The Logic Forum Discussion Area

Logic
This Forum is Locked
Author
Comment
View Entire Thread
Re: Modern Logic vs Traditional Logic

Hi Avi,

I was hoping you would be able to clarify something for me. I think this thread is the appropriate one to post in.

I saw this posted on another forum, the claim was that a categorical syllogism cannot deal with the following:

1. A lamp post is to the left of all the animals.
2. A tiger is an animal.
3. Therefore, a lamp post is to the left of an animal.

Now I don't know whether the following should be regarded as a syllogism in the strict sense, because it has 4 terms, not 3, but here is my solution, which depends on the fact that if there is a relation in which Q stands to S, it can be immediately inferred that there is a converse relation in which S stands to Q.

Thus, if P = lamp post, A = animals, T = tiger, L = to-the-left-of and R = to-the-right-of, we have

1. Some P is L all A
2. all T is A
3. all A is RP (converse of 1)
4. all T is RP (from 2 and 3)
5. Some P is LT (converse of 4)
6. Therefore, Some P is LA (from 2 and 5)

Re: Modern Logic vs Traditional Logic

Hi Mike - I would express the relation "X is bigger than Y" as "X is bigger than Y"! There is no question of changing this into an Aristotelian proposition "X is [bigger than Y]" - this is not the point. This proposition "X is bigger than Y" is treated by ordinary language logic exactly as it stands, or even as "X > Y". The only difference is that we should not engage in pretentious claims that symbolizing it in accord with the conventions of modern logic somehow magically makes it something special, more profound, like some sort of incantation. Behind symbols are always ordinary language. Thus, the claim that modern logic brings something new to logic that classical logic cannot handle is just so much hype.

Something about you (optional) logician

Re: Modern Logic vs Traditional Logic

Hi David.
The example you give seems to be one of Substitutive Syllogism.
A (the lamp post) is related to B (all animals) in the way of C (to the left of);
and D (this tiger) is a B (an animal);
therefore, A (the lamp post) is related to D (this tiger) in the way of C (to the left of).
(The conclusion you have "a lamp post is to the left of an animal" I take to be an unintentional error on your part, since this proposition is subsumed by your major premise without need of the minor premise. The conclusion should mention the tiger mentioned in the minor premise.)
Substitutive syllogism is not ordinary syllogism in the Aristotelian sense, although as I seem to recall it is mentioned somewhere by Aristotle (I may have noted the location in one of my books), or maybe by Theophrastus or some other later Greek logician (this needs further research). Here, a subject is replaced by a subject that it subsumes. See e.g. Future Logic, chapter 19.

With regard to your proposal, viz.
1. This P is to the Left of all A
2. all T are A
3. all A are to the Right of this P (converse of 1)
4. all T are to the Right of this P (from 2 and 3)
5. This P is to the Left of a T (converse of 4)
6. Therefore, This P is to the Left of an A (from 2 and 5)
I see no use for the complication of converting left to right and right to left (re. #3 and #4). For the rest, as already said, I would regard #5 as the conclusion of the syllogism, since #6 is implied by #1 without need of #2).

Something about you (optional) logician

Re: Modern Logic vs Traditional Logic

Hi Student,
sorry I took so long replying to your question (two years)! I must have missed it.

I just want to inform you that in my new book, A Fortiori Logic, published in late 2013, in Appendix 7, you will find further critiques of Modern Logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox.

Something about you (optional) logician

Re: Modern Logic vs Traditional Logic

David,
looking through a work by Aristotle in a very offhand manner I found the following reference to substitution in Topics, Book 1, Chapter 7:

"For all these uses mean to signify numerical unity. That what I have just said is true
may be best seen where one form of appellation is substituted for another. For often when we give the order to call one of the people who are sitting down, indicating him by name, we change our description, whenever the person to whom we give the order happens not to understand us; he will, we think, understand better from some accidental feature; so we bid him call to us 'the man who is sitting' or 'who is conversing over there'-clearly supposing ourselves to be indicating the same object by its name and by its accident."

This is of course just one special case (viz. substituting an individual's name or description), but it clearly lays the foundation and show Aristotle was aware of the thought process. I have no doubt further research would reveal many more references to substitution in Greek logic.
Avi

Something about you (optional) logician

Re: Modern Logic vs Traditional Logic

Hi Avi,

Thanks for the feedback. You're right about my silly error, not sure what I was thinking there.

Regarding steps 4 and 5 in your first reply:

4. all T are to the Right of this P (from 2 and 3)
5. This P is to the Left of a T (converse of 4)

Shouldn't 5. be: This P is to the Left of all T, rather than a T?

Thanks for the reference to your book, I will look at it.

I came across this particular kind of immediate inference in an old logic text "Principles of Logic", by G.H.Joyce, who also says it was recognized by Aristotle (although not sure whether he was referring to substitution as you are).

https://archive.org/stream/principleslogic00joycgoog#page/n126/mode/2up

The modern logic is not to my taste.

Re: Modern Logic vs Traditional Logic

Hi Mike.
Of course, #5 is applicable to all T - but I wrote a T to comply with the conclusion you were seeking!
I have looked at the G.H.Joyce link you gave me, but do not see where Aristotle is mentioned, Could you give me the exact page in that book that you had in mind? Thanks.
Best regards,
Avi

Something about you (optional) logician

Re: Modern Logic vs Traditional Logic

Avi,

Ok, thanks!

The section is in chapter 6, "Immediate Inferences" page 103-104 (Immediate inference by converse relation). The reference to Aristotle is Categ. c. 7, section 6

Re: Modern Logic vs Traditional Logic

Interesting topic. Immediate inference by converse relation seems to work with some relations but not others. An example where it doesn't seem to make sense is this: "Every boy loves some girl", and the converse relation is "Some girl is loved by every boy". But this doesn't have the same meaning as the first statement.

Re: Modern Logic vs Traditional Logic

Thinking about this and after doing a little searching online, it seems there is a name for this fallacy -- it's called quantifier shift.

https://en.wikipedia.org/wiki/Quantifier_shift

The problem is in the ambiguity of "some". In the statement "Every boy loves some girl" does it mean some particular girl or "some girl or other"? If the latter, then every boy could be loving a different girl.

Actually, it seems to me that IF the statement is true (however you interpret "some"), then it does follow that "Some girl is loved by every boy".

ie,

first case:

Every boy loves some (particular) girl
Therefore, Some (particular) girl is loved by every boy

second case:

Every boy loves some girl or other
Therefore, Some girl or other is loved by every boy

The fallacy only arises when the meaning of "some" in the conclusion is different from its meaning in the premise.

Re: Modern Logic vs Traditional Logic

Change of meaning of a term is obviously fallacious, and rather common.

Regarding your specific example and comment, '"Every boy loves some girl", and the converse relation is "Some girl is loved by every boy". But this doesn't have the same meaning as the first statement.' - my feeling is that the two are identical, really, because you could reverse the order of 'conversion' (as you call it). This sort of 'conversion' is, to my mind, just a change in the order of wording, but not really logical conversion.

Like saying, "her, I love" instead of "I love her" - just a small change of emphasis perhaps.

Something about you (optional) logician-philosopher