Menu

Return to Website > Index > Select the appropriate forum > Logic > FUTURE LOGIC - Comments & Queries Recent Posts

Return to Website > Index > Select the appropriate forum > Logic > FUTURE LOGIC - Comments & Queries

Logic

Author

Comment

Chapter 3: Logical Relations

I was wondering how you would define the relation of "no relation", meaning Independent propositions. Could this be defined as a relation between P and Q such that P neither implies nor is implied by Q?

Something about you (optional) student

Hi Greg.

No - "no logical relation" is a denial of not only of implications either way but also of incompatibility and exhaustiveness. That is, in Table 3.1 there would be four question marks.

However, this is only true at this level of consideration, because even with four question marks there may at a deeper level (i.e. more conditionally, dependent on other factors) a logical relation. This is dealt with in detail in The Logic of Causation.

So perhaps we should speak here of no "direct" logical relation.

Something about you (optional) Logician, philosopher

Thanks Avi. Yes, it seems obvious now you point it out; if two propositions are independent then they can't at the same time be mutually exclusive, or exhaustive.

Something about you (optional) student

But Greg, note well that not-implying, not-implied, compatible and inexhaustive are all logical relations of sorts, just weaker ones.

Let me add, just to be clear, if all four of these are true of two propositions, then you have the nearest thing to "no relation" possible at this level of consideration. In truth, as I said before, there may be some still weaker (conditional) relation at a deeper level.

P.S. you will find more about the possible combinations of logical relations in the chapter about Oppositions.

Something about you (optional) Logician, philosopher

Thanks Avi, noted!

I have just finished reading Chapter 10 and am about to start Modal Categoricals, but regarding Actual Categoricals, do they not include syllogisms involving identities? e.g.:

Socrates was the first western philosopher.

The first western philosopher lived in Greece.

So, Socrates lived in Greece.

Something about you (optional) student

Avi, I was referring to propositions in which both subject and predicate are singulars, like "this A is this B" etc. In section 5.3 you say that R and G are effectively distributive, but "this A is this B" is not a component of an R form (because the predicate is not a category, but a singular).

Perhaps I'm making a difficulty where none exists. It just seemed to me that these forms are syllogisms and yet they're not mentioned.

Something about you (optional) student

Hi Greg. You are quite right to raise the question.

First, let me clarify that when I said that this is a normal first figure syllogism, I meant that it does not matter that the minor premise "Socrates was the first western philosopher" is convertible to "The first western philosopher was Socrates", because the latter converse does not affect the inference of the conclusion you gave. As far as this syllogism is concerned, it is redundant information (as we have seen together in another example).

"The first western philosopher was Socrates" could be used in a third figure syllogism yielding (arguably) the same conclusion. But in that syllogism, the converse "Socrates was the first western philosopher" would be redundant. So, in fact there is not involvement of "identities" here as you suggested. These are ordinary arguments. Note that the fact that this proposition is singular is not the issue here, really; the same could be said with regard to a two-way general proposition like "all humans are rational animals and all rational animals are humans".

Secondly, notice that the middle term is an abstraction "the first western philosopher" - this is effectively a class with only one member rather than a singular term of the type "Socrates". (Incidentally, Socrates was not the first Western philosopher by far - but I assume you knew that.) Of course, we could have a proposition like "Socrates is (the same guy as the one we know as) Socco" - so your question still stands. For Aristotle, the middle term had to be an abstraction, at least in the first figure; but I would agree with you that a singular term is in practice occasionally found the middle term as your example suggests. On the other hand, the third figure allows for a singular middle term (see the moods RRI and GRO in FL chapter 9). So we could argue that your argument works because it is really a third figure syllogism rather than a first figure one.

One more thing parenthetically. I recommend when discussing logic to always place the major premise first and the minor premise second, with the conclusion last - even though in ordinary discourse the order is not important. In this way, you show you always know which proposition is which. How to know? The minor premise is the one with the subject of the conclusion, and the major premise is the one with the predicate of the conclusion.

