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Intuitionism

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Re: Intuitionism

#171

Post by cubefox »

tunesmith wrote: post #164
cubefox wrote: post #145

Earlier quoted context omitted.

If there is an independent source of truth (external reality), then classical logic makes sense and intuitionistic logic doesn't. But intuitionists say mathematics, unlike the physical would, doesn't have such an independent reality. There is no platonic mathematical reality apart from explicit mathematical construction. Then classical logic is inappropriate and intuitionistic logic has to be used for mathematics.

So then what kind of logic is the following: "Socrates is a male" has a value of True; "All men are mortal" has a value of True; and a conclusion of "Socrates is mortal" that is "True" because a True "and" a True yields a True. And then an immortal man is discovered, making that first premise "False". And False "and" a True yields a "False". This causes "Socrates is mortal" to have a truth value of "False", which doe…

> "Socrates is a male" has a value of True; "All men are mortal" has a value of True; and a conclusion of "Socrates is mortal" that is "True" because a True "and" a True yields a True.

No, for a logical argument the conclusion must be true if the premises are true. A valid argument (proof) only shows: necessarily, if the premises are true, the conclusion is true.

> And then an immortal man is discovered, making that first premise "False". And False "and" a True yields a "False".

> This causes "Socrates is mortal" to have a truth value of "False"

No...

Re: Intuitionism

#172

Post by Tainnor »

theamk wrote: post #162
Tainnor wrote: post #156

Earlier quoted context omitted.

> "unlike hard sciences, philosophy only affects philosophers" Studying history will very quickly dissuade you from this notion, over and over again. For the perhaps most striking example, consider how different the 20th century would have looked like if a certain philosopher named Marx hadn't tried to marry the works of another philosopher, Hegel, with economic theory.

And yet, it was not Marx or Hegel who took over the country and started campaign on Red Terror. And Lenin did not need to cite Das Kapital to start Russian Civil War. (I have no doubt he was inspired by it though) (It's an interesting thought experiment what would have happened if there were no Karl Marx. February Revolution would have happened anyway.. but would bolsheviks still exist? Would Lenin still do all the t…

Lenin wasn't only "inspired" by Marx, he wasn't even the first Russian socialist. Marxism was simply the framework that a lot of the socialist revolutionaries at that time were operating in (including ones that Lenin ended up opposing later).

Sure, given the economic and political realities of Russia at that time, something might have happened even if Marx hadn't existed, but it might have looked very different.

Philosophy matters to the world because other people read philosophy and are inspired by it to change something about the world. The French Revolution, US independence, Latin American independence and so on were all undertaken in no small part by people who had read a lot and were trying to make some of their ideals reality.

Re: Intuitionism

#173

Post by mistercheph »

mecsred wrote: post #160
cubefox wrote: post #146

Earlier quoted context omitted.

Yeah. There are some approaches in philosophy of mathematics which try to avoid platonism (the view that mathematical objects have a mind independent existence) but while also retaining classical logic. That's not easily done though. (Currently popular is "structuralism", but this theory has its own problems.)

I do appreciate you providing some relevant information instead of just telling everyone else they're wrong. You still haven't put any of your own ideas on the line though. Is there an approach you believe is correct, and why? Here's one of mine so I play by my own rules: philosophical questions don't have any testable hypothesis by nature, they'd be scientific questions if they did. The goal is to massage the questi…

What is testing a hypothesis?

Re: Intuitionism

#174

Post by rambojohnson »

glcheetham wrote: post #87
rambojohnson wrote: post #83

Earlier quoted context omitted.

I understand where you're coming from, and pragmatic perspectives certainly have their place. However, philosophy, including intuitionism, can offer us new ways to comprehend the world. It's not about destabilizing our understanding, but rather enriching it. Although it can be challenging, this exploration can also bring greater depth to our perception and reality, much like the yin and yang you mentioned. Even if we…

Sounds like GPT wrote this comment

and AI thinks the Constitution was written by AI: https://arstechnica.com/information-technology/2023/07/why-a...

