Any recommendations on a book?
Kostas
semi-learned and a few not understood.
I will have a second read which helps me keep more things in memory or
demystify others that I didnt quite grasp from the first read, but I would
like to read another good book on formal logic.
It must not be very abstract or difficult considering it is for a novice
(relatively speaking).
In Amazon, I noticed one from Donald Kalish "Formal aspects of reasoning"
accompanied by high ratings and nice reviews but the number of reviewers was
quite small so I guess the sample was not representative. Opinions vary
largely on other books and I am having difficulties in reaching a decision.
All of you in here look like you ve read at least a few books on the subject
so I am asking for some recommendations and also your opinion on the book I
mentioned if it exists in your library.
Thanks
--
Konstantinos
Paul Holbach
> news:<v50thpl...@corp.supernews.com>...
The following are very recommendable:
1) E.J. Lemmon, BEGINNING LOGIC, Van Nostrand Reinhold, 1965/repr.
1983.
(If you really want to learn the practice of natural deduction, read
this classical textbook!)
2) Samuel Guttenplan, THE LANGUAGES OF LOGIC - An Introduction to
Formal Logic, Blackwell, 2nd ed., 1997.
(Brilliant textbook, didactically optimal for beginners!)
3) Mark Sainsbury, LOGICAL FORMS - An Introduction to Philosophical
Logic, Blackwell, 2nd ed. 2001.
(Brilliant textbook covering a great deal of issues - one of the best
; also a very good introduction to the propositional&predicate
calculus!)
Best online tutorial on logic:
http://logic.philosophy.ox.ac.uk/
Regards
PH
Claudio Jolowicz
> like to read another good book on formal logic.
> It must not be very abstract or difficult considering it is for a novice
> (relatively speaking).
I'm still a novice myself, but I found this very helpful:
Graeme Forbes, Modern logic
Forbes covers sentential logic and first order predicate logic with
identity. He also gives some insights into free logic, modal logic,
intuitionistic logic and fuzzy logic. The book contains about 900
exercises. He uses a nice and intuitive system of natural deduction.
However, you won't find stuff like proofs of completeness or soundness
theorems and so on. It's quite basic. You might also want to try Shapiro's
article in the Stanford Encyclopedia of Philosophy, which is a bit more
advanced:
http://plato.stanford.edu/entries/logic-classical/
HTH.
G. Frege
You might try
E. J. Lemmon, Beginning Logic.
It's o n e of the best introductory texts ever written. This text will give
you the ability to master the technique of natural deduction like a champ.
Moreover, it's quite a cheap text, if you want to buy it.
F.
G. Frege
<claudio-...@gmx.net> wrote:
>
> Graeme Forbes, Modern logic
>
I like the first sentence of the preface of his book:
"I first taught logic in 1976 [...]. The text then in use was
E. J. Lemmon's Beginning Logic, and though I have subsequently
used a variety of books, Lemmon remains one of my two favorites." *)
Yeah...
F. :-)
*) The other one is Gustason and Ulrich's, Elementary Symbolic Logic. [?]
Anders Goeransson
wrote:
>On Mon, 17 Feb 2003 00:44:34 -0500, "Kostas" <noe...@noemail.net> wrote:
>
>You might try
>
> E. J. Lemmon, Beginning Logic.
>
>It's o n e of the best introductory texts ever written. This text will give
>you the ability to master the technique of natural deduction like a champ.
What's the use of that ability?
Claudio Jolowicz
"G. Frege" <in...@simple-line.de> wrote in message
news:9r625voni9u18dog5...@4ax.com...
> On Mon, 17 Feb 2003 18:03:52 +0100, "Claudio Jolowicz"
> <claudio-...@gmx.net> wrote:
>
> >
> > Graeme Forbes, Modern logic
> >
>
> I like the first sentence of the preface of his book:
>
> "I first taught logic in 1976 [...]. The text then in use was
> E. J. Lemmon's Beginning Logic, and though I have subsequently
> used a variety of books, Lemmon remains one of my two favorites." *)
>
>
> Yeah...
>
> F. :-)
>
Seems I won't get around reading this... !-)
BTW have you had a look on Dan's recommendation for an intro to
\-calculus? It seems to be the standard text, unless you're willing to
buy H.P.Barendregt, _The Lambda Calculus, Its Syntax and Semantics_.
