The reason there isn't such a text by an Objectivist is because formal deductive logic is such a small part of Rand's view of logic. As Harry Binswanger explains in his excellent course on logic, the essence of the subject is the proper use of *concepts.* However, if you're looking for a good presentation of Aristotelian logic, you could listen to Leonard Peikoff's "Introduction to Logic." 1156524215:::The Complimenting Commenter:::commenter@gmail.com:::http://complimenter.blogspot.com:::That is a very good observation. Thank you for sharing this quote. I have much to think about. 1156524460:::David Rehm:::user@server.type:::http://davidrehm.com/:::PMB,

Thanks for the clarification. I was aware of both courses you mention, but appreciate their explicit recommendation.

--

I still reiterate my original question looking specifically for anything in text versus audio. Suggestions? 1156524515:::Diana Hsieh:::diana@dianahsieh.com:::http://www.dianahsieh.com/blog:::Dr. Peikoff recommends the Copi text (with some qualifications) available from Paper Tiger books. 1156524555:::David Rehm:::user@server.type:::http://davidrehm.com/:::Err.. that last part should read more like:

I still reiterate my original question looking specifically for anything in text (even if not by an Objectivist) versus audio. Suggestions? 1156524875:::David Rehm:::user@server.type:::http://davidrehm.com/:::Cool.

I'm not seeing what you mean by "Copi text" on Paper Tiger's site, unless its one of the two mentioned in the following link.

I did find an article by Binswanger on the state of logic texts with two of his own recommendations: <http://www.papertig.com/Publishing_TIA_Logic..htm> 1156525158:::PMB:::::::::David, I think Diana was thinking of Ruby. Copi is the most widely used logic text today--it's the one I used to learn logic. I don't have an opinion on its quality though. 1156529425:::Mike Hardy:::hardy@math.umn.edu::::::The "conventions of modern logic" make perfect sense

within a certain narrow mathematical context. Although

I have long been aware that mathematicians for whose

purposes such conventions make sense are oblivious to

the fact that they don't make sense in a broader context,

I only found out about a year ago that apparently lots

of mathematicians don't appreciate the reasons for such

conventions. I wrote in a footnote

(see http://arxiv.org/pdf/math.CO/0601149.pdf?front, page 5):

Perhaps as a result of studying set theory, I was surprised

when I learned that some respectable combinatorialists consider

such things as this to be mere convention. One of them even

said a case could be made for setting the number of partitions

to 0 when $n=0$. By stark contrast, Gian-Carlo Rota wrote in

\cite{Rota2}, p.~15, that ``the kind of mathematical reasoning

that physicists find unbearably pedantic'' leads not only to

the conclusion that the elementary symmetric function in no

variables is 1, but straight from there to the theory of the

Euler characteristic, so that ``such reasoning does pay off.''

The only other really sexy example I know is from applied statistics:

the non-central chi-square distribution with zero degrees of freedom,

unlike its ``central'' counterpart, is non-trivial. 1156557499:::Matt F.:::danconiacopper@yahoo.com::::::That is on hell of an integration--and especially pertinent for me right now as I am currently taking an advanced formal logic course at the University of Houston with the most horrendous of professors. Here is a quote from his website to give you an idea of what I'm talking about: "...my sympathies lie with irrealism: instrumentalism in science, constructivism in logic and math, projectivism in metaphysics, and non-cognitivism in metaethics."

Ugh. 1156570193:::Ergo:::jjdoub@yahoo.com:::http://ergosum.wordpress. com:::Maybe I'm missing something. I'm unable to see what exactly is this "important" and "unique" and "heck of an" integration being made here.

Is it just that logic should conform to reality? That premises need not only be true but also consistent with existing facts and true knowledge? Is it that modern logicians are more preoccupied with logical stunts that are entirely detached from reality but are nevertheless truth-preserving?

