A wonderful and inspiring discussion, great to see an Aussie philosopher. Have added several books to my reading list; legend! ps. amazon links in description are not following thru
@26:25 The proof in math is not a certainty. It's based on you accepting the language and axioms of it. That 3 x 2 = 2 x 3 applies to chairs is a starting point for creating the axioms; but they're still assumptions.
@@jamesfranklin2412 You're incorrect. You're not starting with the definition of 2 and 3. Sorry, James. You're throwing around "logic" while ignoring foundations.
@@jamesfranklin2412 Those truths that you're alluding to have been extracted away into definitions that are then assumed. That they are based on "truths" is immaterial to how math proceeds.
I think I see the issue. The principle of mathematical induction (and its various equivalents) holds because math takes place in a formal language with accepted, non-contradictory rules (and some of those can be debated). What this guy discusses does not take place in a formal language. To say that something has a probability means that it has a collection of mathematical objects with a measure and so on, and takes place in a formal language. That's not happening here. This is more rhetoric shrouded in math/probability speak, which is sure to confuse or impress those without the math background to parse through it. @21:00 See? His example is formal and perfectly correct as long as you stay within the formal language and accompanying rules of that language like he's doing. But then he leaps to non-formal scenarios that can't be formalized, so this no longer math.
Mathematics does not take place in a formal language, even pure mathematics papers, as you can see by reading them. See further An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure, or the relevant Wikipedia article for a summary en.wikipedia.org/wiki/Aristotelian_realist_philosophy_of_mathematics
@@jamesfranklin2412 Yes, it does. You may be communicating it in your meta-language, but it's in a formal language, second-order or not. That may be why you're in logic in the philosophy department and not the math department, and why Statistics is separate from Mathematics. And your PhD is in algebra from a time when finite simple groups were not all classified? You have impressed Emily, like academics impress 20-year-olds, but she knows no mathematics at all, and her words, her strength, just cannot fill that gap. And probably in college never felt the importance or anything of the subject to thinking or application. Invite me on the podcast. Seriously.
Sir am I correct in understanding your basic issue is that maths cannot be 'proven' scientifically and materially? That is to say the existence of say, the number five cannot be proven through the processes of scientific materialism? Do I have that correct? I am asking out of curiosity more than anything else.
@@northernvibe4870 I'm not totally sure of the meaning of the question. Proof must start with something, and understanding of small numbers like 5 is one of the things obviously known that it starts with. It's not easy to fit that kind of understanding into a materialist view of the mind - e.g. AI doesn't have it.
Wow. Awesome interview.
A wonderful and inspiring discussion, great to see an Aussie philosopher. Have added several books to my reading list; legend!
ps. amazon links in description are not following thru
@26:25 The proof in math is not a certainty. It's based on you accepting the language and axioms of it. That 3 x 2 = 2 x 3 applies to chairs is a starting point for creating the axioms; but they're still assumptions.
No they're not. 3 x 2 = 2 x 3 independently of people and their assumptions. You can't assume away those truths.
@@jamesfranklin2412 You're incorrect. You're not starting with the definition of 2 and 3. Sorry, James. You're throwing around "logic" while ignoring foundations.
@@jamesfranklin2412 Those truths that you're alluding to have been extracted away into definitions that are then assumed. That they are based on "truths" is immaterial to how math proceeds.
I think I see the issue. The principle of mathematical induction (and its various equivalents) holds because math takes place in a formal language with accepted, non-contradictory rules (and some of those can be debated). What this guy discusses does not take place in a formal language. To say that something has a probability means that it has a collection of mathematical objects with a measure and so on, and takes place in a formal language. That's not happening here. This is more rhetoric shrouded in math/probability speak, which is sure to confuse or impress those without the math background to parse through it.
@21:00 See? His example is formal and perfectly correct as long as you stay within the formal language and accompanying rules of that language like he's doing. But then he leaps to non-formal scenarios that can't be formalized, so this no longer math.
Mathematics does not take place in a formal language, even pure mathematics papers, as you can see by reading them. See further An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure, or the relevant Wikipedia article for a summary en.wikipedia.org/wiki/Aristotelian_realist_philosophy_of_mathematics
@@jamesfranklin2412 Yes, it does. You may be communicating it in your meta-language, but it's in a formal language, second-order or not. That may be why you're in logic in the philosophy department and not the math department, and why Statistics is separate from Mathematics. And your PhD is in algebra from a time when finite simple groups were not all classified?
You have impressed Emily, like academics impress 20-year-olds, but she knows no mathematics at all, and her words, her strength, just cannot fill that gap. And probably in college never felt the importance or anything of the subject to thinking or application. Invite me on the podcast. Seriously.
Sir am I correct in understanding your basic issue is that maths cannot be 'proven' scientifically and materially? That is to say the existence of say, the number five cannot be proven through the processes of scientific materialism? Do I have that correct? I am asking out of curiosity more than anything else.
@@northernvibe4870 I'm not totally sure of the meaning of the question. Proof must start with something, and understanding of small numbers like 5 is one of the things obviously known that it starts with. It's not easy to fit that kind of understanding into a materialist view of the mind - e.g. AI doesn't have it.
The philosophy of math vs science brings new meaning to « unknown and unknowable ».