[jeffreylkarl]

I bought a copy of Basic Logic by Raymond McCall. The first section delves into the details of Terms. I’m having trouble distinguishing between – what McCall refers to as – “individual concepts” vs. “singular concepts.”

In my book, the two definitions are printed on page 23. His definition of a singular concept is “one whose extension is limited to one singular.” He gives “this man” as an example.

McCall defines “individual concepts” as universal concepts whose natural universality is restricted and taken individually. He gives “my father” as an example.

I’m having a tough time wrapping my head around the difference between the two.

[gerard.casey]

All that material in McCall on ‘Simple Apprehension and the Term’ is, I agree, head-wrecking! Fortunately, for our purposes in formal logic, we don’t have to have an airtight grasp on it – much of this material really belongs to what would now be called the philosophy of logic/epistemology.

Let me see if I can explain simply what McCall is up to.

Let’s take the distinction between ‘singular’ and ‘particular’ first.

A term is singular when it picks out a unique identifiable (in principle) definite entity; for example, the Library of Congress, the Statue of Liberty, etc. Note, a term can be singular even if the unique entity which it picks out is a composite of various parts. Propositions whose subjects are singular terms are singular propositions.

A term is particular when it picks out some individual indefinite entity or other and when such a term is the subject of a proposition, the proposition is particular. for example, ‘Some students have done well in the logic examination’ would be true if there is at least one student who has done well in the examination, even where we don’t know who that student is or even where there is more than one such student.

Now terms (and the concepts they express-what McCall calls ‘proper concepts’) are in themselves neither particular nor singular. The term ‘man’ and the concept it expresses is perfectly general. We can limit or restrict a term by connecting it with other terms so that, for example, ‘some men’, or ‘most men’ or ‘quite a few men’ and the like.

Now, given the examples he uses, what McCall appears to mean by ‘individual concept’ is a concept limited by some indexical expression {‘I’, ‘mine’), for example, ‘my car’ or ‘my father’. Such composite terms (and concepts) will pick out one unique individual and so, for the purposes of formal logic, are equivalent to singular terms though not quite in the same way as the examples I gave above.

I’ve had a quick look through the rest of McCall’s book and he seems to make no further use of the term ‘individual concept’.

So, what should you take from all this?

What we want to know about terms as they are used in propositions is the following: Is the term used to pick out a unique definite individual entity (whether that entity is actually simple ‘or composite)? if so, the term is singular and the proposition of which it is the subject is also singular.Is the term used to refer to all of the things that it can refer to?If so, the term is universal and the proposition of which it is the subject is also universal. If the term is neither singular nor universal, then it can only be particular and the proposition of which it is the subject is also particular.

I hope this helps?

If you have any further questions on this or any other logical matters, please do post it here and send me a quick email at gerard.casey@ucd.ie so that I can respond as expeditiously as possible.

[jeffreylkarl]

Hi Professor,

Yes, that helped. I actually had to read you response, go reread the passage in the book, and then reread your response once more.

It sounds like singular concepts are concepts that extend to one specific thing (I want to avoid using the word “individual” here), while individual concepts are universals, extending to an infinite number of singulars, that are taken individually – or maybe it’s better to say “taken one at a time?”

McCall said earlier in the chapter that as comprehension increases extension decreases. Does an individual concept side step this inverse relationship? I can see how saying “this man” might call to mind the image of a specific man and his unique traits, whereas saying the term “my father” limits the universal concept “father” to just one of its many singulars without at all changing the image of the universal concept. It seems a bit “gentler” or “less restricting” I suppose.

Is this correct? I have just one other question about the chapter on Terms and wanted to see if I could first grasp the singular concept vs. individual concept distinction.

Thank you, again.

[gerard.casey]

You wrote: “It sounds like singular concepts are concepts that extend to one specific thing (I want to avoid using the word “individual” here), while individual concepts are universals, extending to an infinite number of singulars, that are taken individually – or maybe it’s better to say “taken one at a time?””