Something about you (optional) Logician, philosopher

Greg - upon reflection, I'd like to add the following to my preceding comment.

Although the first figure syllogism with a singular minor term (as subject) and a singular middle term is no different from one with a plural middle term, the same is not true of the third figure. In the latter case, the conclusion is not merely particular (as is normally the case for this figure), but more specifically singular. This means that the third figure syllogism with a singular middle term and a singular minor term (as predicate) is indeed special.

So your criticism was correct. I do not remember, frankly, if I dealt with this special case anywhere (do let me know if you come across this issue in FL). If I did not, I ought to have for the sake of completeness. Thank you for your comment.

One other reflection is that the concept "the first western philosopher" is not definitely singular. There may be many simultaneous first western philosophers, in which case of course Socrates (or whoever) would be "among the first". We can only use the term "the first" if we know or believe there is only one first. This confirms my contention that your term "the first western philosopher" is best viewed as a one-member class rather than as a singular term in the usual sense.

Also note, some people claim that Aristotle did not recognize singular syllogism. Here however is an example drawn from his Prior Analytics 2:27 "Wise men [i.e. at least some of them] are good, since Pittacus is not only good but wise". This says: Pittacus is good and Pittacus is wise, therefore [at least some] wise men are good (3rd fig. singular middle term - square brackets mine). This is a normal case, not a special one, note.

Something about you (optional) Logician, philosopher

Hi Avi,

Well I seem to have opened a can of worms here, but actually I think my original criticism (although it wasn't really intended as a criticism) was misplaced, because I was only thinking about the kind of arguments which involve identities between singulars, such as "Mt Everest is the highest mountain", or "Bacon is Shakespeare". But if these are the only kinds of propositions in an argument, it isn't really a categorical syllogism, and so shouldn't be included in part 1 of FL.

Arguments of the form:

a = b

b = c

so, a = c

involve only simple substitution of like for like, so perhaps on this basis can be excluded from the traditional syllogism?

Something about you (optional) student

Hi Greg. There is no can of worms. Every criticism is welcome and may bring to the fore issues that need dealing with, as was the case here. I'm grateful. I almost always learn something from criticism. Always be critical!

That said, I think I have answered your objection correctly earlier.

You bring up now the issue of substitutive syllogism. Here I refer you to FL 19.1 for some general comments. However, as regards your formula - a=b and b=c, so a=c, what you have in mind seems to be more an equation of symbols (words, labels) than a chain of thoughts.

When dealing with the latter, it is wise to refer to syllogisms, and in such case you must proceed with respect to the combinations of syllogism involved (if any) and acknowledge redundant information (if any). If you learn to avoid short cuts, your reasoning powers (accuracy) will increase exponentially.

Something about you (optional) Logician, philosopher

Greg: I return to your formula, a = b, b = c, so, a = c.

I want to make clear to you that this formula is only possible in conceptual logic, as against mathematics, by means of two syllogism. It is not a primary argument, but a derivative compound argument.

What does X=Y mean? If it is singular, e.g. John and Johnny are one and the same person, it means X is Y and Y is X, two predicative propositions. Similarly, if it is plural (general), e.g. all humans are rational animals and vice-versa, it means all X are Y and all Y are X.

Thus, your formula is really constituted of two syllogism, and does not constitute a separate form of reasoning. These are:

b is c and a is b, therefore a is c

and

b is a and c is b, therefore c is a

With predicative propositions, you cannot just convert at will. You must follow the rules of conversion for these forms, and use two propositions to express a two-way relation.

Something about you (optional) Logician, philosopher

Avi,

Ok then, I won't hold back from criticism!

What I like about your work is that it broadens the scope of logic; most books on the subject don't cover anything more than the propositional and predicate calculus ( I'm not a fan of the latter because of the excessively technical symbolism involved ), but then in my work ( computer programming and circuit design ) I haven't had the need for anything more advanced, although I've long had an interest in philosophy. I'm particularly looking forward to the section on factorial induction, which seems to be an integrated system with a definite plan and purpose, but I've a way to go before getting there!

