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From: Bill Taylor on 12 Jan 2010 23:11
> All perfectly standard inductive arguments, none of them fitting your form.

Do so too!

___________________

* Postmodernists still fly in aeroplanes rather than on broomsticks,
* even though they "think all views are equally valid".
From: Jesse F. Hughes on 13 Jan 2010 09:51
Bill Taylor <w.taylor(a)math.canterbury.ac.nz> writes:

>> All perfectly standard inductive arguments, none of them fitting your form.
>
> Do so too!

No, none of the (snipped) examples even have an implication as their
conclusion.

Examples reposted below.

2000 Americans were randomly polled. 70% of respondents said they
like peanut butter. So, most Americans like peanut butter.

The 9:10 bus was late 18 of the last 20 days, so it will probably be
late today.

Every time I ring this bell, a man appears. Thus, the man comes
when he hears the bell.

Three out of five people became ill after lunch. All three had tuna
salad, while the other two did not. Thus, the tuna salad made the
three people ill.

Joe liked "The Birds", "North by Northwest", "Psycho" and "The
Trouble with Harry", four films by Hitchcock. "Rear Window" is also
by Hitchcock, so Joe will probably like that film, too.

>
> ___________________
>
> * Postmodernists still fly in aeroplanes rather than on broomsticks,
> * even though they "think all views are equally valid".

I guess you're trying your hand at postmodernism in this thread. The
bad attempts at formal logic are a good start, but I think you need
some nonsensical jargon to really pull it off.

--
"I'm the theory guy.
Other people are the experimental people.
If you push me on details I get annoyed, as I'm the theory guy.
I'm the theoretical amateur mathematician." --James S. Harris, poet
From: Daryl McCullough on 13 Jan 2010 11:11
In article <87fx6arrbw.fsf(a)phiwumbda.org>, Jesse F. Hughes says...
>
>Bill Taylor <w.taylor(a)math.canterbury.ac.nz> writes:
>
>>> All perfectly standard inductive arguments, none of them fitting your form.
>>
>> Do so too!
>
>No, none of the (snipped) examples even have an implication as their
>conclusion.
>
>Examples reposted below.
>
> 2000 Americans were randomly polled. 70% of respondents said they
> like peanut butter. So, most Americans like peanut butter.
>
> The 9:10 bus was late 18 of the last 20 days, so it will probably be
> late today.
>
> Every time I ring this bell, a man appears. Thus, the man comes
> when he hears the bell.
>
> Three out of five people became ill after lunch. All three had tuna
> salad, while the other two did not. Thus, the tuna salad made the
> three people ill.
>
> Joe liked "The Birds", "North by Northwest", "Psycho" and "The
> Trouble with Harry", four films by Hitchcock. "Rear Window" is also
> by Hitchcock, so Joe will probably like that film, too.

Well, I think that they can be rephrased as implications:
If person P is an American, then he probably likes peanut butter.
If the bus you are waiting for is the 9:10 bus, then it will probably be late.
If you ring the bell, then the man will appear.
If you eat the tuna salad, then you will probably get sick.
If the movie is by Hitchcock, then Joe will probably like it.

But what is misleading in Bill's focus on the propositional
logic is that it misses the implicit set formation. The conclusions
are more informatively thought of in terms of overlaps between
sets. They tend to be of the form: All (or most) Xs are Ys.

Anyway, in my opinion, induction, abduction and all other
"reverse deductions" (where you are given a conclusion, and
you are trying to come up with the axioms, or the rules of
inference that could have produced it) are bogus. There are
infinitely many possible solutions. How do you pick one?

A more principled approach (even though it has its arbitrary
inputs) is Bayesian statistics. You start with an a priori
assignment of probabilities to various axiom sets, and then
you revise the probabilities in light of new information.
In practice, people don't actually do this, because
(1) generating sensible axiom sets is hard, (2) assigning
a priori probabilities is hard, (3) computing posterior
probabilities is hard.

In practice, what people do is deal with one "theory" at
a time. You pick the simplest theory that accounts for all
the facts (or some significant fraction of the most pertinent
facts). Then if there is evidence that this theory is wrong,
you toss it out, and try to come up with a new theory that
accounts for the old and the new evidence.