Singular terms {I’m not sure I’d want to use the expression ‘singular concept’ as concepts by their very nature are usually taken to be applicable to more than one entity. Here, however, Leibniz and some other philosophers might want to start an argument) are terms that refer to a unique entity. Individual concepts, McCall’s examples suggest, are restricted universals which, as I suggested in my last post, appear to function logically as if they were singular terms.

You wrote: “McCall said earlier in the chapter that as comprehension increases extension decreases. Does an individual concept side step this inverse relationship? I can see how saying “this man” might call to mind the image of a specific man and his unique traits, whereas saying the term “my father” limits the universal concept “father” to just one of its many singulars without at all changing the image of the universal concept. It seems a bit “gentler” or “less restricting” I suppose. Is this correct?”

What you are suggesting seems reasonable to me though I would have to think about it quite a bit more before I’d commit to a definitive answer. I repeat what I said in my last post – ‘Fortunately, for our purposes in formal logic, we don’t have to have an airtight grasp on it – much of this material really belongs to what would now be called the philosophy of logic/epistemology.’

You wrote: “I have just one other question about the chapter on Terms and wanted to see if I could first grasp the singular concept vs. individual concept distinction.”

Regardless of whether you are completely clear on the matter in hand, please go ahead and ask your next question.

Best wishes,

GC

[jeffreylkarl]

Thank you, Professor. That definitely helped.

I may have answered my second question as I was typing it up. I was a little confused about real supposition in abstract terms. McCall lists “Justice is a virtue” as an example.

Maybe it’s better just to ask for some further reading on the subject of supposition? McCall lists Jacques Maritain’s ‘Introduction to Logic’ as a great resource, but I’m not sure if this covers informal logic. Or perhaps one of the books on the bibliography page covers the topic of supposition?

[gerard.casey]

Dear Jeff,

The notion of ‘supposition’ (or rather its modern equivalents denotation, connotation, reference, meaning) is now treated in most Philosophy Departments under the rubric of Philosophy of Language and in that dispensation, is no less controversial than it was for the medievals. The subject is enormously complex and controversial and no two thinkers treat it in exactly the same way. The account in McCall is (necessarily) simplified and streamlined. (Apart from material, real and logical supposition, other thinkers discuss absolute and personal supposition!)

All that being said, the distinction between material supposition and all other kinds is pretty obvious. The problems arise in trying to distinguish between real supposition and logical supposition. One test is to ask yourself whether the predicate in a proposition can apply to the particulars that lie under a subject. If it can, then the supposition of the subject term is likely to be real rather than logical.

Your question pertains to a proposition such as ‘Justice is a virtue’ and here, the test doesn’t yield an obvious solution. It seems odd to think of their being particular justices but, if there were any such, they would each be virtues. That being so, the supposition here is real rather than logical.

Maritain’s book doesn’t cover informal logic.

Most handbooks on logic contain little more than you find in McCall. If you really want to investigate this topic, you need to go to specialist texts or back to the originals. In terms of drawing a contrast between logic as it was traditionally conceived and modern logic, Maritain’s book is good but the book that specifically deals with the topic is Henry Veatch’s Two Logics.

Let me give you a specific example of how the two logics differ.

In classical logic, the relationships on the square of opposition all hold completely independently of whether or not the terms in the propositions actually refer to anything in reality or not. The logical relationships are, as it were, meaning relationships, and questions of existence are not relevant..

In modern logic, only contradiction on the square of opposition holds. The reason for this is that for this logic, universal propositions are taken hypothetically and, as such, are deemed to be true even if the antecedent clause of the conditional is false! So, ‘All unicorns are wonderful’ would, for modern logic, be a true proposition. Bu the subordinate proposition, ‘Some unicorns are wonderful’ wold not be true unless there were in fact unicorns. So, for modern logic, the universal could be true but the subordinate proposition false.

For classical logic, however, the question of existence doesn’t arise here.

This has been a long response to a short question and may give you more headaches than it cures. The topics you are raising are important and controversial but with respect to gaining a facility in the formal side of logic, they are not completely relevant.

Best wishes,

Gerard

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