If it is any of the above, I'm not able to see the novelty of the idea. Please can someone care to explain this out for me? I'd appreciate it! 1156571119:::PhilosopherEagle:::::::::I don't know whether the idea is novel, but it was new to me when I discovered it, and I have never heard anyone make the same point. It is important precisely because it goes beyond saying that modern logic is wrong because it doesn't conform to reality. Now I am also able to understand the context of values out of which the whole of modern logic arises, and with that I am better able to understand where modern logicians are coming from, better able to communicate with them, better able to do well on logic tests, and better able to understand the significance of Ayn Rand's view of logic. 1156608599:::Objectivist_PhilGrad:::::::::While I appreciate and agree with the general spirit of this quote, I think it grossly mischaracterizes some fundamental ideas in symbolic logic.

PE writes:

"For example, any argument whose conclusion must be true is said to be deductively valid. So if our premise is that apples are delicious, we can validly conclude that John is either a carpenter or not a carpenter. I submit that this is not a valid deductive argument, because it is not an argument at all."

While I agree that this is not an argument and that this is not valid, it is not true that "any argument whose conclusion must be true is said to be deductively valid." Validity is an issue of form, not of content; an argument is said to be valid when it is an instance of a form in which IF the premises are true then the conclusion must be true. PE makes the error of saying that "if the conclusion is true necessarily, then the arugment is valid"; this is wrong because the conclusion's being necessarily true is not sufficient to qualify as an instance of validity. That a conclusion takes the disjunctive form and is trivially true by virtue of the law of excluded middle has no reflection on the validity or invalidity of the argument as such.

Another way of making this point is to say that the conclusion of a valid argument stands in a certain kind of relationship to the premises adduced to support it. In PE's example (involving apples and carpenters) this relationship is not present, and therefore it is not valid. Moreover, it is not valid because IT IS NOT AN ARGUMENT. An argument is a group of propositions of which one is said to follow from the others (which serve as evidence for it). There is no evidential or inferential relationship between "apples are delicious" and "John is/not a carpenter." It is therefore not an argument, and NO LOGICIAN WOULD REGARD IT AS SUCH. Neither would they regard it as valid (validity being a property of arguments).

I cannot believe that no one brought this up yet, because it is a very VERY gross error, and it leaves PE tilting at a straw man spun from his own confusion.

All that said, I still think his basic psychological point is both true and interesting, but that the argument he produces for it is ridiculous... and I'm kind of sad that no one noticed that. 1156627647:::Luka:::::::::Objectivist_PhilGrad,

I have to admit that I'm a bit confused about whether or not the apples-carpenter pair of statements is a valid argument. It's my impression that some philosophers would say that it is, since there is some sense, perhaps, in which the first statement ensures the truth of the second. But it's also my impression, from asking a fellow phil grad student who is more interested in logic than I am, that there are philosophers who would reject the claim that the pair of statements make up a valid argument. (Actually, I suppose it's more important what logicians, specifically, would say about this stuff than what philosophers, in general, would say. But anyway...) The issue of validity aside, I'm a little skeptical about your claims that no logician would regard the pair of statements as an argument. I don't know that much about what logicians say about this stuff, but I do know a bit about what philosophers, in general, say about it. And I think I know some philosophers that would regard the pair of statements in premise-conclusion form as an argument. Just like they would regard the following as one:

(P) Chicago is in Illinois

---------------------

(C) The sun is a star

I believe that they would say that this is just a REALLY bad argument. And so would I. In fact, it's a great example of a super-duper terrible arugment. But it has the form of an argument and, as far as I can tell, that's all that's needed for something to qualify as an argument. (Well, the statements need to be meaningful, too.) I might be wrong about that though... 1156636811:::PhilosopherEagle:::::::::Objectivist_PhilGrad,

I don't understand your criticism. You said:

"Moreover, it is not valid because IT IS NOT AN ARGUMENT. An argument is a group of propositions of which one is said to follow from the others (which serve as evidence for it)."