Actually it's not really light reading. Citeseer also points you to
another paper of Barendregt's with a more historical perspective,
called _The impact of the lambda calculus in logic and computer
science_ (1997).
http://citeseer.nj.nec.com/barendregt97impact.html
I also found a 273 p. (!) paper called _Lectures on the Howard-Curry
isomorphism_, complete with intro to \-calculus. You get the zipped
postscript via ftp:
ftp://ftp.diku.dk/diku/semantics/papers/D-368.ps.gz
CJ.
G. Frege
<anders.g...@chello.se> wrote:
>
> What's the use of that ability?
>
MU
G. Frege
<claudio-...@gmx.net> wrote:
>
> BTW have you had a look on Dan's recommendation for an intro to
> \-calculus?
>
Yes. (A short look.)
>
> It seems to be the standard text, unless you're willing to
> buy H.P.Barendregt, _The Lambda Calculus, Its Syntax and Semantics_.
> Actually it's not really light reading. Citeseer also points you to
> another paper of Barendregt's with a more historical perspective,
> called _The impact of the lambda calculus in logic and computer
> science_ (1997).
>
Thanx for that hint.
Well, \-calculus will have to wait till I have more time. ;-)
F.
Anders Goeransson
wrote:
>On Mon, 17 Feb 2003 19:34:08 +0100, Anders Goeransson
Do you mean the greek letter my, usually used for a very small
quantity?
Kostas
I am glad that you replied cause I was lost.
Scanning amazon already for those books.
Thanks again!
--
Kostas
"Kostas" <noe...@noemail.net> wrote in message
news:v50thpl...@corp.supernews.com...
Karl Ove Hufthammer
news:8ie25v8u6q5o2k68q...@4ax.com:
>>> What's the use of that ability?
>>>
>> MU
>
> Do you mean the greek letter my, usually used for a very small
> quantity?
He probably means
<URL: http://info.astrian.net/jargon/terms/m/mu.html >.
--
Karl Ove Hufthammer
Kostas
but I slightly hesitate because 2 out of 2 reviewers on Amazon, -although
confirming the quality of the book- present it as a dense text not suitable
for beginners.
You sure its good for beginners?
--
Concépt®303
"G. Frege" <in...@simple-line.de> wrote in message
news:eg625vgddd6a48r0e...@4ax.com...
Anders Goeransson
No, that cannot be the case, at least not according to the explanation
given at the address above:
"mu /moo/ The correct answer to the classic trick question
"Have you stopped beating your wife yet?". "
But the question about the use of the ability to make deductions in
(some (extended) system of) natural deduction is just an ordinary
question.
G. Frege
>
> but I slightly hesitate because 2 out of 2 reviewers on Amazon, -although
> confirming the quality of the book- present it as a dense text not suitable
> for beginners.
>
Yes. I hesitated myself - to recommend this book. It's true: it's dense, in a
certain sense. You might try another book first. On the other hand, I really
don't know a better text.
I mean, if you can afford it, you might buy it for later use - in any case it
can't hurt to have (possess) it.
F.
Claudio Jolowicz
"Anders Goeransson" <anders.g...@chello.se> schrieb im Newsbeitrag
news:irq25voes0t5f3af6...@4ax.com...
You find some alternative translations on
http://www.geocities.com/rosacrux/mu_eng.html
(25 1/2 THINGS A ZEN MASTER MIGHT MEAN WHEN UTTERING THE WORD "MU" UPON
BEING ASKED BY A DISCIPLE WHETHER A DOG HAS BUDDHA NATURE, SOME OF WHICH ARE
LIKELY TO ELICIT ENLIGHTENMENT FROM THE QUESTIONER, SOME OF WHICH AREN'T)
How about 21.
Mu: "What a silly question. I should give you thirty whacks!"
HTH.
Torkel Franzen
> Anders Goeransson <anders.g...@chello.se> wrote in
>
> >>> What's the use of that ability?
> >>>
> >> MU
> >
> > Do you mean the greek letter my, usually used for a very small
> > quantity?
>
> He probably means
> <URL: http://info.astrian.net/jargon/terms/m/mu.html >.
Goeransson is just choosing to very kindly overlook this bit of
tediousness. But as regards his question, surely a proficiency in
the art of natural deduction is no more and no less significant
than a facility in doing crossword puzzles, or Scrabble, or
something of that sort. A harmless bit of fun for those so inclined.
gary thomson
"Sweet Reason", which is very readable.
"Kostas" <noe...@noemail.net> wrote in message news:<v52kno6...@corp.supernews.com>...