Re: Intuitionism

#175

Post by mecsred »

mistercheph wrote: post #173
mecsred wrote: post #160

Earlier quoted context omitted.

I do appreciate you providing some relevant information instead of just telling everyone else they're wrong. You still haven't put any of your own ideas on the line though. Is there an approach you believe is correct, and why? Here's one of mine so I play by my own rules: philosophical questions don't have any testable hypothesis by nature, they'd be scientific questions if they did. The goal is to massage the questi…

What is testing a hypothesis?

If you'd like to ponder this question and more, please sign up for a course called "Philosophy of Science". It won't help answer it, but it's easy marks.

Re: Intuitionism

#176

Post by mistercheph »

mecsred wrote: post #175
mistercheph wrote: post #173

Earlier quoted context omitted.

What is testing a hypothesis?

If you'd like to ponder this question and more, please sign up for a course called "Philosophy of Science". It won't help answer it, but it's easy marks.

Sorry, I just figured from all your chest puffing that you had something to say, it appears you don't.

Re: Intuitionism

#177

Post by mecsred »

mistercheph wrote: post #176
mecsred wrote: post #175

Earlier quoted context omitted.

If you'd like to ponder this question and more, please sign up for a course called "Philosophy of Science". It won't help answer it, but it's easy marks.

Sorry, I just figured from all your chest puffing that you had something to say, it appears you don't.

I made my point above. You're the one with nothing to say, you lead with a generic question.

Re: Intuitionism

#178

Post by cubefox »

mecsred wrote: post #160
cubefox wrote: post #146

Earlier quoted context omitted.

Yeah. There are some approaches in philosophy of mathematics which try to avoid platonism (the view that mathematical objects have a mind independent existence) but while also retaining classical logic. That's not easily done though. (Currently popular is "structuralism", but this theory has its own problems.)

I do appreciate you providing some relevant information instead of just telling everyone else they're wrong. You still haven't put any of your own ideas on the line though. Is there an approach you believe is correct, and why? Here's one of mine so I play by my own rules: philosophical questions don't have any testable hypothesis by nature, they'd be scientific questions if they did. The goal is to massage the questi…

> I do appreciate you providing some relevant information instead of just telling everyone else they're wrong. You still haven't put any of your own ideas on the line though. Is there an approach you believe is correct, and why?

I think a form of logicism (the view that mathematical statements are logical tautologies in disguise) is true at least for arithmetic. There are some ways to interpret them using logical truths from pure higher-order logic. I'm not sure about most other parts of mathematics.

> Here's one of mine so I play by my own rules: philosophical questions don't have any testable hypothesis by nature

I think they are testable by performing conceptual analysis, which consists in organizing data from semantic intuitions about the involved concepts.

Re: Intuitionism

#179

Post by nextaccountic »

theamk wrote: post #161
nextaccountic wrote: post #143

Earlier quoted context omitted.

Intuitionism has had a great impact on computer science and the design of many programming languages. It's now widely known that an intuitionistic proof has computational content (through the curry-howard correspondence) Those things have a real world impact

I have no doubt it had an impact on Curry personally, but it does not it has direct impact to on the the computer science. The Curry–Howard correspondence is formulated entirely in mathematical terms, and no philosophy is required to understand and use it. For example, Robert Goddard, who invented first liquid-fueled rocket, became interested in space when he read Wells' "The War of the Worlds". So did Wells' work ha…

The philosophy has an impact in the mental model and the learnability of the mathematical theories. Technically you could learn and use the mathematics without knowing the philosophy behind it but in practice almost nobody does that.

It's like knowing design patterns in OO: it's ultimately all software right? But software exists first in the mind of the programmer, and what's written in the IDE is just a shadow of what the programmer imagined. This makes one appreciate the point that there are things in software that exists entirely inside our heads

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