And this was precisely the point I made in the paragraph that Diana quoted. However, I gave a citation from "The Logic Book," which seems to be a pretty conventional text on symbolic logic. Just prior to that citation, the authors state that examples of the sort I provided ARE valid arguments. Here is the definition of deductive validity that is given in the book: "An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion to be false."

If you're saying that this is wrong, I agree with you. But at least one commonly used text on symbolic logic does not. 1156637176:::PhilosopherEagle:::::::::Another way of putting The Logic Book's definition is: an argument is valid if and only if: if the premises are true, then the conclusion is true. Objectivist_PhilGrad seems to agree with this way of putting the definition, but The Logic Book takes this conditional as a material conditional. Hence there need not be a relationship between the premises and conclusion, according to this text, to have an argument or even a valid argument. 1156642016:::Objectivist_PhilGrad:::::::::I think you're misinterpreting that definition to suit your purposes.

From Ruby's "Logic: An Introduction":

"An argument is valid when the premises necessitate the conclusion." (p.156)

From Copi's Logic:

"A deductive argument is VALID when, if its premises are true, its conclusion MUST be true."

From Klenk's "Understanding Symbolic Logic" 4th Ed.

"A valid deductive argument in which the truth of the premises absolutely guarantees the truth of the conclusion" (p.7)

Validity is a matter of the formal relationship between premises and a conclusion; any other interpretation is esoteric as far as I'm concerned. Absolutely everyone I've ever discussed the matter with has maintained the same. I think a big thing throwing you off is the fact that you have a conclusion which is necessarily true without the presence of any other premises. It boils down to "S is either A or Non-A" - something which cannot be false; I think your point is that because the conclusion must be true, then the argument is valid. However...

"A deductive argument is one whose conclusion is claimed to follow from its premises with absolute necessity, this necessity not being a matter of degree and not depending in any way on whatever else may be the case." (Copi). The fact that the conclusion is necessarily true, in this case, counts as a fact which falls into "whatever else may be the case." That apples are delicious has no bearing whatever on the truth of the conclusion; it certainly does not necessitate the conclusion in the manner required for validity to obtain. I doubt the examples given in the logic text reflect the same form (I'll have to track down a copy, if I think it's worth pushing the point).

I don't mean to be nit-picky.

Regards! 1156691595:::John Dailey:::Phyrm_1@hotmail.com::::::~ Present day 'symbolic/mathematical/modern' logic is nothing more than what boils down to what I call 'conjunction' logic: the logic of conjunctions. Such logic is inherently limited to Rules of Equivalence re the negation-sign, conjunction, and disjunction usage, and, in effect, translations of each to the other and into the resultingly very-limited-meaning of the conditional-terms 'if-then'. (Brand Blanshard wrote of such limitations in his "Reason and Analysis".) The term 'consistency' with non-contradiction (ie: 'validity') is the only determinant of the worth of 'conclusions' which are thereby merely logically-true/false (by definition of the original premises, of course), the latter being considered irrelevent to actually-true/false.

~ It has its useful place, no argument, as any (especially electronic) circuit-designer/analyzer will tell you. The problems about it come up in philosophical tracts/arguments, including intro-texts, re it's being justified as the be-all and end-all of what 'logic' is supposedly all about. That this perspective limits any meaning of logic to being ONLY deduction (and ONLY about conjunctions) should be a tip-off that something's really...illogically, (irrationally?) if I may...off here; that plus the distinction 'twixt logically-true and actually-true. That such regards Aristotelian logic as derivative (after mucho complicatedness of advanced syntax symbology required in the later 'Predicate Logic'), and not merely 'consistently' Equivalent, begs for justification that never has been forthcoming from its promoters, epistemologically speaking. But then, though they argue about truth-values, they never argue in terms of 'knowledge.' It's all a symbol-game with rules akin to chess, and nothing more.