Avi

If you learn to avoid short cuts, your reasoning powers (accuracy) will increase exponentially.

Interesting. I would have thought that short cuts would HELP your reasoning powers.

This is the first time I've been exposed to the "traditional" Aristotelian syllogism in such detail, and I must admit I'm finding it pretty hard going. Not because of any conceptual difficulties, but because of the large amount of data involved. All the tables, figures, moods, relationships etc. Do you have any advice on how best to assimilate it all? I was hoping you might have a few short cuts!

There are no exercises or problems in the book, but I suppose I can make up my own. I think logic is like maths in that you can't learn it merely by passively reading about it; you have to actively solve problems.

Something about you (optional) student

Hi Avi,

In reply to your last post, I've taken on board your comments. The reason I used "=" in the argument was because the word "is" is ambiguous. It seemed to me that the "=" better reflected the meaning of an identity, whereas the usual meaning of "is" in a proposition is predication.

Something about you (optional) student

Hi Greg.

About my last post concerning the "=" - I should have added at the end of it that, of course, as you imply, if X and Y are both singular, then X is Y is convertible to Y is X and vice-versa (whereas if they are universals, such conversion is not possible and both propositions must be given).

Regarding your latest comments, you are right to look forward to the chapters on inductive logic. They are a mind opener as to the way we actually reason - very far really from the deductive method that logic is usually associated with. Once induction is understood, many philosophical problems just melt away.

About short cuts - you don't want them. There is no need to memorize stuff. What is important is to understand, and to do that you must look at the details and not just skim over them. But once you have understood through scrutiny of the details, you are free to forget, because when you need the information you will be able to generate it by yourself.

Something about you (optional) Logician, philosopher

Hi Avi,

Thanks for the advice. Are there any dependencies between the parts of FL? I'm tempted to skip ahead to read the sections on factorial induction (which seems to depend only on knowledge of modal categoricals), or do you recommend that I work linearly through the book?

Something about you (optional) student

H Greg. The only part you could skip is Class Logic (Va).

You need parts I-V and Vb to understand part VI. The latter, on Factorial Induction, is the culmination of the former parts and depends on them for its full understanding.

Take your time.

Best regards,

Avi

Something about you (optional) Logician, philosopher

Hi Avi, I'm a little way into reading Future Logic and have a query. On page 37, under table 6.1 you say:

"The seven definite oppositional relations are mutually exclusive (i.e. contrary, to be exact), but one of the seven must hold."

But according to the table, contrary relations allow nonP + nonQ (i.e. all the relations can be false together), but if that's the case, doesn't that contradict the proposition that "one of the seven must hold"?

Or perhaps my logic is faulty.

Hi JayDee, in reply to your question.

When two propositions are contrary it means that they cannot be both true, but may be both false.

In the case of seven (or any set of three or more) propositions, we can well say that more than one of them cannot be true, but still at least one of them must be true (i.e. they cannot be all false).

That 'only one of them can be true' does not exclude that 'one of them must be true'.

This holds, notice, even if you take any two at random and say that they are contrary to each other, i.e. that the pair may be both false.

Something about you (optional) logician-phil.osopher

Thanks Avi, I guess I'm still a bit confused. If the relations (propositions) are mutually exclusive and exhaustive I understand that to mean that for any pair of propositions, one and only one of the relations *must* be true. Am I wrong?

By "exhaustive" I mean as fits the definition as given on page 25 and in table 3.1. Here, nonP + nonQ is logically impossible, but in table 6.1 it isn't (although "contrariety" isn't the same as "exhaustive").

It seems to me that the relations (taken as a set) are contradictory and not contrary because they are mutually exclusive, meaning if one is true then the others must be false, and also since one must be true then they cannot all be false. I.e., a "no" under columns P+Q and nonP+nonQ (which meets the criteria of contradictory).

I understand your point that 'only one of them can be true' does not exclude that 'one of them must be true', but isn't the issue rather that they cannot all be false?

