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Extensional modals?

Hello Avi,

In your book "Future Logic" you explain the various types of modality, the main ones discussed being extensional, natural, and temporal. Are the extensional propositions just the "Actual Categoricals" you cover in the previous chapter (A,E,I,O,R,G)?

On page 76 you list the propositions for the natural and temporal modalities, but the "actual categoricals" are a subset of the naturals. You mention that the subscript "a" for "actuals" is omitted (and then go on to talk about some ambiguities).

So am I right in thinking that the natural and temporal propositions are also extensional in the sense that their subjects refer to quantity? It's only that their predicates refer to different modalities and are not "actual".

I'm really enjoying the book.

Re: Extensional modals?

HI MCCOY - MY REPLIES BELOW.

In your book "Future Logic" you explain the various types of modality, the main ones discussed being extensional, natural, and temporal.

ALSO LOGICAL, DON'T FORGET.

Are the extensional propositions just the "Actual Categoricals" you cover in the previous chapter (A,E,I,O,R,G)?

THE FULL SIGNIFICANCE AND DIFFERENCE OF EXTENSIONAL PROPOSITIONS ONLY APPEARS WHEN DEALING WITH CONDITIONALS - see CHAPTER 39 http://tl-archive.net/2_future_logic/2_chapter_39.htm
In categorical form, Some X are Y simply becomes X may be Y, this X is Y becomes X is Y, all X are Y becomes X must be Y. THAT IS TO SAY THE "ACTUALITY" OF EXTENSIONAL MODALITY IS THE SINGULAR PROPOSITION, WHILE THE MODAL FORMS ARE THE PLURAL PROPOSITIONS. But in conditional form and thence in causation, extensionals have no substitute, so this is where they come into play really.

On page 76 you list the propositions for the natural and temporal modalities, but the "actual categoricals" are a subset of the naturals. You mention that the subscript "a" for "actuals" is omitted (and then go on to talk about some ambiguities).

ACTUALS ARE THE CENTER OF NATURAL CATEGORICALS, MUST IMPLYING IS AND IS IMPLYING CAN. Similarly actuals are the center of temporal categoricals, is always implying is at a given time, and is at a given time implying is sometimes. We can have the subscript, but we can do without it.

So am I right in thinking that the natural and temporal propositions are also extensional in the sense that their subjects refer to quantity? It's only that their predicates refer to different modalities and are not "actual".

YOU COULD THINK OF CATEGORICALS WITH TEMPORAL OR NATURAL MODALITY AS ALSO HAVING EXTENSIONAL MODALITY (SUPERIMPOSED) IN LIEU OF QUANTITY, AND IN PRACTICE PEOPLE SOMETIMES DO. HOWEVER, I RECOMMEND YOU DO NOT DO SO - BUT STICK TO QUANTITY IN CATEGORICALS TO EXPRESS THE EXTENSIONAL MODALITY, TO AVOID CONFUSION. AS ABOVE SAID, WAIT FOR CONDITIONALS, AND YOU WILL FULLY GRASP THE VALUE AND MEANING OF EXTENSIONAL MODALITY.

AS REGARDS NATURAL AND TEMPORAL MODALITY, IT IS WRONG TO VIEW THEM AS AFFECTING THE PREDICATE. THEY ARE MODIFICATIONS OR QUALIFICATIONS OF THE COPULA. THAT'S VERY IMPORTANT TO UNDERSTAND. YOU CANNOT ATTACH THEM TO THE PREDICATE (E.G. IS "POSSIBLY Y") BECAUSE SUCH 'PERMUTATION' LEADS TO LOGICAL ERRORS.

Re: Extensional modals?

Hi Avi, thanks for the clarification and advice. I have another query: in chapter 11 section 5 on Temporal Modality you write about how sometimes permutation can result in wrong inferences, and give two examples.

1. S is M, M are always-P, therefore S is always-P
2. S is M, M are sometimes-P, therefore S is sometimes-P

Maybe I'm getting ahead of myself here, because in a later paragraph you write "All this will become clearer by and by", but aren't the above syllogisms valid?

Re: Extensional modals?

Hi McCoy. No, that is the point, these syllogisms are not valid, as you will see when you get to syllogism. The modality cannot be attached to the predicate - it is a modification of the copula (i.e. the relation between the subject and predicate).
Avi - P.S. sorry my previous post was difficult to read, I was very busy with other things at the time.

Re: Extensional modals?

Avi Sion
Hi McCoy. No, that is the point, these syllogisms are not valid, as you will see when you get to syllogism. The modality cannot be attached to the predicate - it is a modification of the copula (i.e. the relation between the subject and predicate).


Right. I'm getting ahead of myself again.

P.S. sorry my previous post was difficult to read, I was very busy with other things at the time.


No problem, I understood what you said.

Re: Extensional modals?

Feel free to ask questions when in doubt.

Note that the first syllogism you quote, viz. 1. S is M, M are always-P, therefore S is always-P, has a lesser valid conclusion, viz. S is P (without the always).

Whereas the second one, viz. 2. S is M, M are sometimes-P, therefore S is sometimes-P, does not have any valid conclusion.

Re: Extensional modals?

Hi Avi,

I've got to page 66 of the book and am struggling to understand why those syllogisms are invalid.

If S is M and all the M's are 'within' always-P, why is it invalid to conclude that S is always-P?

In terms of sets, if M is a subset of always-P and S is a subset of M, then surely it must follow that S is a subset of always-P?

Confused... :(

Perhaps you could give a concrete counter-example? I've been trying to think of one but haven't been able to.

Re: Extensional modals?

Hi algojack.
The answer is that, in temporal modality, the actual form "(all/some/this) S is M" means "S is-now M" (i.e. the S-M predication is applicable only to the present time, as far as we are told). Thus, even if "All M are always P" is true, it does not follow that S, per se, is always P - because it is not necessarily the case that S is always M. If perchance S is momentarily not M, then it no longer falls under the generality that all M are always P. If this is still not clear to you, tell me.
Example: John is right now a boy scout; all boy-scouts are always ready-to-help; but it does not follow that John is literally always ready-to-help - because tomorrow John may cease to be a boy-scout, or yesterday he maybe was not a boy-scout.
The generality to understand is that the modality (whether temporal or natural or logical) is a qualification of the copula (is) and not part of the predicate. If you grasp that, you can never go wrong.

Something about you (optional) logician-philosopher

Re: Extensional modals?

Hi Avi,

Thanks very much for your clear explanation and example, it really helped. I see now that I've been mislead because the text I've learned basic logic from used examples which made that very error you've pointed out (putting the modality in the predicate). I find this quite disappointing. From now on your book will be my go-to reference!

Thanks again.

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.