~ Advocates of it as superceding the worth of Aristotelian logic's concern with proper concept-relating hinge on the 'if-then' conditional as being considered ONLY in terms of a conjunction: P->Q (IF 'P', THEN 'Q') means absolutely nothing more than NOT-{P & not-Q}. All truth-table analysis follows from there, deductively, albeit with an arbitrary truth-interpretaion of {Not-P and Q}. Blanshard, as mentioned, argued about this. Peikoff, in his "Intro To Logic", somewhere in the Q&A if I remember, showed a much more worthwhile broader and meaningful interpretation allowing for more obvious analysis in terms of Aristotelian logic.

~ 'Truth preservation' is certainly a characteristic of logic (deductive, anyway); but its being regarded as the DEFINING characteristic seems to be a bit myopic; as myopic as regarding non-contradiction (ignoring 'relevence', as some contemporary logicians complain about) as the ONLY criteria for evaluating a conclusion as such. Hence "{I am typing} AND {either my cat is dead or it is not dead}" is logically consistent, but clearly, as others argue, when such is rephrased in the 'if-then' form, 'concluding' anything is not really concluding an argument in any worthwhile sense of the words. Technically, as modern symbolic logicians would probably agree...it is (as so much of this territory)...trivial.

~ All said and done though, the biggest probs 'twixt the advocates of each are apparently subtle differences in meaning re the terms 'valid', 'conclusion', 'truth', and probably 'must' as well. In other words, as in abortion debates, most is cross-talk and mis-understanding with little agreement on basic definitions of the necessary terms used.

LLAP

J:D

P.S: I read Copi a long time ago. Little different from Peikoff's coverage. Quite good. Binswanger's course sounds worthwhile. 1156704006:::Freddy Ben-Zeev:::benzeev(at)comcast(dot)net::::::The way I see it, the difference between "if P then Q" and "NOT-(P and NOT-Q) is that the first imply causuality, while the second doesn't. 1156711125:::Freddy Ben-Zeev:::benzeev(at)comcast(dot)net::::::Just to clarify (a little) my previous post: when I say that "if P then Q" imply causality, I mean that this statement implies that there is some causal connection between P and Q - not necessarily that P causes Q. 1156713209:::John Dailey:::Phyrm_1@hotmail.com::::::Freddy:

~ If it's one thing that 'symbolic logic' advocates advocate, it's that to speak in terms of 'if-then' really "implies" NOTHING about causality. --- Worse: the term "imply" itself also has a very restricted and logically myopic meaning along with the other terms I specified; I should have specified THAT term above all in my last post. Given that, there's a built-in disagreement 'twixt advocates and denigrators on any and all subjects re A 'implies' B. Advocates see NO difference between 'if P-then Q' and 'not-(P & not-Q)'; indeed the conditional and the conjunct are definitionally logically equivalent within this area of...thinking. And that's the very starting point of symbolic/conjunction logic.

~ Check out a beginner's text...when you have time to kill.

LLAP

J:D 1156714243:::Freddy Ben-Zeev:::benzeev(at)comcast(dot)net::::::John, I've read some logic texts, but it was many years ago.

What you say is exactly my point. What I see is symbolic logic supporters attempting to eliminate any dependence on causality which in practice disconnects them completely from reality. 1156722264:::John Dailey:::Phyrm_1@hotmail.com::::::Freddy:

~ Well, we're on the same page. This 'disconnect' is precisely what makes Conjunction-Logic's philosophically-justified basis of being the most worthwhile starting-point in studying (and especially defining) LOGIC to be nothing more than being arbitrarily picked in its own starting-point definitions and rules-for-validity. It's not only 'rationalistic', but, inherently tautologically so. As Peikoff says: "It's for those who like maze-puzzles."

~ Logically, it has worth...to a point. Rationally, it lacks logic...about logic; put another way, it lacks a 'meta'-level allowance for self-recursivities which are more than mere (tautological?) redundancies. --- It's a closed system...like Latin.

