My previous post was quite brief, so here are a few more thoughts on the two paragraphs quoted therein. The first paragraph was about estimating the danger posed by the LHC to the planet (if not the universe), and the big argument for safety is that cosmic rays produce such collisions all the time. Whatever a collider might produce, it’s very likely that such has already been produced on the moon, for example, lots and lots of times. And of course, the moon’s still there. That argument doesn’t seem to depend upon the niceties of particle physics. But cosmic rays spread out from the sun. So they are most concentrated near the sun. What if some merging of products of collisions is most likely nearest the sun? Such events might not occur on the moon, but might occur in the most concentrated beams of our biggest colliders. So how likely is it that such an event causes tiny ripples on the sun? The problem is that such an event would destroy the earth. And our most popular theories have little to say about such questions (and did fail to predict dark matter).
Furthermore, suppose we could estimate the answer at no more than one in a billion. Would that be safe? We are talking about the possible destruction, not only of less than ten billion people, but of all possible future human beings. What figure should be given to that? So we also need some way of determining just how safe a oneinabillion chance of destroying the human race really is (as Sample noted). Since that problem is so intractable (cf. the St. Petersburg Paradox), surely the main thing here is that we do have better things to do, things associated with more mundane risks (and more immediate benefits). Even theoretical physicists have plenty of other puzzles to solve. A competitive Academia may encourage them to excel at the language game of string theory, but surely the most puzzling thing in theoretical physics (given the materialism there) is the absence of anything at the fundamental level that could conceivably give rise to awareness when the fundamental particles are parts of complicated biochemical systems (the elephant in the room in which we debate synthetic biology).
Or they could address their big methodological problem, which is the question of what they should be thinking they’re doing. The language of science is mathematics, but standard mathematics is heavily influenced by Formalism, which encourages the move from general interest in a new type of theory, to the adoption of the presuppositions of that type of theory. We all know what is meant by ‘1 + 1 = 2’, but standard mathematicians will tell you that it means that {0, {0}} follows {0} in the von Neumann series (where those are ZFC sets, and ‘0’ denotes the empty set). They will say that that is just the language game that is modern mathematics. But mathematics is not a game, but the language of science; and that word ‘language’ is being used metaphorically. The literal languages of science are our natural languages, which include mathematical terminology when one is doing science. It is a philosophical question, what those terms refer to, if anything; but the meaning of mathematical statements is clearly akin to logic (not a madeup, formal logic, but the logic that all scientists should apply).
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4 comments:
Sorry to be pedantic, but I disagree to the statement: "standard mathematicians will tell you that `1+1=2' means that {0, {0}} follows {0}". Most standard mathematicians will tell you it's true by definition, that `2' is 1+1 *by definition*, where `1' and `+' are not specified concrete objects but rather are given by the axioms of a ring.
Even a logician who does take the von Neumann series literally, would not say that. "Follows" is a statement about orders, about the set <. "1+1=2" is a statement about the set +, namely that it contains the triple (1,1,2)...
I agree that 2 is 1 + 1 by definition, and that most mathematicians would say that; but standard mathematics is based on standard set theory.
If you were ever to have a problem with the standard real numbers, standard mathematicians would tell you so. That's what makes them standard. I would say that '+' is a special sort of operation when it comes to the real numbers. Two units of measure need to be put together in the right way to get a measure of two. Standard mathematicians don't like to think like that (nor do most analytic philosophers).
I don't know about rings; is what you say true? I take rings to be algebraic entities. So they are usually defined using sets, in standard maths books. I would try to define them (and all other algebraic entities) more generally than that. But then, I'm not standard. Maybe you're right about standard mathematicians using rings. The books I was referred to by standard mathematicians all used the von Neumann series.
But my point is the same either way. Rings are either defined Formalistically (or Fictionalistically, etc.), or they are defined in terms of real structural properties, in which case axioms are descriptive, and not fundamental.
By 'follows' I mean 'is the successor of', where that's an undefined functional relationship between ordinal numbers. Intuitively, 2 follows 1 in the series 0, 1, 2...
The Paradox is overcome if one treats language and math as expressions only. Even a definition is but an expression, or really bad poetry or very precise poetry. This pushes language into a state of embodiment, or neurology and as thus eliminates the conceptual split between the idea of expression vs, description. Description is best understood as simply expression and not a something unto itself true. Primate speaks, thus expresses, not disembodied Abstractive being that evolved from primate that generates description apart or separate from expression literally. Language and math are narratives, pictures, photographs of the world around us that we share. To think otherwise is to be as an aboriginal thinking that the camera has magically created you inside the paper.
David, by your own admission what you say just expresses your feelings. In fact, you are one person. That 'one' is not poetry but counts such things as you, or that word itself, or any thing. Atheists are, I think, forced to treat even such words as poetic, for such reasons as you give. But why you think that that overcomes rather than generates paradox I can only imagine. Perhaps it is like how problems disappear when one is very drunk.
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