The Logic Forum Discussion Area

Start a New Topic 
View Entire Thread
Re: FUTURE LOGIC - Comments & Queries


If you switch 1st fig. premises you get a 4th fig. syllog. BUT the term symbols S and P must be changed.

P is M
M is not S
S is not P – valid

P is not M
M is S
S is not P – valid

As discussed in FL, and as Aristotle considered, the 4th fig. is somewhat artificial, not so natural a movement of thought as the other figures. But still, in some cases it brings an interesting conclusion not otherwise evident.

As regards the 1st fig. valid mood with a negative minor premise, as I said before it is unusual for a 1st fig. syllog. to so behave - and the explanation is given by me with reference to the 2nd. fig. in my previous post.

Something about you (optional) logician-philosopher

Re: FUTURE LOGIC - Comments & Queries

Avi, with regard to chapter 15, section 3 (validations), I'm having a hard time convincing myself that pnp in the 1st figure is invalid, although I've taken on board your comments on it.

I've tried comparing it with the 3rd fig. pnp, which is valid, but it's still not clear to me how the differences make one valid and the other invalid.

e.g. an invalid mood in pnp (1st fig.) would be:

All M can be P (p)
All S must be M (n)
therefore, All S can be P (p)

Rephrasing in terms of "circumstances", this would be

In some circumstances all M is P
in all circumstances all S is M
therefore in some circumstances all S is P

I'm trying to come up with suitable concepts for the terms which makes this syllogism intuitively invalid, but so far haven't been able to. Any suggestions?

Re: FUTURE LOGIC - Comments & Queries


In the first figure, the 'all circumstances' of the minor premises are those applicable to the minor term S, they are not all circumstances concerning the middle term M. For this reason, there is no guarantee that the 'some circumstances^concerning M in the major premise are covered.

On the other hand in the third figure, M being the subject in both premises, you can be sure of overlap of circumstances.

Best, Avi.

Something about you (optional) logician-philosopher

Re: FUTURE LOGIC - Comments & Queries

Thanks Avi, for some reason I just wasn't getting it. I think I was confusing myself by reading the premises as "all S in all circumstances is what P is in some circumstances". I was looking at the quantity and not the modality. Then I drew a diagram to represent the circumstances "surrounding" the terms. Being more of a visual thinker, the invalidity then became clear.

But still, some of these modal syllogisms aren't at all obvious.

Re: FUTURE LOGIC - Comments & Queries

In fig. 1, if you tried converting the minor premise, you would have immediately seen that while S was distributed, M was not. All S must be M converts to Some M can be S. Remember All S means: Each S - it is distributive, not collective or collectional. So, the all circumstances are all circumstances concerning each S, which are not the same set of circumstances... The universal proposition is a mere summary formula.

Note additionally that in the past, some logicians thought that a universal potential major premise in the first fig. could yield a valid conclusion. They did not realize the issues involved. So, you are in good company!

Something about you (optional) logician-philosopher