LLAP

J:D 1156787649:::Mike Hardy:::hardy@math.umn.edu::::::: What I see is symbolic logic supporters attempting

: to eliminate any dependence on causality which in

: practice disconnects them completely from reality.

There is no causality in the multiplication table

or the proof of the Pythagorean theorem.

Some aspects of reality simply don't involve causality. 1156794610:::Mike Hardy:::hardy@math.umn.edu::::::Modern logic and cell-phone etiquette:

Go down the list of all persons expected to be

in attendance at a meeting over which you're

presiding (e.g. students in a class you're teaching).

Call their names one-by-one:

"John Doe"

: "Present!"

"Mr. Doe, have you turned off any and all cell

phones you are carrying?"

: "Yes."

"Richard Roe"

: "Present!"

"Mr. Roe, have you turned off any and all cell

phones you are carrying?"

: "Yes."

Etc.

By the conventions of modern logic, if a person is

carrying no cell phones, then, _a_fortiori_, he has

turned of all cell phones he's carrying. Therefore

he answers "yes".

That makes sense. You're just trying to make sure

everyone's shut of all their cell phones before the

session gets underway. To elicit the additional

information, whether they've got a cell phone or not,

just complicates things pointlessly; you don't want

a census of turned-off cell phones.

A large part of scientific and mathematical reasoning

consists of exerting prodigious efforts to reach an

end result that consists of making things appear as

simple as they really are, where to the untutored they

look more complicated. 1156825020:::John Dailey:::Phyrm_1@hotmail.com::::::~ "Some aspects [?] of reality simply don't involve causality." --- I totally agree. The most noteworthy examples are of arbitrary assertions...such as that one (supposedly summarizing an innuended conclusion from the following examples-slash-premises [not the most cogent way to argue, btw]):

~ Pythogoras' proofs weren't 'caused' by anyone or anything; they just, well, WERE (or ARE). *** R-i-g-h-t...we're talking 'proofs' here, non?

~ Multiplication tables weren't 'caused' by anyone or anything. *** R-i-g-h-t...they're exactly like mud puddles: they just naturally, well, 'ARE'. Same goes for Hamiltonian equations (with its Imaginary parts) and math functions for calculus as well as trig. Hell, ALL math tools just..well...'ARE'. --- Ever wonder what (or who) these tools' 'evolutionary' history involves? Non-causally, that is.

~ Am totally unclear as to the point of what the cell-phone scenario ("...conventions of modern logic..." nwst) has to do with anything heretofore discussed; the pointlessness of empirically searching for a null-set, maybe, or...what?

~ Am also unclear as to the point of discussing those who may be 'untutored'. One is searching for a 'tutor' on the subjects, mayhaps? Or one is finding problems with the 'conventions' as modernly tutored? Care to elaborate?

LLAP

J:D 1156881648:::Adrian Hester:::::::::John Dailey writes: "~ Pythogoras' proofs weren't 'caused' by anyone or anything; they just, well, WERE (or ARE). *** R-i-g-h-t...we're talking 'proofs' here, non?

~ Multiplication tables weren't 'caused' by anyone or anything. *** R-i-g-h-t...they're exactly like mud puddles: they just naturally, well, 'ARE'."

Seems to me you've thoroughly misunderstood Mike Hardy's comments. Where does causality enter in the actual proof of the Pythagorean theorem? Where does causality enter in saying 2*4=8? What part of a^2+b^2=c^2 is the cause and which part is the effect, and what part of 2*4=8 is the cause and which part the effect? 1156887786:::Freddy Ben-Zeev:::benzeev(at)comcast(dot)net::::::Adrian, the pythagorean theorem a^2+b^2=c^2 is true because of (or caused by) the nature (i.e. the identity) of a, b, and c as the sides of a right triangle. 1156889637:::John Dailey:::Phyrm_1@hotmail.com::::::ADRIAN:

~The 'proof' is the effect of the cause which is the 'prover' after the 'prover' discovered/identified the relationships which already existed. Maybe your question is about the nature of the relationships...and not really about the 'proofs'?

