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Re: Extensional modals?

Welcome.

Something about you (optional) logician-philosopher

Re: Extensional modals?

Avi, I found an example of an argument in which the temporal aspect is part of the quantity/subject rather than the predicate.

T = times;
S = times when Alex studies hard;
H = times when Alex gets a headache

Sometimes Alex studies hard. = some T are S
Whenever he studies hard he gets a headache = all S are H
So, sometimes Alex gets a headache. = so, some T are H

But as a temporal syllogism it's invalid (assuming the following is the correct interpretation) :

Alex sometimes studies hard = This A is sometimes S
When Alex studies hard he always gets a headache = This S is always H
So, Alex sometimes gets a headache = This A is sometimes H

Just wondering what your thoughts are on this?

Re: Extensional modals?

First note: remember to always place the major premise first, then the minor then the conclusion – this is a useful convention for clarity.
Second note: don’t change and mix your symbols – you only confuse your reasoning.

1st format, syllogism:
All times when Alex studies hard (S) are times when Alex gets a headache (H)
Some Times (T) are times when Alex studies hard (S)
So, some Times (T) are times when Alex gets a headache (H)
Syllogism 1/AII = a valid mood. This is not temporal syllogism, even though the word time is used. Just ordinary extensional reasoning.

2nd format, apodosis:
When Alex studies hard, he always gets a headache (This S is always H)
Alex sometimes studies hard (This A is sometimes S)
So, Alex sometimes gets a headache (This A is sometimes H)
Here, the terms have been changed and mixed up a bit by you.
We can correct them as follows:
When Alex (A) studies hard (S1), he (A) always gets a headache (H1)
Alex (A) sometimes studies hard (S1)
Alex (A) sometimes gets a headache (H1)
This is not a syllogism, but an apodosis affirming the antecedent of a temporally general hypothetical with a temporally partial minor premise and conclusion.
It is valid, since given the major premise, for each moment that the minor premise is true, then the conclusion is true.

Thus, neither of your examples are really cases of temporal syllogism such as we discussed.
3rd format, temporal syllogism.
Anyone who studies hard (S1) always gets a headache (H1)
Alex (A) sometimes studies hard (S1)
Alex (A) sometimes gets a headache (H1)
This would be a valid temporal syllogism (1st fig. mood AcItIt).
Note that from a temporally general major premise,
- If the minor premise is temporally partial, so is the conclusion
- If the minor premise is temporally singular, so is the conclusion
But in neither case is the conclusion temporally general, unless the minor premise is also so.

Something about you (optional) logician-philosopher

Re: Extensional modals?

Avi, thanks, but doesn't the major premise in your temporal syllogism assume something that wasn't given?


Anyone who studies hard (S1) always gets a headache (H1)


The proposition said only that when Alex studies hard, he gets a headache, not anyone who studies hard gets a headache.

Re: Extensional modals?

Of course. That was intentional - to show you the kind of major premise you'd need to form a temporal syllogism. The major premise was not given by you, nor considered as true by me! Just intended as an example. If you want to limit the argument to Alex, then the apodosis format (the 2nd) is the correct one - but that's not, to repeat, a temporal syllogism.

Something about you (optional) logician-philosopher

Re: Extensional modals?

Thanks Avi. This modal stuff is quite tricky and will take time to understand because some of the ideas are subtle. There are so many ways of expressing propositions in English that it's sometimes hard to see whether some proposition is natural, temporal, or neither. Your writing is clear but I wish there were more concrete examples because it would make the distinctions easier to grasp. Maybe I'm just not smart enough.

Re: Extensional modals?

algojack, don't blame yourself. Even I, before I replied to your questions, had to think twice, before I could sort them out. Logic studies involve being careful and precise in language and in thought - that's what's good about it. And you are right in saying that people use modal qualifiers in somewhat mixed-up ways. E.g. we might say "People are sometimes very foolish," when we rather mean "some people are very foolish" or maybe both "some people are sometimes very foolish." Logic raises our awareness of the different possibilities of meaning and the possible errors. So, it is worth studying and practicing.

Something about you (optional) logician-philosopher

Re: Extensional modals?

Thanks for the encouragement. I'll keep reading a few pages everyday and if there's something I'm struggling with I'll post my queries and hopefully you'll be able to clarify, as you already have. Cheers,
Jack.