Actually, it should. Communication is communication. (How's that for a piece of Sartrean wit?)
Or, in other words, and God knows I've been reading you for 30 years because you obviously believe in this, language is about clarity.
(It's still a side-issue, though.)
I can't think of a single instance of a logical or mathematical framework that allows you to "induc[e] a state of affairs in the world from a single instance in the future."
Well, I can, actually. That single instance (and as I say, it doesn't have to be a single instance -- as long as it covers the problem domain) is by necessity the single instance from which you infer the subsequents. Given my assumption that there is a part of the proof space where deduction is exactly equivalent to induction (and don't forget, I'm not sure there is one; I'm just allowing you that possibility), then, I believe, you are taking a deductive proposition such as
D <- C <- B <- A
and, in your words, "inducing [actually inducting, I think] a state of affairs in the world from a single instance."
I wish to put forth the proposition (in a Jim Morrison sort of way) that you cannot induce D from A. You cannot. Dum de dum de soft machine dum de dum ...
Your single instance is in the historical present. Your conclusions are based upon analysis of the historical past.
That would be deduction -- not induction.
Induction is normally represented as a recursive process. There is no recursion present in your argument.
On the side: No, you weren't using Holmesian elimination. You weren't even suggesting that you were. I used that as a metaphor, and you are throwing it back as an accusation. What you were doing was to use a set of (reasonably assumed) preconditions and arguing based on those preconditions. That still makes it a deduction when you are talking about the set of results based upon those preconditions.
Basically, I think what I'm saying is that you can inductively generate a statistical spread on "first principles," without history. If you are going to use (perfectly validly) a set of historical results (which already represents a statistical spread), then it's deduction. If only because you know more. (Which is what I thought was the point at issue in the first place.)
Of course, this might only go to prove that I was right to do two A-levels in Maths & Mechanics rather than one in pure maths and one in stats.
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Re: 1 In 4, Baby, 4 In 1
Date: 2010-07-10 06:36 pm (UTC)Or, in other words, and God knows I've been reading you for 30 years because you obviously believe in this, language is about clarity.
(It's still a side-issue, though.)
I can't think of a single instance of a logical or mathematical framework that allows you to "induc[e] a state of affairs in the world from a single instance in the future."
Well, I can, actually. That single instance (and as I say, it doesn't have to be a single instance -- as long as it covers the problem domain) is by necessity the single instance from which you infer the subsequents. Given my assumption that there is a part of the proof space where deduction is exactly equivalent to induction (and don't forget, I'm not sure there is one; I'm just allowing you that possibility), then, I believe, you are taking a deductive proposition such as
D <- C <- B <- A
and, in your words, "inducing [actually inducting, I think] a state of affairs in the world from a single instance."
I wish to put forth the proposition (in a Jim Morrison sort of way) that you cannot induce D from A. You cannot. Dum de dum de soft machine dum de dum ...
Your single instance is in the historical present. Your conclusions are based upon analysis of the historical past.
That would be deduction -- not induction.
Induction is normally represented as a recursive process. There is no recursion present in your argument.
On the side: No, you weren't using Holmesian elimination. You weren't even suggesting that you were. I used that as a metaphor, and you are throwing it back as an accusation. What you were doing was to use a set of (reasonably assumed) preconditions and arguing based on those preconditions. That still makes it a deduction when you are talking about the set of results based upon those preconditions.
Basically, I think what I'm saying is that you can inductively generate a statistical spread on "first principles," without history. If you are going to use (perfectly validly) a set of historical results (which already represents a statistical spread), then it's deduction. If only because you know more. (Which is what I thought was the point at issue in the first place.)
Of course, this might only go to prove that I was right to do two A-levels in Maths & Mechanics rather than one in pure maths and one in stats.
Can't say I feel the loss after all these years.