Monday, September 9, 2024

All Equalities are Tautologies

 There are some moments of truly shocking intellectual incompetence. I have a hunch I shouldn't be shocked, but nevertheless. They're moments like the following.

 Every true equation takes the form A=A.  E.g, let's imagine B=C, an allegedly meaningful statement. But, if it is true, we can do the substitution: C=>B, therefore B=B. The fact it's true is what makes it a tautology. All true statements without exception are some variant of the statement that 0=0.

 The only way for a statement to avoid being a tautology is to be false. It's a wholly useless distinction, a wholly useless idea, and a wholly useless word. Furthermore, the issue is not complicated. Furthermore, it doesn't turn on some tricky distinction or a recursive feedback. If you just check whether your favourite statement is isomorphic to a tauatology, you find that it is. 

 How did this ever become a famous issue in intellectual circles? Do they all have bus-tunnel-sized holes in their brains?
 But, if they do, how did they ever produce the slightest sliver of anything worth reading?

8 comments:

rezzealaux said...

“Suppose you have two theories, A and B. Both completely different psychologically, different ideas and so on. But all the consequences they computed are exactly the same. They may even agree with the experiments. The two theories, although they sound different at the beginning, have all the consequences the same. […] Suppose we have two such theories: how are we going to decide which one is right?

No way. Not by science. Because they both agree with experiments there’s no way to distinguish one from the other. So two theories, although they may have deeply different ideas behind them, may be mathematically identical, and usually people say then in science ‘one doesn’t know how to distinguish them’. And that’s right.

However, for psychological reasons, in order to get new theories, these two things are very far from equivalent. Because one gives a man very different ideas than another. By putting a theory in a certain kind of framework you get an idea what could change. Which in theory A would talk about something, you say I’ll change that idea here, but to find out what corresponding things you’re going to change in B could be very complicated. It may not be a simple idea. In other words, a simple change here makes maybe a very different theory than a simple change there. In other words, although they are identical before they’re changed, there are certain ways of changing one which look natural, which don’t look natural in the other. Therefore psychologically, we must keep all those theories in our head. Every theoretical physicist that’s any good knows six or seven different theoretical representations for exactly the same physics, and knows that they’re all equivalent, and that nobody is ever going to be able to decide which one is right – at that level – but he keeps them in his head, hoping that they’ll give him different ideas.”

Foster said...

I took too many levels of fighter to be able to read these runes. Lol wut?

Alrenous said...

If they can't be experimentally distinguished they are in fact the same theory.
This guy is talking about stupid physicists who have to use hacks to get around the fact they're stupid. Which makes sense: they gave up training intelligent scientists in 1945. Banned anyone above around IQ 145 from universities. (Easy to remember that pair of numbers.)

Philosophy example: determinism and libertarianism are in fact the same theory. Haha, whoops. Turns out philosophers are dumb too. Also trained at the now-nationalized universities, after all. Nationalization = desecration.

rezzealaux said...

i dunno, seems clear to me. though that may be because i am below 145.
maybe i'm not sure what your question is either though. what exactly is the problem? "truth isn't supposed to be a tautology"? is that what someone is saying?

Alrenous said...

It's true that lowbrow physicists can use different formulations of the same theory to come up with different new proposals for theories.
However, what they should be doing is trying to understand how they see two of the same thing as different, because it's guaranteed to be due to a delusion. They're hallucinating.

--

"The problem of constructing practical algorithms to determine whether sentences with large numbers of propositional variables are tautologies is an area of contemporary research in the area of automated theorem proving."
https://en.wikipedia.org/wiki/Tautology_%28logic%29

Super easy: if it's true, it's a tautology. If it's not true, it's not a tautology.
Just wrecked an entire field, automated proving, with one sentence.

This also works for physicists. The provers are having trouble determining whether something is a tautology apart from being true...because it isn't. Likewise, physicists have trouble when they believe false things.

rezzealaux said...

they're seen as different because of their originally different purposes, right? like having cartesian vs polar coordinates. i suppose purpose and value are, in the wealth cap sense, delusions.

Alrenous said...

Nature per se doesn't have a human purpose. It's something mortals layer upon Nature for Envy competition purposes. It tells you about the narcissist who formulated the theory, and nothing about the underlying Reality it's allegedly about.

rezzealaux said...

"The next point is the question of whether when we try to get a new law, whether we should use a seat-of-the-pants feeling and philosophical principles - "I don't know the minimum principle" or "I do like the minimum principle", or "I don't like action at a distance" or "I do like action at a distance" - the question is to what extent models help, and it's a very interesting thing.

Very often models help and most physics teachers try to teach how to use these models and get 'a good physical feel for how things are gonna work out'. But the greatest discoveries, it always turns out, abstract away from the model, it never did any good. Maxwell's discovery of electrodynamics was first made with a lot of imaginary wheels on idlers and everything else in space. If you got rid of all the idlers and everything else in space: the thing was okay. Dirac discovered the correct laws of quantum mechanics simply by guessing the equation. And the method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows that mathematics is a deep way of expressing nature, and attempts to express nature in philosophical seat-of-the-pants mechanical feeling is not an efficient way.

I must say that it is possible and I've often made the hypothesis, that physics will ultimately not require a mathematical statement, that the machinery will be revealed [to be] just a prejudice, like one of these other prejudices. It always bothers me, that in spite of all this 'local' business, what goes on in no matter how tiny a region of space and no matter how tiny a region of time, according to the laws as we understand them today, takes a computing machine an infinite number of logical operations to figure out. Now how can all that be going on in that tiny space? Why should it take an infinite amount of logic to find out what one stinky tiny bit of space-time is going to do? I've made a hypothesis often that the laws are going to turn out to be in the end simple like the checkerboard, and all the complexities are from size.

But that is of the same nature as the other speculation that other people make, "I like it" "You don't like it" It's not good to be too prejudiced about this sort of thing."