Moufang Loop
>
> Finishing my first book on logic, with many things learned, many
> semi-learned and a few not understood.
>
What was the first book?
I recommend Tarski "Introduction to Logic and to the Methodology of
Deductive Sciences" Oxford University Press as an introduction, and
Mendelson "Introduction to Mathematical Logic" International Thomson
Publishing next.
Then, if you're serious, Church, Kleene and Shoenfield; and the Davis
and Heijenoort source books.
Moufang Loop
Oh, thank you, thank you, thank you, Torkel!
When one starts doing logic it's nice to be able to _prove_ something
"for one's self" rather than just following the mechanics of truth trees
(note 1). But when one has done it a few times he needs to move on.
Note: truth trees are to logic what l'Hospital is to analysis. And, yes
I know that "mechanical" is the wrong word to use where 1st order logic
is concerned.
ML
Moufang Loop
>
> On Mon, 17 Feb 2003 00:44:34 -0500, "Kostas" <noe...@noemail.net> wrote:
>
> You might try
>
> E. J. Lemmon, Beginning Logic.
>
> It's o n e of the best introductory texts ever written. This text will give
> you the ability to master the technique of natural deduction like a champ.
A challenge for would-be champs: prove A v ~A, _not_ in the Lemmon
"linear" system, but in a Gentzen "tree" system. Rules supplied by
request.
ML
Moufang Loop
>
> On Mon, 17 Feb 2003 00:44:34 -0500, "Kostas" <noe...@noemail.net> wrote:
>
> You might try
>
> E. J. Lemmon, Beginning Logic.
>
> It's o n e of the best introductory texts ever written. This text will give
> you the ability to master the technique of natural deduction like a champ.
Which, the op should be warned, is not the same as learning logic, any
more than learning rules like (d/dx)(x^n) = n*x^(n-1) and applying them,
is learning calculus.
ML
Moufang Loop
When Frege wrote "MU" he meant "I don't know", but having previously
written "It's o n e of the best introductory texts ever written. This
text will give you the ability to master the technique of natural
deduction like a champ." he could hardly make such an admission, could
he?
Note that here I say nothing against Lemmon which is not a bad book.
ML
G. Frege
<Moufan...@btinternet.com> wrote:
>
> Which, the op should be warned, is not the same as learning logic, any
> more than learning rules like (d/dx)(x^n) = n*x^(n-1) and applying them,
> is learning calculus.
>
ML you are a braindead asshole, really.
F.
G. Frege
<Moufan...@btinternet.com> wrote:
>
> A challenge [...]: prove A v ~A, _not_ in the Lemmon
> "linear" system, but in a Gentzen "tree" system.
>
Proof:
A v ~A
Pleased? :-o
In case we do not have this "Grundformel" (which Gentzen suggested in his
Investigations into Logical Deduction) for a classical calculus, we might as
well use the rule
(~~E)
~~A
-----
A
to prove the theorem.
Leading to:
2
P
1 -------- vI
~(P v ~P) P v ~P
----------------------------------- ~E
_|_
-------- ~I 2
~P
1 -------- vI
~(P v ~P) P v ~P
---------------------- ~E
_|_
---------- ~I 2
~~(P v ~P)
---------- ~~E
P v ~P
We might compare this quite cumbersome notation with the elegant linear notation
adopted by Lemmon:
1 (1) ~(P v ~P) A
2 (2) P A
2 (3) P v ~P 2 vI
1,2 (4) f 1,3 ~E
1 (5) ~P 2,4 ~I
1 (6) P v ~P 5 vI
1 (7) f 1,6 ~E
(8) ~~(P v ~P) 1,7 ~I
(9) P v ~P 8 ~~E
// I used Gentzen's rules here instead Lemmon's original slightly (simplified)
// rules
Now what the heck should this silly "challenge" prove?
F.
G. Frege
> // I used Gentzen's rules here instead of Lemmon's original (slightly)
> // simplified rules
>
In fact, Lemmon would have written:
|- P v -P
1 (1) -(P v -P) A
2 (2) P A
2 (3) P v -P 2 vI
1,2 (4) (P v -P) & -(P v -P) 1,3 &I
1 (5) -P 2,4 RAA
1 (6) P v -P 5 vI
1 (7) (P v -P) & -(P v -P) 1,6 &I
(8) --(P v -P) 1,7 RAA
(9) P v -P 8 DN
Now it's quite interesting to read _Gentzen's own comments_ concerning his
tree-like formed proofs [at hoc "translation"]:
With demanding a tree-like formed configuration we deviate
a little bit from our analogy with actual deduction. Since
1. actual/real deduction necessarily is connected with a
linear sequence of propositions, as a result of the
linearity of our thinking, and 2. it's quite usual here
to re-use a already reached result, whereas the tree-like
form only allows for a single usage of derived formula.
