarded as a proof. Even at the time of publishment, Antoine Arnauld criticized Descartes for his circular reasoning in God and the truth rule.

This exemplifies the difference between physics and metaphysics. Any physical theory or postulate can be tested and - agreeing with experimental results is a key test. Arguing whether God exists may be useful in its own way, but unless and until he/she reveals him/herself, there's never going to be an answer.

I might argue that man cannot be made in God's image, because why wouild God need eyes, ears, ribs, a heart, liver and kidneys etc.? But, unless I can medically examine God, there's no way to tell whether he/she has kidneys or not. All I can say is that it seems unlikely to me! But, there is no definite way to resolve that question. A believer would have an answer, no doubt. Possibly simply redefine what is meant by "in God's image", and then you're back to square one.
 
  • #18
fresh_42 said:
To add an important hint here: We do not discuss philosophy on PF. So this thread is very much on the edge and might get closed by the administrators.
Done. Lordy.
 

Related to Mathematics: A Key to Understanding Metaphysics?

What is the relationship between mathematics and metaphysics?

The relationship between mathematics and metaphysics is a complex one. Some philosophers argue that mathematics is a necessary tool for understanding metaphysical concepts, while others argue that mathematics is simply a language we use to describe the physical world and has no bearing on metaphysical truths. Ultimately, the exact relationship between mathematics and metaphysics is still a subject of debate.

Can mathematics be used to prove metaphysical claims?

Many philosophers believe that mathematics can be used to support or disprove metaphysical claims. For example, the concept of infinity in mathematics can be used to argue for the existence of an infinite universe in metaphysics. However, it is important to note that mathematics alone cannot prove or disprove metaphysical claims, as there are other factors and arguments that must also be considered.

Is mathematics objective or subjective in metaphysics?

This is a highly debated question in the field of philosophy. On one hand, some argue that mathematics is an objective truth that exists outside of human perception and is discoverable through logical reasoning. On the other hand, some argue that mathematics is a human construct and therefore subjective to our own perceptions and biases. Ultimately, the answer may depend on one's perspective and interpretation of metaphysics.

How does mathematics relate to the concept of reality in metaphysics?

Mathematics plays a significant role in our understanding of reality in metaphysics. Many scientists and philosophers argue that mathematics is the language of the universe and that it allows us to make sense of the world around us. Mathematics is also used to describe and explain many metaphysical concepts, such as causality and determinism, which are essential to our understanding of reality.

Are there limitations to using mathematics in metaphysics?

While mathematics has been a valuable tool in understanding metaphysical concepts, there are limitations to its use. For example, some philosophers argue that certain metaphysical concepts, such as consciousness, cannot be fully explained or understood through mathematical equations. Additionally, there are some metaphysical questions that may not have a mathematical solution or may fall outside the scope of mathematics entirely.

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