- Aug 4, 2003It was written:

> > > If H is true then I is true

I replied:

> > > I is true

> > > Therefore H is true

> > The "argument" above is only

Steven D'Aprano wrote:

> > fallacious if we understand it

> > as a deductive argument. But

> > we MUST NOT understand it

> > that way. In a valid deductive

> > argument the word 'therefore'

> > expresses the fact that the

> > premises GUARANTEE the

> > conclusion, but here the

> > "premises" just give us a

> > stronger reason to believe that

> > the "conclusion" is true.

> However, your argument that this

Me again:

> reasoning is valid for inductive

> arguments isn't correct.

-- I didn't say this was an "inductive argument", and don't think we should

understand it like that.

First, I recommend that we reserve the word 'induction' for simple

"enumerative" induction ("the sun has risen every day so far, so it'll

probably rise again tomorrow"). I agree with Quine's view that enumerative

induction is a special case of the more general method of hypothesis (i.e.

the "hypothetico-deductive method").

Second, I think it's wrong to think of the above sequence as an "argument".

It is much better understood as a sort of DESCRIPTION of what happens when

a hypothesis is "confirmed".

Compare the following sequence of sentences, which describe a test to see

if a cake is fully cooked:

1. Push a metal skewer into the thickest part of the cake, withdraw it, and

see if it is "clean".

2. It is clean.

Therefore, the cake is done.

There is no temptation to think of this sequence of sentences as an

argument, probably because the "premises" do not contain the key

information expressed in the "conclusion", about the cake's "being done".

But it's easy to see how the test works -- it would be an "unlikely

coincidence" if the cake passed the test, and yet somehow remained

underdone. We would have to fall back on unusual circumstances to explain

it -- perhaps the oven does not heat evenly, or the thickest part of the

cake does not coincide with the point furthest away from the heat source,

or...

Similarly, if a hypothesis yields a prediction that turns out to be true,

and then does it again, and again, it becomes harder and harder to explain

how the hypothesis itself could be false. Passing a test is an "unlikely

coincidence" unless the hypothesis is in fact true, or at least

approximately true.

Jeremy Bowman

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