Thus it became a challenge to formulate a philosophical theory of mathematics that was free of platonistic elements. In the first decades of the twentieth century, three non-platonistic accounts of mathematics were developed: logicism, formalism, and intuitionism. There emerged in the beginning of the twentieth century also a fourth program: predicativism.
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Four theories of math
- Thread starter Hume
- Start date
Formalism
David Hilbert agreed with the intuitionists that there is a sense in which the natural numbers are basic in mathematics. But unlike the intuitionists, Hilbert did not take the natural numbers to be mental constructions. Instead, he argued that the natural numbers can be taken to be symbols. Symbols are strictly speaking abstract objects.I like the idea that an infinite number of prime numbers "exist" even though we haven't discovered them, and never will discover them.Thus it became a challenge to formulate a philosophical theory of mathematics that was free of platonistic elements. In the first decades of the twentieth century, three non-platonistic accounts of mathematics were developed: logicism, formalism, and intuitionism. There emerged in the beginning of the twentieth century also a fourth program: predicativism.
Perry the PhD only laughed and was incredulous at the concept of math being objectively true in a Platonic sense because he does not have the background or perception to enable him to encompass such concepts.
^^That is a strange limitation for a dude who claims to have studied philosophy at University.
I like the idea that an infinite number of prime numbers "exist" even though we haven't discovered them, and never will discover them.
Perry the PhD only laughed and was incredulous at the concept of math being objectively true in a Platonic sense because he does not have the background or perception to enable him to encompass such concepts.
^^That is a strange limitation for a dude who claims to have studied philosophy at University.
Jesus Christ, dude, let up on it for a bit. STOP JUST INSULTING.
If you don't understand what I'm saying just ask! Or google the words you don't understand.
Try discussing the TOPIC rather than just coming on here to bitch about people
Perry the PhD only laughed and was incredulous at the concept of math being objectively true in a Platonic sense
Incorrect. I said you are using "platonic" in a sense that doesn't really have any meaning. You couldn't explain what you mean by "math being objectively true in a platonic sense" any more than you could fly to the moon.
This is why I asked you the question you dodge over and over again.
If math had to be "established" for the universe in some fashion; do you believe that 1+1 = 2 had to be ESTABLISHED or is it simply the only way something CAN be?
Maybe this is what you mean by "platonic sense", but you have yet to actually explain your position (because you lack the intellectual honesty to admit you are just stringing impressive sounding words together that you don't understand)
It may be that you and I actually agree (we actually DO agree on many things, but your unquenchable hatred of me keeps you from admitting it), but it would require you to explain your position in some manner that actually indicates YOU know what your position is.
Or you can do what you USUALLY do and just stamp your feet and scream insults at me.
@Cypress: do you believe that before the Big Bang that in whatever "hyperspace-existence-free-whatever" that existed before the Universe Existed that the concept a thing being what it is and not some other thing did NOT exist? That it had to be ESTABLISHED?
Are you marveling at the EXISTENCE of math or the VALUE of the constants? Those are two VERY different things.
Are you marveling at the EXISTENCE of math or the VALUE of the constants? Those are two VERY different things.
I honestly think that the first 4 posts in this thread are posted by someone who has no ability to explain what ANY of them mean.
A challenge to the great "thinkers" @Cypress and @Hume : try expressing those posts in simple language (preferably your own).
I'll admit I don't understand them and I bet you don't either.
If you just shout insults at me instead of taking the challenge I'll know for CERTAIN!
A challenge to the great "thinkers" @Cypress and @Hume : try expressing those posts in simple language (preferably your own).
I'll admit I don't understand them and I bet you don't either.
If you just shout insults at me instead of taking the challenge I'll know for CERTAIN!
Predicativism
As was mentioned earlier, predicativism is not ordinarily described as one of the schools. But it is only for contingent reasons that before the advent of the second world war predicativism did not rise to the level of prominence of the other schools.
This is not an explanation of what Predictivism is. Would you care to try to explain it to a non-mathematician?
Logicism
The logicist project consists in attempting to reduce mathematics to logic. Since logic is supposed to be neutral about matters ontological, this project seemed to harmonize with the anti-platonistic atmosphere of the time.
Neutral about matters ontological. Please explain.
Screaming at me in ALL CAPS again?STOP JUST INSULTING.
That's not consistent with your claim that you follow me around and comment on my posts because it's "fun". An ALL CAPS screaming rant is not somebody having fun.
You don't believe in objective truth, whether it comes to morality, maths, or the laws of physics. Your faith is in human opinion, human omniscience, materialism, relativism, and frantic Googlism
I never expected you to be able to grasp concepts like Platonism, ontology, objective truth.
You couldn't explain what you mean by "math being objectively true in a platonic sense"
Simple.
That which is objectively true independent of human opinion and human experience.
Platonism and ontology -- objective truth and reality independent of human experience and perception -- should have been covered in the first three weeks of your philosophy classes. How did you miss this, since you claimed to have studied philosophy at university?
Why did you ban me from your thread on the meaning of the cosmos? Please tell me before I ban you from all my threads.I like the idea that an infinite number of prime numbers "exist" even though we haven't discovered them, and never will discover them.
Perry the PhD only laughed and was incredulous at the concept of math being objectively true in a Platonic sense because he does not have the background or perception to enable him to encompass such concepts.
^^That is a strange limitation for a dude who claims to have studied philosophy at University.
Please educate yourself. If you do not know what "ontological" means, look it up. Stop being a lazy asshole.Neutral about matters ontological. Please explain.
No, you're a jerkoff troll.This is not an explanation of what Predictivism is. Would you care to try to explain it to a non-mathematician?
You are an asshole troll. I am getting ready to put you on ignore for good.I honestly think that the first 4 posts in this thread are posted by someone who has no ability to explain what ANY of them mean.
I didn't ban you. It must have been an accident, or one of the Mods did it independently of me. I'll see if I can fix itWhy did you ban me from your thread on the meaning of the cosmos? Please tell me before I ban you from all my threads.
It's remarkable that someone who claimed to have studied philosophy in college is so confused about what Platonism and ontology are.Please educate yourself. If you do not know what "ontological" means, look it up. Stop being a lazy asshole.
Since I did not request the ban, I assume one of the moderators banned you without asking me. I sent a request to get you unbanned from the thread.Why did you ban me from your thread on the meaning of the cosmos? Please tell me before I ban you from all my threads.