Learning the foundations of logic isn't going to mess you up. Learning about the philosophical grounding of science isn't going to mess you up.

Nobody is claiming anything close to that.

My claim has been and continues to be that it causes confusion and weakens his message for the good of science when it's not clear which one he's doing and his message gets mixed between advocating for science and just pontificating on various topics.

Would you say that philosophy will mess you up and cause you to not be able to do science?

But then why is the consistency of ZF critical to these proofs, given we can't even prove the consistency/existence of those definitions with ZF?

I agree with you that math is about writing some stuff down and doing things that are verifiably correct and writing something down at the end which must be correct because every step along the way was correct. But this is not the same are writing down an axiomatic system and rigidly demanding proofs from this system. If we did that math wouldn't be a ton further than where Euclid left it.

So now foundations are critical? I think you know more about this than me, so I have a question for you: what is a good example of an axiomatic system in math that is known to be consistent?

Same ballpark? How are you defining "axiomatic system"?

I think with something like products, because that is a very basic construction in math. If you don't know what products are categorically, then you don't really know what products are.

One might interpret category theory as saying that function composition is the most fundamental thing of all. Of course I don't think that category theory should be taught in schools, but I absolutely think that sets, functions and function composition in the abstract should be. (In most schools in the UK they are not, but in the schools that the wealthy pay for their children to go to they are.)

Don't think I said/implied that.


[qutoe]I think you know more about this than me, so I have a question for you: [/quote]

I prob don't know more than you....my advisers were philistines .....

I'm not sure tbh.....From random elevator/bar conversations with foundation/logic experts, I think it comes down to defining logical systems so weak that you can just list all expressible statements and brute force consistency. There are Euclidean Geometry style systems that can prove their consistency but I'm not sure why/if they couldn't prove their inconsistency.

To me, a real "axiomatic system" would mean that anything humans prove could be checked by a modern computer.

No need to wait for Witten to verify your proof of Yang Mills....no reason for the Poincare conjecture delay/ABC saga etc.

He never said don't learn the foundations of logic or science. Not once.

This is how modern computers came about.

http://en.wikipedia.org/wiki/Computer

Mine too. Constructivists who believed in the axiom of infinity FFS.

Those foundations are philosophy which he said not to think about. People who thought about such philosophy invented the enlightenment. I suppose he feels that it's no longer necessary to think about such things since we can't do any better than what we have. He has that in common with the religious fanatics from the dark ages who felt the same way.

That part of "philosophy" is now called "science." He never said that we shouldn't think about science and he certainly didn't say that what we now call science wasn't called philosophy in the past.

It is simply a rejection of old methods of discovery that don't work.

He said (in the other video) that if the philosophers figure out some interesting answers to "deep"* questions, that would be cool. At best, they seem to be taking their time about it.

*non-vulgar questions (using the old definition)

Modern computers came about because of transistors.....not really the existence of universal Turing Machines.

But without people conceptualizing such things first, nobody would really have thought to try to create things that behave like this.

Name dropping, for all of its rhetorical power, usually works best when you spell the name right.

In any event, there may be a bit more to the Galileo affair than you are aware. The high school history textbook version of the story is usually oversimplified, for the sake of promoting the same "science vs. religion" narrative we find in Cosmos.

Church authorities had made clear to Galileo almost two decades before 1633 (his trial) that there needed to be a scientific demonstration of Copernicanism before Galileo could insist that Scripture needed to be reinterpreted to accommodate this cosmological theory. Galileo failed to produce any such demonstration; such demonstration is impossible, since Copernicanism is false.

I realize that it's an extremely foreign and strange notion that the Church had anything to say at all about what books could be published or what claims about physics were allowed to be advanced publicly, but that's really a separate issue from the "science vs. religion" narrative. A huge component of Galileo's trial was the weighing and rejection of his scientific arguments for Copernicanism. If he had been able to advance a scientific proof for Copernicanism (which, again, he couldn't, because Copernicanism is false), then the Church would have agreed that a reinterpretation of Scipture (away from its prima facie meaning in various passages) was necessary.

I'll humbly disagree with Von Neumann there. I think Babbage essentially conceptualized a computer without having any notion of Turing style universality.

http://en.wikipedia.org/wiki/Analytical_Engine

Philistines.

I'll focus on this linked blog-post.

There is definitely irony in using the word philistine to denote someone as lacking in knowledge about history, so in that sense I think Damon Linker's blog-post fails before it even begins.

That said the quotation by Tyson as presented could be construed as controversial, but I also think it would be impossible to give a summary of history, science or philosophy that could not be criticized by someone. Also; Tyson's statement might be somewhat crude, but the linked blog about the quote is very crude. I find the extrapolation from Tyson's commentary about philosophy to also include "literature, history, the arts, or religion" to be extremely strenuous.

The worst example however, is when Damon Linker implicitly states that "middle managers" and "used car salesmen" are anti-intellectuals. Such elitist statements about people's intellectual interests and capacity based on their vocation are fairly absurd in a blog-post that applauds "reflecting on human nature". A used car salesman or a middle-manager could be very knowledgeable about arts, history, philosophy or culture.

In the beginning there was philosophy.

In the end there will be philosophy.