But why is math a "descriptive aid"? One aspect of mathematics that does not seem to be a fiction is its logical consistency. That logical consistency seems to be the essence of its ability to capture certain truths about the world. I don't believe mathematics can merely be useful if it's indispensable.
"Useful" is one of the non-empty concepts of human languages. Here, non-empty concepts mean the meaning of a concept is partially independent to or partially free from the self-definition nature of the language. Other terms, such as applied, surviving etc., also have similar characteristics. Purpose, or usefulness, is the ultimate demarcation to defined the huaman defined realities and real realities. All science is applied science by means of graspability of the true realities. The true reason why many people, especially scientists believe things such as true reality, the beauty of mathematics, math is observed rather than invented, etc. etc., is because they have confused the difference between pure science and applied science. Real reality may or may not exist. Either way, it is either undefined yet or un-definable forever.
If a real reality may or may not exist then how can you state that "useful" is one of the non-empty concepts of human languages. If reality doesn't exist then a human created reality, in reality doesn't exist. As to math being observed rather than invented, well that is a questionable reality because everything about math is a human construct. If you have two apples and I have two apples then we have four apples and that is a certainty in our shared reality and how you come to realize that certainty is of your of your own doing and that doing may even amaze you, and you may even believe that you, or someone else discovered it instead of inventing it. I did enjoy your comment and my reply was deliberately argumentative and I mean no offense to your belief or mental acuity.
@@sedevacantist1 [If you have two apples and I have two apples then we have four apples and that is a certainty in our shared reality and how you come to realize that certainty is of your of your own doing?] ------ Simple. first, chimpanzees may not share with us. Second, some human tribes still can't count the number larger than 3 and they are going to categorize "4" to "many. "
I have to admit , the interviewer nailed it in this one. Questions were on point and he had an iron grip on the subject matter all the way through. Pity he isn't so astute with all the woowoo merchants he entertains on this channel.
Thinking about whether numbers exist or not, since commonsense can lead us astray, would it be better to start by considering a fractional, negative or imaginary number, or zero, rather than a small natural number we can show on our fingers? Aren't numbers in general hypostasized abstract relations?
I really can't wrap my mind around nominalism. Pity they finished on that note. How could it possibly be the case that the math is false but somehow it works in the world? It would require belief in some really weird 'conspiracy theory' type arrangement of reality, of the type of Descartes' Evil Demon who is perpetually deceiving us.
Truth and beauty are ideas/concepts which have a reality of their own. Units of time or length or temperature are arbitrary units created by the human mind and they have a predictive quality. These predictive abilities breakdown in the quantum realm which proves free will and disproves determinism, which should be obvious to any honest person.
Love this episode platonic realism... got to be true for any grounding. I'm betting that beauty is a real universal. have you done an episode on the transcendental argument for God (TAG)? this is really the best argument for God in my opinion; I think it gives us a logical reason to believe that logic, reason & mathematics are something beyond simple grunts and gestures grounded in nothing more than practicality. using a familiar metaphor,I think abstraction is probably causal in a way similar to source code utilized by a program, and run through hardware... the code (the Word) is a timeless universal. our mathematics & logic is a representative sub language fit for finite humans. don't ask me to prove it, unless I can say that two plus two equals four because two plus two equals four and that is enough for you... it's just axiomatic. It just Is.
I love Mark’s wrinkled shirt! When he was my professor, I never saw him in anything but a t shirt. One the best teachers I’ve ever had.
It’s my experience that the professors of the philosophy of mathematics tend to be the best ones in the philosophy departments.
I agree! He's all growed up.
Best position on math I have heard discussed yet
Good to see a philosopher of mathematics speak on this
best interview in the series in by opinion. More from this guy please
Excellent
Also really impressed with Mark Balaguer. I want to know more about what he is saying and what he thinks.
