Tom writes in the comments:
No, no, no, no, NO. Induction does not follow from mere logic. No matter how many times you flip the coin and it comes up heads, that does not logically imply that it will come up heads the next time. It doesn't, logically, imply anything about the future at all. That is Hume's case against induction, which generations of philosophers have acknowledged and wrestled with.
Deduction does follow from the principles of logic, i.e. if "Socrates is a man," and "all men are mortal," then "Socrates is mortal" follows. But since we can never prove "all men are mortal" without induction, this doesn't do us much good.
The universe cannot disobey logic. You may call that a "faith-proposition" if you like, though I will call it an axiom. Since the universe obeys logic, induction necessarily follows. It's no more complicated than that.
No, no, no, no, NO. Induction does not follow from mere logic. No matter how many times you flip the coin and it comes up heads, that does not logically imply that it will come up heads the next time. It doesn't, logically, imply anything about the future at all. That is Hume's case against induction, which generations of philosophers have acknowledged and wrestled with.
Deduction does follow from the principles of logic, i.e. if "Socrates is a man," and "all men are mortal," then "Socrates is mortal" follows. But since we can never prove "all men are mortal" without induction, this doesn't do us much good.
posted by Nathanael at
11:12 AM
7 Comments:
I guess one could say that if the universe must follow a set of equations, the contingent facts of our observable universe will always follow the same rules. After all, modern physics treats time as an extended dimension of the same kind as length or width. Subject to the same stochastic effects limning spatial interaction, there's no more additional wiggle room for time to change interaction dynamics than space, which is to say, none.
Of course, we came to out math by way of scientific empiricism, so it's not inter alia a mathematical proof of induction. I do wonder, however, if a completed, unified model will show that the rules (not necessarily our observed instantiation thereof) can only be one fundamental way, in which case mathematics will have drilled down to an a priori proof of induction.
This is a sort of side note, because I think Tom's rhetoric may have overshot in the case Lance cites.
By
Anonymous, at 11:43 AM
Perhaps I was not being clear. I am well familiar with Hume's argument, and it boils down to saying that just because A+B=C at some point in time doesn't mean that A+B=C at all points in time. I think that argument is untenable and illogical. There is no "chance" the sun could have not come up the day it was observed coming up. The particular configuration of the universe that lead to the sun coming up must necessarily always produce that outcome if the universe is to be coherent at all. Hume argues that the universe could still be incoherent and merely give the impression of coherence by seeming to obey logical patterns. But there is no difference between seeming to obey and obeying logic. Obeying logic is a necessity, and thus induction follows.
By
Anonymous, at 12:27 PM
Let me put it another way. If we tightly control starting conditions for an experiment, and perform it over and over again, then induction allows us to predict within a certain margin of error, determined by a statistical analysis of the experiment, the outcome of future experiments with the same or similar conditions. If the universe were incoherent, then induction would not work. Hume argues that the universe could merely seem coherent over the course of many many experiments/observations, but that doesn't actually prove that the universe is coherent, ie that the next experiment/observation will agree with prior experiments/observations. Now, my point is that if you take the coherence of the universe to be true de facto, then induction follows.
By
Anonymous, at 1:11 PM
My point: if the universe is coherent, then induction works.
Hume's point: if the universe is incoherent, then induction might still seem to work; the utility and veracity of induction cannot prove the universe to be coherent or incoherent either way.
Indisputable: induction definitely seems to work.
Up for grabs: is the universe coherent, or not?
I assume that the universe is coherent. You may choose to assume otherwise if you wish.
By
Anonymous, at 1:28 PM
On second thought, the coherence of the universe is not really up for grabs, it's necessarily true like I stated earlier. If an outcome occurred that totally went against everything we know, it would still fit into some logical framework that we haven't figured out yet. It's impossible for something to be void of logic, just like it's impossible for nothingness to be instantiated. So given all of that, I maintain my previous statement that induction is a logical necessity.
By
Anonymous, at 1:37 PM
Ah, but in this last you definitely get controversial, philosophically speaking. More commentary later.
By
Anonymous, at 2:57 PM
One should say that something truly devoid of logic is inconceivable.
Besides German grammar, of course.
By
Anonymous, at 3:11 PM
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