Both deviations will serve a convenient formulation of
the notion of derivation, and are not essential.
(G. Gentzen, Investigations into Logical Deduction)
Hence Lemmon's usage if a "linear" (proof) system instead of a "tree-like"
(proof) system seems to be quite reasonable (- if not preferable).
In fact, Lemmon's system makes use of both features (1., 2.) mentioned by
Gentzen. See proof above.
F.
G. Frege
<Moufan...@btinternet.com> wrote:
>
> I recommend Tarski "Introduction to Logic and to the Methodology of
> Deductive Sciences" Oxford University Press as an introduction.
>
Actually I can second that!
John L. Kelley for example writes in his General Topology:
"A working knowledge of elementary logic is assumed, but acquaintance
with formal logic is not essential. However, an understanding of the
nature of a mathematical system (in the technical sense) helps to
clarify and motivate some of the discussion. Tarski's excellent
exposition*) describes such systems very lucidly and is particularly
recommended for general background."
*) A. Tarski, 'Introduction to Logic', 2nd Ed., New York, 1946.
Or Carl G. Hempel in his article "On the Nature of Mathematical Truth" -
footnotes (2) and (3):
(2) A precise account of the definition and the essential
characteristics of the identity relation may be found in
A. Tarski, Introduction to Logic, New York, 1941, ch. III.
(3) For a lucid and concise account of the axiomatic method,
see A. Tarski, loc. cit., ch. VI.
Still it's definitely a introductory book.
F.
G. Frege
>
> You might try
>
> E. J. Lemmon, Beginning Logic.
>
> It's o n e of the best introductory texts ever written. This text will give
> you the ability to master the technique of natural deduction like a champ.
>
"The best way to find out what logic is is to do some." (E. J. Lemmon)
F.
G. Frege
Typo:
>
> 2
> P
> 1 -------- vI
> ~(P v ~P) P v ~P
> ----------------------------------- ~E
> _|_
> -------- ~I 2
> ~P
> 1 -------- vI
> ~(P v ~P) P v ~P
> ---------------------- ~E
> _|_
> ---------- ~I 1 <--------
Chris Menzel
> Kostas wrote:
> >
> > Finishing my first book on logic, with many things learned, many
> > semi-learned and a few not understood.
>
> What was the first book?
>
> I recommend Tarski "Introduction to Logic and to the Methodology of
> Deductive Sciences" Oxford University Press as an introduction, and
> Mendelson "Introduction to Mathematical Logic" International Thomson
> Publishing next.
Enderton's A Mathematical Introduction to Logic, 2nd edition, should be
mentioned in this regard.
> Then, if you're serious, Church, Kleene and Shoenfield.
Though venerable texts all (I am still fond of Kleene) I think there are
many modern advanced texts that would make better choices for someone
learning the field.
Chris Menzel
G. Frege
>>
>> A challenge [...]: prove A v ~A, _not_ in the Lemmon
>> "linear" system, but in a Gentzen "tree" system.
>>
>
> 2
> P
> 1 -------- vI
> ~(P v ~P) P v ~P
> ----------------------------------- ~E
> _|_
> -------- ~I 2
> ~P
> 1 -------- vI
> ~(P v ~P) P v ~P
> ---------------------- ~E
> _|_
> ---------- ~I 1
> ~~(P v ~P)
> ---------- ~~E
> P v ~P
>
Of course we also might adopt Gentzen's _sequent calculus_ (LK) in tree-form:
A |- A
---------- ~IS
|- A, ~A
-------------- vIS
|- A, A v ~A
-------------- Transposition
|- A v ~A, A
------------------- vIS
|- A v ~A, A v ~A
------------------- Contraction
|- A v ~A
Actually a quite elegant approach, I have to admit.
F.
