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Avi,

I've been reading the chapter in your book "RUMINATIONS" in which you discuss modern logic. I found this very interesting and agree with what you say, but what about the claims of modern logic to be more powerful than the traditional Aristotelian syllogistic? For example, I don't know how you would express a relation such as "X is bigger than Y" using a syllogism, but this is easily done with modern predicate logic.

I would certainly agree with you that the classical logic is more "user friendly" than modern symbolic logic, but does it have an equal range of expression?

Something about you (optional) student

Dec 6th, 2009 - 11:08 AM

Hi Mike. The issue is not exactly “modern logic” versus “traditional logic” – but rather symbolic logic versus ordinary language logic. Human beings think first in ordinary language before they convert these thoughts to symbolic terms. Conversely, when we read a symbolic statement, we must in our head convert it to ordinary language for it to mean something to us.

Symbols have meaning for us only insofar as we have assigned them meaning through ordinary language. Therefore, they do not add any meaning – if anything, they tend to obscure the original meaning and to oversimplify it. They are sometimes useful, but sometimes they are serious obstacles.

In particular, the use of symbols alienates laypeople from logic theory, whereas one of the main tasks of logicians is to improve the logic capacities of non-logicians.

Symbols are only useful to abbreviate long ordinary language formulas or processes, or to repeat and mechanize what has already been painstakingly thought beforehand in ordinary language. But they cannot help us discover much of anything. Real discoveries in logic depend on ordinary language – on awareness and capture of actual human thought processes.

I would never have managed to formalize a fortiori argument or the logic of causation if I had been mentally imprisoned in symbolic logic. Such radical innovations in logic theory are inconceivable using artificial symbols (though they can be expressed symbolically ex post facto, of course).

This issue is dealt with more fully in Future Logic, e.g. in chapter 64, which I recommend to you.

Please note for future reference that I have now introduced a very nice talkback facility (Echo by js-kit.com) on all webpages of The Logician. Just click on the Comments hyperlink there. The present Discussion Area is more intended for The Logic Forum. Thank you.

Something about you (optional) writer in logic, philosophy, spirituality

While I acknowledge Avi's points, it seems to me that he hasn't really answered Mike's question regarding the scope of modern logic compared to the traditional logic. The wikipedia entry on "Logic" says that:

The fundamental difference between modern formal logic and traditional or Aristotelian logic lies in their differing analysis of the logical form of the sentences they treat.

...the modern view is more powerful: medieval logicians recognized the problem of multiple generality, where Aristotelean logic is unable to satisfactorily render such sentences as "Some guys have all the luck", because both quantities "all" and "some" may be relevant in an inference, but the fixed scheme that Aristotle used allows only one to govern the inference. Just as linguists recognize recursive structure in natural languages, it appears that logic needs recursive structure.

...the modern view is more powerful: medieval logicians recognized the problem of multiple generality, where Aristotelean logic is unable to satisfactorily render such sentences as "Some guys have all the luck", because both quantities "all" and "some" may be relevant in an inference, but the fixed scheme that Aristotle used allows only one to govern the inference. Just as linguists recognize recursive structure in natural languages, it appears that logic needs recursive structure.

Now I'm not sure whether this is entirely correct or where exactly the line is drawn between the traditional and modern logics, as there was much development in the intervening period between Aristotle and Frege. It's possible to express complex propositions formally (as Avi shows in his "Future Logic") without resorting to the predicate calculus. As to the particular example given ("Some guys have all the luck") it may be that it can be rendered using the so-called "quantification of the predicate".

Aug 22nd, 2011 - 3:59 AM

Hi Jacobite. What you say in your last comment is incorrect.

The main thing to understand is the pretentiousness of those who claim that modern logic is "more powerful" than Aristotelian logic. Let's take this example "Some guys have all the luck" (very briefly) - one can see immediately the paucity of their analysis by their picking such an ambiguous example. What does "all the luck" mean? All they focus on is the word "all" - whereas in fact here the intent is not "all the luck in the world" but perhaps "more luck than average or more luck than most people," which implies a whole nuther formal analysis. Moreover, if we change the example to, say, "all the marbles in this bag," and we assume the modern logician correctly analyzes that statement, what is the innovation brought on by such analysis? Zilch - what he and we know of the relation between various quantities is entirely a product of the Aristotelian analysis of these parts of speech (e.g. that all the marbles implies some of the marbles). All the modern logician does is apply what he has learned from Aristotle to a specific case and then pretentiously claims to have outdone Aristotle. That is dishonest. Moreover, I would suggest offhand that "all the marbles" here behaves more as a collective term than as a distributive one - so that even such syllogistic analysis would be inappropriate.

