- Aug 11, 2003Also false is the idea that while inductive evidence may not guarantee some

hypothesis with absolute certainty, it increases the probability that the

hypotheses is true. To take a simple example, it is true that if John is

immortal, he will be alive next week. However, it is not true that the longer

John lives the greater the probability that he will live forever. if John is

alive next week, he is actually closer to the date of his death than he is

today.

It is true that that if the implication of a hypothesis is true our

confidence in the hypothesis is greater, but this is only true

psychologically, not logically. This is the real "scandal" of Hume's argument

about induction. Someone on the list (I don't recall who) invoked Popper, and

Popper had the right of it. All you can really say if the implication of an

hypothesis is true is that the hypothesis is still viable; however there are

an indefinite number of other explanations which may have identical

implications. I am not arguing that we may not have reasonable grounds for

preferring some hypotheses (or theories) over others, but these grounds

transcend the simply empirical, at least in its narrower definitions. If I

believe that Darwinian ideas describe the evolution of life on Earth, it is

not simply because someone can demonstrate empirically that natural selection

occurs in some limited circumstances. It is also because those ideas

integrate so many different kinds of biological data from so many different

sources. It's really a very elegant, simple and conceptually satisfying

explanation.

Fredric Weizmann

Steven D'Aprano wrote:

> On Fri, 1 Aug 2003 04:47, Jeremy Bowman wrote:

>

> > > One way to test hypotheses it by

> > > examining test implications;

> > >

> > > If H is true then I is true

> > > I is true

> > > Therefore H is true

> > >

> > > This is a logical fallacy known as

> > > the 'Fallacy of Affirming the

> > > Consequent' and is logically invalid.

> >

> > My reply:

> > The "argument" above is only 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.

>

> This is an example of a deductive argument that you would agree is

> fallacious:

>

> If a man has two feet then he therefore has two legs.

> Fred has two legs.

> Therefore Fred has two feet.

>

> It is fallacious because Fred might have lost his feet in an accident,

> or otherwise have less than two feet. We agree with this.

>

> However, your argument that this reasoning is valid for inductive

> arguments isn't correct. Here is an inductive argument:

>

> I've seen 100,000 bus drivers, and they have all had two feet.

> Hence I use induction to conclude that all bus drivers have two feet.

> If a person is a bus driver, then inductively she is almost certain to

> have two feet.

>

> And the Fallacy of Affirming the Consequent would be:

>

> If a person is a bus driver, then inductively she is almost certain to

> have two feet.

> Susan has two feet.

> Therefore Susan is likely to be a bus driver.

>

> Alas for my reasoning ability, Susan is a chemist. Furthermore, bus

> drivers only make up a tiny minority of two-footed people.

>

> Affirming the Consequent is a fallacy whether one is talking about

> inductive or deductive reasoning. Regardless of whether you use

> deduction or induction to derive "X implies Y", it is always a fallacy

> to argue the reverse "Y implies X" without further evidence.

>

> > > Science is a matter of observation,

> > > hypothesis, and degrees of

> > > confidence - not truth.

> >

> > -- Oh yes it is! Consider the sentence 'Everest is higher than the

> > tallest mountain on Venus'. I have no idea whether this is true or

> > false -- my confidence in it is zero -- but as a matter of objective

> > fact, it IS either true or false. Furthermore, it is "absolutely"

> > true or false.

>

> I don't know. How do you define "height"? From sea level? From the

> lowest point on the planet? From the surrounding plains (if any)? From

> some arbitrary marker? Depending on how you define height, you may get

> a completely different answer to the question of which is higher.

>

> A few hundred years ago, a statement that a chemist might have asked

> might have been "Flowers of Sulphur contains more phlogiston than Aqua

> Regina". Was this statement absolutely true? If it were absolutely

> false, can we conclude that therefore Aqua Regina contains more

> phlogiston than sulphur?

>

> If X is false, and Not X is also false, then what have we discovered?

>

> I doubt that the concept of "height" will ever go the way of phlogiston,

> but it is conceivable that it might. In which case, neither Everest nor

> the mountain of Venus will be higher than the other.

>

> And even if height doesn't, who knows what will? If we knew, we wouldn't

> be wasting our time with incorrect scientific theories.

>

> --

> Steven D'Aprano - << Previous post in topic