G. Frege
<Moufan...@btinternet.com> wrote:
>
> ...prove A v ~A, _not_ in the Lemmon "linear" system
>
Another variant (in the manner of a natural deduction system),
Gensler's system (lightly "streamlined" by G.F.):
|- P v ~P
* 1 | ~(P v ~P) A
2 | ~P 1 vS
3 | P 1 vS
4 P v ~P 1,2,3 RAA
Actually Gensler's system has some quite pleasing feature. :-)
F.
Moufang Loop
Oh yes, I'm sure there are! I simply betray my age :-) Don't old back
on making your own recommendation.
ML
>
> Chris Menzel
Moufang Loop
I do find your tone unpleasant sometimes. What this silly challenge
proves is just what you have demonstrated: the differnce in complexity
between tree-like and linear proofs. I wonder why, if it's so silly,
you rose to the challenge and posted three follow-ups to yourself.
ML
G. Frege
<Moufan...@btinternet.com> wrote:
>
> I do find your tone unpleasant sometimes.
>
Just deal with it. ;-)
>
> What this silly challenge proves is just what you have demonstrated:
> the difference in complexity between tree-like and linear proofs.
>
I see. On the other hand... As I have just "discovered" here, they might help to
make VISUAL the logical dependencies of the formulas employed in a proof.
Probably not the worst feature. [?]
>
> I wonder why, if it's so silly, you rose to the challenge and posted three
> follow-ups to yourself.
>
I like the topic. :-)
F.
Moufang Loop
Hee, hee, a Freudian slip I suppose, for "hold".
ML
Buridan
"Paul Holbach" <paulholba...@freenet.de> wrote :
> > Finishing my first book on logic, with many things learned, many
> > semi-learned and a few not understood.
> > I will have a second read which helps me keep more things in memory or
> > demystify others that I didnt quite grasp from the first read....
> > I am asking for some recommendations and also your opinion on the book I
> > mentioned if it exists in your library.
>
> The following are very recommendable:
> 1) E.J. Lemmon, BEGINNING LOGIC, Van Nostrand Reinhold, 1965/repr.
> 1983.
> (If you really want to learn the practice of natural deduction, read
> this classical textbook!)
>
This is now rather a dated work ( dated in terms of its examples,
method of presentation), and there are many more lively
works available. Of course Lemmon is a 'classic' text, and is very
rigourous.
> 2) Samuel Guttenplan, THE LANGUAGES OF LOGIC - An Introduction to
> Formal Logic, Blackwell, 2nd ed., 1997.
> (Brilliant textbook, didactically optimal for beginners!)
>
Agreed . This is an excellent modern text, and would be a much better
choice than Lemmon imo.
> 3) Mark Sainsbury, LOGICAL FORMS - An Introduction to Philosophical
> Logic, Blackwell, 2nd ed. 2001.
> (Brilliant textbook covering a great deal of issues - one of the best
> ; also a very good introduction to the propositional&predicate
> calculus!)
>
Good choice, but a better intoduction to philosophical logic would
be Grayling's Introduction to Philosophical Logic. ( Blackwell).
If you are trying to consolidate your knowledge of logic, a good
choice would be Copi's Symbolic Logic ( perhaps you should read this
alongside one of the philosophical logic books above).
You will need as newish editition which includes an intoruction to ZF.
The best introduction
to mathematical logic that I have seen, is Kelly's 'The Essence of
Logic' which is written for computer scientists rather than mathematicians.
Doesn't go into the subject as deeply as Enderton or Mendelsohn
however.
Jim Humphreys
Buridan
"G. Frege" wrote in message:
> >Graeme Forbes, Modern logic
> I like the first sentence of the preface of his book:
> "I first taught logic in 1976 [...]. The text then in use was
> E. J. Lemmon's Beginning Logic, and though I have subsequently
> used a variety of books, Lemmon remains one of my two favorites." *)
>
It offers a thorough treatment, but it is debateable whether
dependencies ( which appear to the left of Lemmon's
deductions) are really necessary- many more modern
texts eschew these, as they tend to slow the beginner
down, making it harder for him to get to grips with
the nuts and bolts of logic. I would not recommend
Lemmon, although I can understand that as it was
a first text for many, it may hold a special place
in their affections. ( my first logic text was Hodge's 'Logic'
which is superb).
Does anyone have any views on the merits/demerits of Langer's
introductory 'Symbolic Logic' btw, which is even older than
Lemmon?
Jim Humphreys
Buridan
"Moufang Loop" wrote:
Kostas wrote:
> > Finishing my first book on logic, with many things learned, many
> > semi-learned and a few not understood.