Secondly, your suggestion that the example here might be "rendered" by the idea of quantification of the predicate is inaccurate. There is an analogy of sorts, but not exact correspondence. Here I would suggest you make the same error as above, thinking simply that just because you find the word "all" embedded in the middle of a sentence it will behave in the same way. This is a typical misleading simplification of the modern logician's mind. Every form requires separate analysis and the important thing is to understand the general principles and insights of true formal logic, and not oversimplify. As regards quantification of the predicate, it is not as you seem to think a doctrine of Aristotelian logic, but an invention of early modern logic (mid 19th cent. - I forgot who offhand, maybe it was Hamilton, check it out). Aristotelian logic rejects such artificial simplistic contraptions. If you want to understand why, I suggest you study Joseph's critical analysis or at least mine in chapter 19.4 of Future Logic.

Dear Jacobite - I appreciate your enthusiasm, but again I must ask you not to put me in a position where I have to answer your comments, as I am very busy writing a new and important book, which requires all my concentration without distraction. Thanks and keep on truckin'

Something about you (optional) logician

Just would like to confirm that the "quantification of the predicate" was a theory of Hamilton and was criticized by many Aristotelian and Scholastic Logicians at the time including H.W.B. Joseph, G.H. Joyce, S.H. Mellone and P. Coffey among others.

Aug 23rd, 2011 - 12:28 PM

Hi zahc, thanks for your input. I was aware that quantification of the predicate was a fairly recent development (in fact it would be more accurate to say it was a suggestion) which wasn't particularly well received, it was only after the work of Frege, Peirce and others that certain kinds of inferences involving relations could be handled.

Dear Avi,

It appears to me that you're the one who is not being honest in denying that modern logic is capable of validating a wider range of inferences than Aristotelian logic. Augustus De Morgan complained that the traditional logic couldn't handle relational arguments such as "All dogs are animals; therefore all heads of dogs are heads of animals". Modern logic can. Since there is a large class of arguments which fall into this category,to suggest that this development is mere pretentiousness is absurd. However, I've gone on enough about this and it's my intention to make a positive contribution here so this is the last you'll hear from me on the subject.

Modern logic was developed in order to study the foundations of mathematics, (since maths is primarily about relations the modern logic is particularly well suited to it - try expressing the notion of a limit using a syllogism, it can't be done) but it isn't particularly appropriate for everyday use or philosophical arguments. However, you may be aware that in recent years philosopher Fred Sommers has developed a "Term" logic which is much more like the old logic, but has all the inferential power of the predicate calculus. (see "A revival" in http://en.wikipedia.org/wiki/Term_logic) It's very easy to learn and I'll post the basics of it in another thread.

Aug 24th, 2011 - 11:08 PM

Hi Jacobite -

I think your criticism of Avi is a bit unfair.

Have you read Future Logic?

If not I highly recommend that you do.

I don't think Avi is denying that Modern Logic has made very useful and welcome advances beyond Traditional Logic. I think his point is that the many advances of Modern Logic do not replace Traditional Logic but is just an extension of it.

"All dogs are animals; therefore all heads of dogs are heads of animals". Such an inference is called "Immediate Inference by added determinants" which Avi mentions in passing in Chapter 19 of Future Logic.

Anyway, nice to see another person as passionate about logic as I am

Aug 25th, 2011 - 7:45 AM

Zahc,

Thanks for that, I have dipped into Future Logic but have only very recently started studying it seriously from the beginning. I'm finding it very interesting, especially the chapters on Modal logic which is quite new to me.

I realise I have some "unlearning" to do of my previous study of logic, which was mainly in relation to computer science. Logic is much more interesting and has a lot more depth than I had previously thought. I'm looking forward to studying Avi's work which seems to be unique.

So Avi, apologies for my previous post - please ignore it and continue with your work. There seem to be so few people interested in logic these days, I wonder why that is? In my opinion, it should be taught in all schools on a level with the 3 'R's.

And I won't bother posting the stuff on Sommer's Term logic (unless you're interested). From now on I'll concentrate on Future Logic.

Aug 25th, 2011 - 9:15 AM

By the way Zahc, since you've read Future Logic hopefully you can help me with any questions I might have, since Avi is busy.

Aug 25th, 2011 - 9:23 AM

Sure, I'd be glad to correspond with you. Just send an email. I'm sure we can learn from each other.

Aug 25th, 2011 - 9:30 AM

Hi zahc and jacobite - if you would like to send each other your emails, you can do so through me.

Jacobite, sorry I cannot be more helpful right now. Certainly cannot engage in debates, which take a lot of time, and are not in my view the best way . I prefer long studies.

You might find some answers to your questions about in Ruminations (see table of contents), also in the first two books of Logical and Spiritual Reflections.