The logic of oppositions is best understood by matrix analysis.

In the case of two propositions, the matrix is:

1) P + Q

2) P + notQ

3) notP + Q

4) notP + notQ

These are the 4 general, prima facie, logical possibilities for two propositions.

If the propositions are shown to be contradictory, it means that the alternatives 1 and 4 are impossible, while the alternatives 2 and 3 are possible. If the propositions are contrary, then the alternative 1 is impossible, but the other three are possible. If the propositions are subcontrary, then the alternative 4 is impossible but the otherr three are possible. And so on.

Now when you deal with three or more (e.g. seven) propositions, obviously the matrix is going to be accordingly larger, with more alternatives, and more ways they might be combined. For instance, with three propositions we have:

P + Q + R

P + Q + not R

P + notQ + R

notP + Q + R

and so on... till notP + notQ + notR (this is given in full in the book somewhere).

That's how we know we have exhausted the logical possibilities - by listing them all.

Something about you (optional) logician-phil.osopher

Thanks Avi, I guess I'm still a bit confused. If the relations (propositions) are mutually exclusive and exhaustive I understand that to mean that for any pair of propositions, one and only one of the relations *must* be true. Am I wrong?

NOT WRONG. THIS IS THE DEFINITION OF CONTRADICTION (NOT CONTRARIETY).

By "exhaustive" I mean as fits the definition as given on page 25 and in table 3.1. Here, nonP + nonQ is logically impossible, but in table 6.1 it isn't (although "contrariety" isn't the same as "exhaustive").

YES, EXHAUSTIVE MEANS THE NEGATION OF ALL THE PROPOSITIONS IS IMPOSSIBLE. MUTUALLY EXCLUSIVE MEANS THE AFFIRMATION OF ALL THE PROPOSITIONS IS IMPOSSIBLE.

It seems to me that the relations (taken as a set) are contradictory and not contrary because they are mutually exclusive, meaning if one is true then the others must be false, and also since one must be true then they cannot all be false. I.e., a "no" under columns P+Q and nonP+nonQ (which meets the criteria of contradictory).

THIS WORKS WITH TWO PROPOSITIONS, WITH THREE OR MORE PROPOSITIONS THERE ARE MORE POSSIBILITIES, AS IS CLEAR WITH REFERENCE TO MATRICES.

I understand your point that 'only one of them can be true' does not exclude that 'one of them must be true', but isn't the issue rather that they cannot all be false?

ONE MUST BE TRUE MEANS THE SAME EXACTLY AS THEY CANNOT ALL BE FALSE. IN SOME CASES, ONLY ONE CAN BE TRUE. IN OTHERS, MORE THAN ONE MIGHT BE ALLOWED TO BE TRUE (UP TO ALL BUT ONE).

Something about you (optional) logician-phil.osopher

Ok, thanks Avi, sorry about the confusion.

Do these relations hold for ALL the forms of proposition which are covered in the book? (categorical, modal, conditional, etc).

I notice that the unconnectedness relation has no column in which a pair of propositions is not possible. Would it be true to say that in general, the "strength" of a relation is correlated (positively) with the number of impossible combinations? So the strongest relations are implicance and contradiction, each having two "no's", and the weakest is unconnectedness, which has none.

Hi JD,

Do these relations hold for ALL the forms of proposition which are covered in the book? (categorical, modal, conditional, etc).

THE LISTED OPPOSITIONS (CONTRADICTION, CONTRARIETY, ETC.) ARE OBVIOUSLY APPLICABLE TO ANY PAIR OF PROPOSITIONS OF ANY SORT, IN THIS BOOK OR ANY OTHER. THEY ARE JUST EXTENSIONS OF THE THREE LAWS OF THOUGHT.

I notice that the unconnectedness relation has no column in which a pair of propositions is not possible. Would it be true to say that in general, the "strength" of a relation is correlated (positively) with the number of impossible combinations? So the strongest relations are implicance and contradiction, each having two "no's", and the weakest is unconnectedness, which has none.