> >
> What was the first book?
>
> I recommend Tarski "Introduction to Logic and to the Methodology of
> Deductive Sciences" Oxford University Press as an introduction, and
> Mendelson "Introduction to Mathematical Logic" International Thomson
> Publishing next.
>
Both rather demanding works, surely, for the beginner ( and someone
who us seeking to consolidate understanding obtained from
an introductory work as Kostos is), particularly if he
has not studied mathematics to undergraduate level ( Kostos
does not say what his mathematical background is)
A better introduction might
be Boolos, Burgess and Jeffrey 'Computability and
Logic'.
Jim Humphreys
Buridan
"Kostas" <noe...@noemail.net> wrote:
> I found the book, [ E. J. Lemmon, Beginning Logic.]
>looks like the way to go from what you guys say,
> but I slightly hesitate because 2 out of 2 reviewers on Amazon, -although
> confirming the quality of the book- present it as a dense text not
suitable
> for beginners.
>
It is for beginners ( as the title implies), and its
rigo(u)rous, but there are
more recent texts which make the process of learning
logic easier and more enjoyable imo. Lemmon is
a 'classic' ( publihed in the sixties), but is rather dated
in terms of its pedagogy.In particular Lemmon's insistence on writing
dependencies slows the beginner down. The Guttenplan
book, which someone mantioned earlier is much better
( although it , too, employs dependencies). To get up
and running quickly get Scaum's Logic Guide- it will have
you doing proofs far more quickly than Lemmon.
Or try Hodge's 'Logic'.
Jim Humphreys
Moufang Loop
>
> "Moufang Loop" wrote:
> Kostas wrote:
>
> > > Finishing my first book on logic, with many things learned, many
> > > semi-learned and a few not understood.
> > >
> > What was the first book?
> >
> > I recommend Tarski "Introduction to Logic and to the Methodology of
> > Deductive Sciences" Oxford University Press as an introduction, and
> > Mendelson "Introduction to Mathematical Logic" International Thomson
> > Publishing next.
> >
> Both rather demanding works, surely, for the beginner ( and someone
Both? I must disagree with you that Tarski is rather demanding. The
suggestion may have been poor for someone seeking a second book (not
even sure about that, it epends what the first book was, the op didn't
tell us!), but as a first book my recommendation stands.
You may be right about Mendelson. My edition (_not_ the International
Thomson Publishing edition, I was simply referring to the currently
in-print work in case the op wanted to buy it) is not attractively laid
out, the text is too dense on the page for my liking.
> who us seeking to consolidate understanding obtained from
> an introductory work as Kostos is), particularly if he
> has not studied mathematics to undergraduate level ( Kostos
> does not say what his mathematical background is)
> A better introduction might
> be Boolos, Burgess and Jeffrey 'Computability and
> Logic'.
I have Boolos and Jeffrey "Computability and Logic" if yours is a latter
edition of this then I agree, it's a first-class book.
ML
>
> Jim Humphreys
G. Frege
<j...@nospamma.humph65.fsworld.co.uk> wrote:
>
> In particular Lemmon's insistence on writing
> dependencies slows the beginner down.
>
This may be true. But ACTUALLY quoting the dependencies at the left is one of
the main (and distinctive) features of Lemmon's system!
Hence it has been retained in modern approaches to Lemmon's system. See Allan
Hand's "Logic Primer", for example: http://logic.tamu.edu/Primer/
They write:
"We prefer systems of natural deduction to other ways of representing
arguments, and we have adopted Lemmon's technique of explicitly tracking
assumptions on each line of a proof. We find that this technique
illuminates the relation between conclusions and premises better than
other devices for managing assumptions. Besides that, it allows for
shorter, more elegant proofs."
F.
G. Frege
<j...@nospamma.humph65.fsworld.co.uk> wrote:
>
> It offers a thorough treatment [...]
>
Agree. :-)
>
> but it is debateable whether dependencies (...) are
> really necessary [...]
>
Well..., ACTUALLY quoting the dependencies is one of the main (and distinctive)
features of Lemmon's system!
Hence it has been retained in modern approaches to _Lemmon's_ system. See Allan
Hand's "Logic Primer", for example: http://logic.tamu.edu/Primer/
They write:
"We prefer systems of natural deduction to other ways of representing
arguments, and we have adopted Lemmon's technique of explicitly tracking
assumptions on each line of a proof. We find that this technique
illuminates the relation between conclusions and premises better than
other devices for managing assumptions. Besides that, it allows for
shorter, more elegant proofs."
