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.
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?
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.
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.