YES, THAT IS CORRECT. THE MORE COMBINATIONS ARE IMPOSSIBLE, OBVIOUSLY THE STRONGER THE 'OPPOSITION' RELATION BETWEEN THEM.

JD, keep in mind that the named oppositions refer to PAIRS of propositions. When dealing with sets of 3, 4, 5, 6, etc. propositions, the different possibilities of 'impossible' and 'possible' rows are ALSO 'oppositions', except that we have not given them any specific names because that would require a never-ending vocabulary! Instead we resort to descriptive sentences like "one of them must be true" or "all but one of them must be false" etc. All this, to repeat, is merely application of the laws of thought.

Something about you (optional) logician-phil.osopher

Avi

Hi JD,

JD, keep in mind that the named oppositions refer to PAIRS of propositions. When dealing with sets of 3, 4, 5, 6, etc. propositions, the different possibilities of 'impossible' and 'possible' rows are ALSO 'oppositions', except that we have not given them any specific names because that would require a never-ending vocabulary!

JD, keep in mind that the named oppositions refer to PAIRS of propositions. When dealing with sets of 3, 4, 5, 6, etc. propositions, the different possibilities of 'impossible' and 'possible' rows are ALSO 'oppositions', except that we have not given them any specific names because that would require a never-ending vocabulary!

Thanks Avi. Noted!

I've spotted a couple of typos in the book, they're not serious but thought I'd mention them anyway.

page 6 (Table of Contents) : NATURALS CONDITIONALS... and the same for the corresponding title on page 209 (a superfluous 's' on the end of 'NATURAL').

page 41 (bottom) : 'Although these may [be] tedious details...'

If I see any more I'll post them here.

Hi Avi,

In FL Part 1 you discuss plural categoricals and singulars where only the subject term is singular, but not what you might call "double" singulars where the predicate is also a singular. E.g.

Paris is the capital of France

Is this a deliberate oversight because that form is too trivial to mention? I suppose technically they are not even syllogisms, maybe that's why you haven't included them. Just wondered...

Hi MDB. I do not remember if I mention singular predicates anywhere and deal with it. Thanks for the remark. Some offhand comments:

Various forms (with copula is) are conceivable. If the predicate is singular, and the proposition positive, the subject will be singular (or a list of singulars). But in a negative proposition with a singular predicate, the subject might be plural (e.g. no Asian city is Paris).

Obviously, a singular-singular proposition is convertible (to the same polarity), whether positive or negative.

In syllogism, the middle term can in such case be singular, either as subject in the major and predicate in the minor (1st fig.), or as predicate in both premises (2nd), or as subject in both premises (3rd), etc.

I let you work out the valid moods (according to the polarities involved), and share your findings with us. It should be a good exercise for you.

Best regards, Avi

Something about you (optional) logician-philosopher

Ok Avi, I will do what you suggest and post my results here over the weekend.

Most books on Logic treat singulars as universals, so Socrates is a man would be put into the form All S is M. You do mention in FL that this is essentially the case. This being so, is there any particular reason why you have included separate propositions R & G and their analyses?

Yes, it is very useful to engage in theoretical research yourself - nothing sticks better in the mind than that. Become a logician yourself.

Yes, singular-singular are like universals but not exactly. This is most true of a negative proposition (like no x is y). A positive proposition would have the joint value of two universals (like all x are y and all y are x), since it is also convertible. The issue here is playing the role of middle term...

Actually, modern logicians have given these forms much attention. But I didn't for lack of time (at the time). I believe (like most) that all propositional forms deserve attention, however.

The ordinary singulars R and G are very valuable. I introduced these symbols in FL (from affiRmo and neGo), because I perceived the need. Since then, I have also seen the value of this deed in later works.

Another small innovation in FL was the introduction of two more oppositional relations Implicance (mutual implication) and Unconnectedness (none of the five other relations). I mention this because I've recently seen a number of works which mention this innovation of mine as if it was a voluntary thing, and wonder why I did it. No - it is essential to have a complete list of all possible relations to work with (and not just the traditional four - contradiction, contrareity, subcontrareity, and subalternation). Also subalternating is different from being-subalternated. As you proceed through FL (and other works), you'll see these oppositional relations are all useful.