Completely agree with them.
>
> many more modern texts eschew these, as they tend to
> slow the beginner down, making it harder for him to
> get to grips with the nuts and bolts of logic.
>
Imho, this "simplification" is not really a plus point but rather a weakness of
this "more modern texts".
Actually the assumption lists Lemmon presents as part of his approach proves
quite useful in more modern branches of logic. See the part "Proof Theory" at
http://plato.stanford.edu/entries/logic-relevance/
>
> I would not recommend Lemmon...
>
Actually, I (too would) hesitate to recommend it as a _very first_ book. But
imho one should have read it [especially if concerned with the _teaching_ of
logic]. (There's a nice treatment of the completeness proof for PC in it.)
F.
G. Frege
<j...@nospamma.humph65.fsworld.co.uk> wrote:
> >
> > 1) E.J. Lemmon, BEGINNING LOGIC, Van Nostrand Reinhold, 1965/repr.
> > 1983.
> >
> This is now rather a dated work (...)
>
Sure. On the other hand...
> of course Lemmon is a 'classic' text, and is very
> rigourous.
>
And THAT would be the reason (for me) still to use it as a textbook (say in a
course of logic, etc).
>
> If you are trying to consolidate your knowledge of logic, a good
> choice would be Copi's Symbolic Logic.
>
Well... I know the version of 1954 - it's actually a quite rigorous approach
too, yes. And one can learn A LOT from it (-things you won't find in Lemmon's
book), that's certainly true! [In fact I wouldn't compare this two books
directly: Copy is more "general" and Lemmon very "special". Both text's might
prove useful.]
F.
Buridan
"G. Frege" <g.f...@simple-line.de> wrote:
"Buridan" wrote:
> > > 1) E.J. Lemmon, BEGINNING LOGIC, Van
> > > Nostrand Reinhold, 1965/repr.
> > > 1983.
> > >
> > This is now rather a dated work (...)
> >
> Sure. On the other hand...
>
> > of course Lemmon is a 'classic' text, and is very
> > rigourous.
> >
> And THAT would be the reason (for me) still to use
> it as a textbook (say in a course of logic, etc).
>
Absolutely. I assumed that Kostos was studying at home,
and would like something which a) is stimulating b) will get
him "up and running" ie doing proofs asap. Lemmon
would not seem to be the best text available to meet
these requirements. Of course it has many merits as
a text.
> >
> > If you are trying to consolidate your knowledge of logic, a good
> > choice would be Copi's Symbolic Logic.
> >
> Well... I know the version of 1954 - it's actually a quite rigorous
approach
> too, yes. And one can learn A LOT from it (-things you won't find in
Lemmon's
> book), that's certainly true! [In fact I wouldn't compare this two books
> directly: Copy is more "general" and Lemmon very "special". Both text's
might
> prove useful.]
>
Yes. Perhaps Kostos could specify in more detail why he is studying
logic eg as part of a course etc..
I would incidently be interested to hear you view of Langer's Symbolic
Logic if you are familiar with it.
Jim Humphreys
Buridan
"G. Frege" <g.f...@simple-line.de> wrote in message
news:drd16v4g13u6i2hf1...@4ax.com...
> On Sat, 1 Mar 2003 10:20:15 -0000, "Buridan"
> <j...@nospamma.humph65.fsworld.co.uk> wrote:
>
> >
> > It offers a thorough treatment [...]
> >
> Agree. :-)
>
> >
> > but it is debateable whether dependencies (...) are
> > really necessary [...]
> >
>
> Well..., ACTUALLY quoting the dependencies is one of the main (and
distinctive)
> features of Lemmon's system!
> Hence it has been retained in modern approaches to _Lemmon's_ system. See
Allan
> Hand's "Logic Primer", for example: http://logic.tamu.edu/Primer/
> They write:
> "We prefer systems of natural deduction to other ways of representing
> arguments, and we have adopted Lemmon's technique of explicitly
tracking
> assumptions on each line of a proof. We find that this technique
> illuminates the relation between conclusions and premises better than
> other devices for managing assumptions. Besides that, it allows for
> shorter, more elegant proofs."
> Completely agree with them.
>
influential,
and many instructors favour his approach. However, some do not, on the
grounds that it takes the beginner longer to actually start doing proofs.
Schaum's Logic does quote dependencies for example.