But why is math a "descriptive aid"? One aspect of mathematics that does not seem to be a fiction is its logical consistency. That logical consistency seems to be the essence of its ability to capture certain truths about the world. I don't believe mathematics can merely be useful if it's indispensable.
watching it again..
Why didn't you interview some mathematicians?
This is a ten min clip, if you look up the full episode I'm sure he does.
"Useful" is one of the non-empty concepts of human languages. Here, non-empty concepts mean the meaning of a concept is partially independent to or partially free from the self-definition nature of the language. Other terms, such as applied, surviving etc., also have similar characteristics. Purpose, or usefulness, is the ultimate demarcation to defined the huaman defined realities and real realities. All science is applied science by means of graspability of the true realities. The true reason why many people, especially scientists believe things such as true reality, the beauty of mathematics, math is observed rather than invented, etc. etc., is because they have confused the difference between pure science and applied science. Real reality may or may not exist. Either way, it is either undefined yet or un-definable forever.
Bruce Lee eh?
@@torqueshock7236 I am a philosophical version of Bruce Lee.
@@JeffChen285 Kudos to you for what's a clever distinction on your part. Suffice it to say, whatever the context it's a name that I've always liked.
If a real reality may or may not exist then how can you state that "useful" is one of the non-empty concepts of human languages. If reality doesn't exist then a human created reality, in reality doesn't exist. As to math being observed rather than invented, well that is a questionable reality because everything about math is a human construct. If you have two apples and I have two apples then we have four apples and that is a certainty in our shared reality and how you come to realize that certainty is of your of your own doing and that doing may even amaze you, and you may even believe that you, or someone else discovered it instead of inventing it. I did enjoy your comment and my reply was deliberately argumentative and I mean no offense to your belief or mental acuity.
@@sedevacantist1 [If you have two apples and I have two apples then we have four apples and that is a certainty in our shared reality and how you come to realize that certainty is of your of your own doing?] ------ Simple. first, chimpanzees may not share with us. Second, some human tribes still can't count the number larger than 3 and they are going to categorize "4" to "many. "
I have to admit , the interviewer nailed it in this one. Questions were on point and he had an iron grip on the subject matter all the way through. Pity he isn't so astute with all the woowoo merchants he entertains on this channel.
Thinking about whether numbers exist or not, since commonsense can lead us astray, would it be better to start by considering a fractional, negative or imaginary number, or zero, rather than a small natural number we can show on our fingers?
Aren't numbers in general hypostasized abstract relations?
Yes exactly
I really can't wrap my mind around nominalism. Pity they finished on that note. How could it possibly be the case that the math is false but somehow it works in the world? It would require belief in some really weird 'conspiracy theory' type arrangement of reality, of the type of Descartes' Evil Demon who is perpetually deceiving us.
Nice Simpson analogy
Truth and beauty are abstractions. So are abstractions. Concrete isn't though.
Truth and beauty are ideas/concepts which have a reality of their own. Units of time or length or temperature are arbitrary units created by the human mind and they have a predictive quality. These predictive abilities breakdown in the quantum realm which proves free will and disproves determinism, which should be obvious to any honest person.
I wish he chose 1-1=
5-1=4
me this stuff not know. wish me knew stuff it. well oh
Can I argue my credit card bill is not true?
2+2=4
Self-evidently true.
Love this episode
platonic realism... got to be true for any grounding. I'm betting that beauty is a real universal. have you done an episode on the transcendental argument for God (TAG)? this is really the best argument for God in my opinion; I think it gives us a logical reason to believe that logic, reason & mathematics are something beyond simple grunts and gestures grounded in nothing more than practicality.
using a familiar metaphor,I think abstraction is probably causal in a way similar to source code utilized by a program, and run through hardware... the code (the Word) is a timeless universal. our mathematics & logic is a representative sub language fit for finite humans.
don't ask me to prove it, unless I can say that two plus two equals four because two plus two equals four and that is enough for you... it's just axiomatic. It just Is.
Nonsense.