In The Logic of Causation, notably, the issue of opposition becomes still more complex, with the realization that there are conditional oppositions. Two propositions may be unconnected prima facie, but they may turn out to have some sort of (positive or negative) connection under specific conditions...

Something about you (optional) logician-philosopher

Ok, here is my attempt to find the valid syllogisms for singular-singular propositions. I have named them R2 and G2, following the standard singulars:

R2 : This S is this P

G2 : This S is not this P

So altogether there are 8 x 8 = 64 possible premises for each figure. However, since R2 and G2 are both convertible, isn't it the case that results for any one figure will apply to all? Anyway, I'll just give the results for the first figure.

Premises involving the plurals can be discounted since there will be no connection, which leaves just the following 7 (ignoring those in which the premises are the same but the order is different):

R,R2

R,G2

G,R2

G,G2

R2,R2

R2,G2

G2,G2

And here are the full syllogisms:

R This M is P

R2 This S is this M

con This S is P

R This M is P

G2 This S is not this M

con NONE

G This M is not P

R2 This S is this M

con This S is not P

G This M is not P

G2 This S is not this M

con NONE

R2 This M is this P

R2 This S is this M

con This S is this P

R2 This M is this P

G2 This S is not this M

con This S is not this P

G2 This M is not this P

G2 This S is not this M

con NONE

So there are only 4 valid syllogisms (first figure):

R R2 R

G R2 G

R2 R2 R2

R2 G2 G2

I may return to the other figures later, but for now I'm keen to continue on to part II of the book. Hopefully I haven't completely messed up!

So altogether there are 8 x 8 = 64 possible premises for each figure.

This should have been 64 possible pairs of premises, of course.

Hi MDB, well done, but you missed one valid mood.

Not so interesting are the moods you listed with a plural major term (P). To be thorough, you need to also look into moods with a plural minor term (S) (I mention a negative example higher up - No Asian city is Paris ... a positive example would be ?). Let's just focus for now on the fully singular syllogisms.

sing-sing syllogs:

Let S, M, P be three singular terms (or this S, this M, this P, as you have it) (e.g. the present capital of France, the location of the Eiffel Tower, Paris or Vienna). We have three out of four valid moods in the first figure.

M is P

S is M

S is P – valid

M is not P

S is M

S is not P – valid

(You missed this one)

M is P

S is not M

S is not P – valid

M is not P

S is not M

No conclusion

The most interesting mood here is of course the third one, because it has a negative minor premise and yet is valid, which is atypical/exceptional. For this mood alone it was worth looking into.

Let us compare this mood to plural syllogism. If the major premise was compound, with both directions universal, then the conclusion would be valid, because a 2nd fig. syllogism would actually be operative (not really the 1st fig. one).

(All M are P and) All P are M

No S is M

conclusion No S is P is valid

So that's why the sing-sing version works, really.

Regarding the other 3 figures, as you say, we just need to convert the major premise (2nd fig.) or the minor premise (3rd fig.) or switch the premises (4th fig.). Since all these propositions are fully convertible, there will be 3 valid moods out of 4 in each figure.

Something about you (optional) logician-philosopher

Avi, thanks for the feedback.

M is not P

S is M

S is not P – valid

(You missed this one)

M is P

S is not M

S is not P – valid

Aren't these essentially the same? I did have both on my list but discarded one because it's just a repeat of the other with Major/Minor premises reversed. This isn't the same as saying that in the plural syllogisms (fig. 1), EAE is the same as AEE, because the latter is invalid, but with singular-singular syllogisms both terms are the same from a distribution point of view. i.e. S is P = P is S and S is not P = P is not S. What am I missing?

Hi MDB.

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

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?

Hi MDB,

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

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.

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

Return to Website > Index > Select the appropriate forum > Logic > FUTURE LOGIC - Comments & Queries