Peterdjones comments on Intuitions Aren't Shared That Way - Less Wrong

31 Post author: lukeprog 29 November 2012 06:19AM

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Comment author: Peterdjones 05 December 2012 11:22:01AM -2 points [-]

How does it not match? Take the 4 color problem. It says you're not going to be able to construct a minimally-5-color flat map. Go ahead. Try.

That doesn't matfch reality because it would still be true in universes with different laws of physics.

'predict accurately or you're wrong' the same as 'anything goes'?

It isn't. It's a standard of truth that too narrow to include much of maths.

I mean, if astrology just wants to be a closed system that never ever says anything about the outside world

That doens't follow. Astrologers can say their merchandise is about the world, and true, but not true in a way that has anything to do with correspondence or prediction.

Comment author: Luke_A_Somers 06 December 2012 06:47:32PM * 0 points [-]

That doesn't matfch reality because it would still be true in universes with different laws of physics.

If you're in a different universe with different laws of physics, your implementation of the 4 color problem will have to be different. Your failure to correctly map between math and reality isn't math's problem. Math, as noted above, is of the form 'if X and Y and Z, then A' - and you can definitely arrange formal equivalents to X, Y, and Z by virtue of being able to express the math in the first place.

That doens't follow. Astrologers can say their merchandise is about the world, and true, but not true in a way that has anything to do with correspondence or prediction.

It's about the world but it doesn't correspond to anything in the world? Then the correspondence model of truth has just said they're full of shit. <voice actress="Hayashibara Megumi">Victoreeee!</voice>

(note: above 'victory' claim is in reference to astrologers, not you)

Comment author: Peterdjones comment score below threshold [+] (32 children)

Comment author: RobbBB 06 December 2012 07:11:28PM 1 point [-]

People who have different 'theories' of truth really have different definitions of the word 'truth.' Taboo that word away, and correspondence theorists are really criticizing astrologists for failing to describe the world accurately, not for asserting coherentist 'falsehoods.' Every reasonable disputant can agree that it is possible to describe the world accurately or inaccurately; correspondence theorists are just insisting that the activity of world-describing is important, and that it counts against astrologists that they fail to describe the world.

(P.S. Real astrologists are correspondence theorists. They think their doctrines are true because they are correctly describing the influence celestial bodies have on human behavior. Even idealists at least partly believe in correspondence theory; my claims about ideas in my head can still be true or false based on whether they accurately describe what I'm thinking.)

Comment author: Peterdjones 06 December 2012 07:23:38PM -1 points [-]

People who have different 'theories' of truth really have different definitions of the word 'truth.'

That is not at all obvious. Let "that which should be believed" be the defintiion of truth. Then a correspondence theorist and coherence theorist stlll have plenty to disagree about, even if they both hold to the definition.

Comment author: RobbBB 06 December 2012 07:31:43PM * 0 points [-]

That is not at all obvious.

Agreed. However, it's still the right view, as well as being the most useful one, since tabooing lets us figure out why people care about which 'theory' of 'truth' is.... (is what? true?). The real debate is over whether correspondence to the world is important in various discussions, not over whether everyone means the same thing ('correspondence') by a certain word ('truth').

Let "that which should be believed" be the defintiion of truth.

You can stipulate whatever you want, but "that which should be believed" simply isn't a credible definition for that word. First, just about everyone thinks it's possible, in certain circumstances, to ought to believe a falsehood. Second, propositional 'belief' itself is the conviction that something is true; we can't understand belief until we first understand what truth is, or in what sense 'truth' is being used when we talk about believing something. Truth is a more basic concept than belief.

Comment author: Luke_A_Somers 06 December 2012 09:53:55PM 0 points [-]

I don't have to implement it at all to see its truth. Maths is not just applied maths.

At the very least, you can make something formally equivalent if you're capable of talking about it.

If your branch of mathematics is so unapplied that you can't even represent it in our universe, I suspect it's no longer math.

Comment author: Peterdjones 07 December 2012 11:21:19AM -2 points [-]

If your branch of mathematics is so unapplied that you can't even represent it in our universe, I suspect it's no longer math.

Any maths can be represented the way it ususally is, by writing down some essentially aribtrary symbols. That does not indicate anything about "correspondence" to reality. The problem is the "arbitrary" in arbitrary symbol.

Lets say space is three dimensional. You can write down a formula for 17 dimensional space, but that doens't mean you have a chunk of 17 dimesional space for the maths to correspond to. You just have chalk on a blackboard.

Comment author: Luke_A_Somers 07 December 2012 03:47:23PM 1 point [-]

Sure. And yet, you can implement vectors in 17 dimensional spaces by writing down 17-dimensional vectors in row notation. Math predicts the outcome of operations on these entities.

Comment author: Peterdjones comment score below threshold [+] (25 children)

Comment author: Luke_A_Somers 07 December 2012 07:25:45PM 3 points [-]

(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6) is a perfectly valid 17-vector.

The predictions of the mathematics of 17-dimensional space would, yes, depend on the outcome of other operations such as addition and multiplication - operations we can implement more directly in matter.

I have personally relied on the geometry of 11-dimensional spaces for a particular curve-fitting model to produce reliable results. If, say, the Pythagorean theorem suddenly stopped applying above 3 dimensions, it simply would not have worked.

Comment author: Peterdjones 08 December 2012 03:50:01AM 1 point [-]

(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6) is a perfectly valid 17-vector.

I'm seing pixels on a 2d screen. I'm not seeing an existing 17d dimensional thing.

The mathematics of 17d space predict the mathematics of 17d space. They couldn't fail to. Which means no real prediction is happening at all. 1.0 is not a probability.

Comment author: Luke_A_Somers 10 December 2012 09:29:50AM 3 points [-]

There are things we can model as 17-dimensional spaces, and when we do, the behavior comes out the way we were hoping. This is because of formal equivalence: the behavior of the numbers in a 17-dimensional vector space precisely corresponds to the geometric behavior of a counterfactual 17-dimensional euclidean space. You talk about one, you're also saying something about the other.

Is this point confusing to you?

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Peterdjones comments on Intuitions Aren't Shared That Way - Less Wrong

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