~ Given that the proofs (of really anything, for that matter) are here, doesn't the question "How did they get here?" really call for some answer beyond "Somehow; who cares?" ? Pythagoras' Proof has it's name for a reason, non? Consider: where (or who) did the 'proof' for E=mc2 get caused by? We do know that the proof did not always exist, don't we?

LLAP

J:D 1156896297:::Mike Hardy:::hardy@math.umn.edu::::::Freddy Ben-Zeev and John Dailey know how to miss the

point. If you observe that crime rates rise when ice

cream sales rise, you might erroneously infer that one

causes the other, although they're both caused by hot

weather. If you somehow become able to control the

weather and then observe that crime rates rise when

you make the weather hot, you might legitimately infer

that one caused the other.

But NOTA BENE: The cause of one argument is not the

subject matter of ones argument. Something does cause

a mathematician to write a proof. But causality is

not part of the subject matter of the proof. If you

prove something causes a high crime rate, then causality

IS part of the subject matter of the proof. Causality

is never part of the subject matter of a mathematical

proof. I challenge you to show me a counterexample

written by a mathematician. 1156900505:::Freddy Ben-Zeev:::benzeev(at)comcast(dot)net::::::John, my original point about causality was not in the sense that you are using, as "prover" causing "proof", but in the sense that what make the theorem or any statement true is the causal links between the facts or the entities that were abstracted into that theorem (see my comment #28 above). Also, as I mentioned in comment #20, I don't mean necessarily direct cause and effect, but SOME causal connection (cause and effect, effect and cause, two effects of a common cause, etc). 1157051631:::John Dailey:::Phyrm_1@hotmail.com::::::Mike and Adrian:

~ Ok. You've clarified as well as anyone could as to where I'm incorrect in what I said/argued/interpreted.

~ Unfortunately, I'm a bit too untutored to understand what all this has to do with, not 'the' point, but *my* point about where causality relates to (that WAS the question, wasn't it?) "proofs" caused/created by a prover vs. the subject of what proofs are proving. The latter subject is what 'the' point apparently is...as I already questioned re in my last post...which really has nothing to do with 'proofs' per se.

~ Generally, I see 'proofs' as paths which are found (or searched for) between an accepted starting point (or sets of them) and a final intended goal (Fermat's Theorem/4-color-Map-Prob or the latest contemporary prob:'proof'-by-computer="Proof"?) I see them to be like using a machete in a jungle searching for...'X.' Some find a path (not necessarily the only possible or even shortest one, but, at least one); some find that there isn't any from whatever starting point used; some find that it's not even possible because 'X' (some math 'conjectures' or physics concepts [like 'phlogiston'/'ether'], if you will) just doesn't exist to begin with. That's my view of 'proof's, whether math, philosophy or a detective's down-to-earth empirical whodunnit-prob.

~ Mike: you challenged me. I'd tackle it but for the fact that you've ignored all of *my* questions, hence...as with insults, one good ignore deserves another.

~ I can see that this discussion is going nowhere at this point (my being 'untutored' and all), hence, I'm dropping the subject. Y'all c'n have the last word.

LLAP

J:D 1157053512:::Mike Hardy:::hardy@math.umn.edu::::::John: Proofs are caused. But the content of proofs in

mathematics---the subject matter---the things that the

proofs are about---are objects that do not act over time,

so nothing _causes_ them to do anything. Numbers are

eternal, i.e. the exist outside of time. That 2 x 3 = 6

is not _caused_; it is not an _event_ happening in time.

What _causes_ humans to identify such facts and write

proofs and recognize them as logically valid proofs is

a far more complicated question.

Logic as used by mathematicians in writing and reading

mathematical proofs is essentially a way of judging

validity or invalidity of arguments.

(I'm not sure if that answers your questions or not.)