--
Daryl McCullough
Ithaca, NY

From: Jesse F. Hughes on 13 Jan 2010 11:58
stevendaryl3016(a)yahoo.com (Daryl McCullough) writes:

> In article <87fx6arrbw.fsf(a)phiwumbda.org>, Jesse F. Hughes says...
>>
>>Bill Taylor <w.taylor(a)math.canterbury.ac.nz> writes:
>>
>>>> All perfectly standard inductive arguments, none of them fitting your form.
>>>
>>> Do so too!
>>
>>No, none of the (snipped) examples even have an implication as their
>>conclusion.
>>
>>Examples reposted below.
>>
>> 2000 Americans were randomly polled. 70% of respondents said they
>> like peanut butter. So, most Americans like peanut butter.
>>
>> The 9:10 bus was late 18 of the last 20 days, so it will probably be
>> late today.
>>
>> Every time I ring this bell, a man appears. Thus, the man comes
>> when he hears the bell.
>>
>> Three out of five people became ill after lunch. All three had tuna
>> salad, while the other two did not. Thus, the tuna salad made the
>> three people ill.
>>
>> Joe liked "The Birds", "North by Northwest", "Psycho" and "The
>> Trouble with Harry", four films by Hitchcock. "Rear Window" is also
>> by Hitchcock, so Joe will probably like that film, too.
>
> Well, I think that they can be rephrased as implications:
> If person P is an American, then he probably likes peanut butter.

But that's not the conclusion. The conclusion is that most Americans
like peanut butter. Your conclusion is similar, but not the same,
since it is about probabilities regarding one particular thing rather
than a claim about proportions of a group.

> If the bus you are waiting for is the 9:10 bus, then it will
> probably be late.

This is much farther from the conclusion, of course.

> If you ring the bell, then the man will appear.

You've lost the causal connection here, replacing it with a related
conditional statement. There's a similarity, but they're not the same
thing.

> If you eat the tuna salad, then you will probably get sick.

This presumes that there is still tuna salad to eat and also confuses
a causal explanation of what has already happened with a conditional
statement.

> If the movie is by Hitchcock, then Joe will probably like it.

This is not the conclusion, since the conclusion was about one
particular movie.

All of your conclusions are related to the given conclusions, but they
are not the same. Note as well that they have nothing to do with
Bill's form. Let us take, for example, your proposed conclusion

If the bus you are waiting for is the 9:10 bus, then it will
probably be late.

Bill's form was

P
Q
------
P => Q

Clearly, the premises for my argument were not:

You are waiting for the 9:10 bus.
It will probably be late.
So, if the bus you are waiting for is the 9:10 bus, then it will
probably be late.

Moreover, I chose arguments from several standard forms of inductive
argument and stated the conclusions in their generally recognized
form, which are *not* conditional statements. For instance, the first
argument has the form

X % of observed subset B of A has property P.
So, about X % of A has property P.

while the second has the form

Most A have property P.
So, this A probably has property P.

The third is a causal inference along the lines of Mill's method of
agreement, and the fourth an example of Mill's joint method. The
fifth is an example of argument by analogy.

A1, A2 and A3 have property P.
A1, A2 and A3 are similar to B in relevant ways.
So, B probably has property P.

Again, these are all fairly common forms of inductive argument, found
in standard introductory logic and critical thinking texts. Not a
damn one of them has the form

P
Q
---
P => Q


> But what is misleading in Bill's focus on the propositional
> logic is that it misses the implicit set formation. The conclusions
> are more informatively thought of in terms of overlaps between
> sets. They tend to be of the form: All (or most) Xs are Ys.
>
> Anyway, in my opinion, induction, abduction and all other
> "reverse deductions" (where you are given a conclusion, and
> you are trying to come up with the axioms, or the rules of
> inference that could have produced it) are bogus. There are
> infinitely many possible solutions. How do you pick one?
>
> A more principled approach (even though it has its arbitrary
> inputs) is Bayesian statistics. You start with an a priori
> assignment of probabilities to various axiom sets, and then
> you revise the probabilities in light of new information.
> In practice, people don't actually do this, because
> (1) generating sensible axiom sets is hard, (2) assigning
> a priori probabilities is hard, (3) computing posterior
> probabilities is hard.
>
> In practice, what people do is deal with one "theory" at
> a time. You pick the simplest theory that accounts for all
> the facts (or some significant fraction of the most pertinent
> facts). Then if there is evidence that this theory is wrong,
> you toss it out, and try to come up with a new theory that
> accounts for the old and the new evidence.
--
"In terms of story, this one is tops. All of the 'good' characters grow and
become much more than they were when the movie began. This film celebrates
friendship at it's basest level and demonstrates the triumph of good people
above overwhelming odds." -- IMDB user comments are tops, at the basest level
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