For instance, in the book on Kant chapter 2, I have some comments on Frege. In Ruminations, chapter 4.5 I have some comments on added determinants.

My point throughout is what I said to you from the beginning - viz. that modern logic is superficial and simplistic. It gets quickly caught up in definitions, axioms, symbols and well... doodling - but is short on empirical analysis as to how humans really conceptualize and reason, on the wider epistemological context surrounding logic, and in particular it focuses on deduction and does not see its place in the larger context of induction.

The people who claim modern logic is unsurpassable are people who don't know better.

P.S. Do post the Sommers material, of course I'm interested. Or mail it to me.

Thanks.

Something about you (optional) logician

Thanks Zahc and Avi, and no need to apologise, I'm not that keen on debates either.

As I mentioned in my previous post, my knowledge of logic was acquired in relation to computer science - specifically in a course on modelling algorithms using symbolic logic. Being a closed and artificial system consisting of nothing but 1's and 0's (unlike the messy real world), a computer doesn't have much need of wider epistemological issues, or even induction, so I suppose it's not surprising that my view of formal logic is rather narrow.

Although, thinking about it, I suppose if your program fails you could always use inductive logic to help find the bug (the cause of the crash) Hey, your logic of causation might come in handy there!

I'll start posting the Term logic stuff in the next couple of days. In the meantime, you can get a flavour of it from reading the intro to "Something To Reckon With" on google books.

Aug 25th, 2011 - 1:55 PM

Thanks for the info, jacobite. I will eventually study it and maybe even respond to it.

The Logic of Causation has lots of zeros and ones, so you should feel right at home there. Maybe one day you will try to symbolize it, as already discussed.

You will also find my resorting to zeros and ones in Future Logic, for factorial induction.

zahc has been studying Future Logic and other books for years.

Good luck, Avi

Something about you (optional) logician

Here is a logical problem which seems difficult to formalize using the traditional syllogism:

p: Every boy loves some girl.

p: Every girl adores some cat.

p: All cats are mangy.

p: Whoever adores something mangy is a fool.

From these premises, derive -

c: Every boy loves a fool.

You can puzzle it out just by thinking about it, but that's not a formal proof is it?

Thanks in advance for any help!

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

Hi student - I responded to the wrong post.

What is involved here is not subsumptive syllogism but a set of substitutive syllogisms.

Every B loves some G, every G adores some C, all C are M and whoever adores something M is an F.

From the 2nd and 3rd premises, by substitution: every G adores something that is M.

And since "every G adores something M" is subsumed under "whoever adores something M", it follows from the 4th premise that: every G is an F.

Now again substitute into the 1st premise: every B loves some G becomes every B loves an F.

Notice that the relation "loves" plays no role - it could be anything.

Thus, so special field of logic is needed here to arrive at the conclusion - just subsumption and substitution.

I mention substitution in my Future Logic, chapter 19.1: http://www.thelogician.net/2_future_logic/2_chapter_19.htm#1. Substitution.

Something about you (optional) logician

Hi Avi,

Thanks a lot for that. I've read the section in Future Logic which you refer to and it seems to me that the method of substitution could be used for any argument which involves relational terms, is that correct?

Being able to deal with relations is supposedly one of the great advantages of the predicate calculus over the traditional logic, which is considered by modern logicians as much "weaker" by comparison. I'm beginning to understand what you mean by pretentiousness; the predicate calculus certainly looks impressively mathematical, but the amount of effort involved in proving even fairly simple arguments is large. The old way is much more natural, and it seems that it sacrifices nothing in terms of power.

I must say, I feel like I've been conned!

Not only that, but the predicate calculus doesn't seem able to derive conclusions which aren't given, because it works by reductio ad absurdum. You need to have the conclusion in order to prove it, but what if you want to draw conclusions from a set of premises? With a syllogism you can do it, but not with the predicate calculus. I've only just realized this, but it seems an important distinction.

Substitution is nothing new - I seem to recall seeing it in Aristotle somewhere. We use it commonly in many contexts.

As for "modern logic," not only does it often make a mountain out of a molehill, but it often indulges in errors, so well hidden they think no one can spot them.

I give many examples in my forthcoming book. If you register your email, I will add you to the mailing list and advise you when it is out, in a few months.

Best regards, Avi

Something about you (optional) logician

Thanks Avi, please add me to your mailing list.

May I ask what is the subject of your new book? You seem to have covered pretty much everything already!

By the way, thanks to jacobite for posting the link to the book by Englebretsen. I'm still reading the book but that's where I got the above problem from.

Jul 19th, 2012 - 12:03 AM

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)

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

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

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

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.

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

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*

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.

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.

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

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