> > many more modern texts eschew these, as they tend to
> > slow the beginner down, making it harder for him to
> > get to grips with the nuts and bolts of logic.
> >
> Imho, this "simplification" is not really a plus point but rather a
weakness of
> this "more modern texts".
>
Debateable. Of course some texts ( Jeffrey or Hodges) start the beginner
with the tableau method, an approach which also has some merits
> Actually the assumption lists Lemmon presents as part of his approach
proves
> quite useful in more modern branches of logic. See the part "Proof Theory"
at
> http://plato.stanford.edu/entries/logic-relevance/
>
> >
> > I would not recommend Lemmon...
> >
> Actually, I (too would) hesitate to recommend it as a _very first_ book.
But
> imho one should have read it [especially if concerned with the _teaching_
of
> logic]. (There's a nice treatment of the completeness proof for PC in it.)
>
I agree here.
Jim Humphreys
Buridan
"Buridan" <j...@nospamma.humph65.fsworld.co.uk> wrote in message news:...
Jim H
G. Frege
<j...@nospamma.humph65.fsworld.co.uk> wrote:
>
> I would incidently be interested to hear your view of Langer's Symbolic
> Logic if you are familiar with it.
>
I'm sorry, I don't know the book. But you make me courous. :-)
F.
G. Frege
<j...@nospamma.humph65.fsworld.co.uk> wrote:
> >
> > Yes, you are quite right about this- Lemmon's text has been very
> > influential, and many instructors favour his approach. However,
> > some do not, on the grounds that it takes the beginner longer
> > to actually start doing proofs.
> >
Hmmm... I'm not really sure concerning this question. But [besides that] imho
speed is not everything. :-)
>
> Schaum's Logic does not quote dependencies for example.
>
Well, probably a good reason NOT to recommend that book... ;-) // Actually no
one mentioned it so far. [Why not?]
> >
> > Imho, this "simplification" is not really a plus point but rather a
> > weakness of [some of] this "more modern texts".
> >
> Debateable.
>
Sure. In fact, it's _worth_ to be discussed, imho.
>
> Of course some texts (Jeffrey or Hodges) start the beginner
> with the tableau method, an approach which also has some merits
>
Yes. (Though I don't know the book of J&H).
F.
Moufang Loop
Is that Susan K Langer? If so, I was about to remark that the book is
rather old. But that might be construed as an un-gallant remark about a
lady's age!
ML
Moufang Loop
Two books surely? Both use truth trees = one sided Beth tableaux (due
to Smullyan?).
ML
>
> F.
G. Frege
<Moufan...@btinternet.com> wrote:
>
> Is that Susan K Langer?
>
Sure... :-)
>
> If so, I was about to remark that the book is rather old.
>
So what?
Ok... the first edition of Langer's book "Introduction in Symbolic Logic" was
published in 1937, hence it's actually "rather old". :-)
On the other hand, I REALLY can't understand all that talking about "old books".
(...)
I recently read good old Frege's "Begriffsschrift" from 1879 with great
pleasure. It's still a quite nice approach. (Though I would not really recommend
it for a beginner these days. :-)
F.
Susanne Katherina Knauth Langer
(1895-1985)
This outstanding twentieth century philosopher was born on December 20, 1895 in
New York City, New York, U.S.A. In 1920, she graduated from Radcliffe College in
Cambridge, Massachussets, and married a historian, William L. Langer in 1921.
She went with her husband to study at the University of Vienna and then came
back to Radcliffe to get her M.A. in 1924 and a Ph.D. in philosophy in 1926.
Following this she taught at Radcliffe, Wellesley and Smith Colleges. Despite
her excellent qualifications and recommendations from outstanding philosophers,
her titles were always limited to "lecturer" or "assistant" or "visiting"
professor. During this time she gave birth to two children. After her divorce in
1942, she left the Boston area and held temporary positions in many co-ed
institutions. In 1943, she taught philosophy at the University of Delaware and
from 1945 to 1950 she lectured at Columbia University. From 1954 she taught at
Connecticut College until her retirement in 1962.
She became recognized after publication of several books on linguistic analysis
and aesthetics: The Practice of Philosophy (1930), An Introduction to Symbolic
Logic (1937) and especially Philosophy in a New Key (1942), which was reissued
several times due to high demand. In 1953 she published Feeling and Form,
followed by Problems of Art (1957), Philosophical Sketches (1962), and three
volumes of Mind: An Essay on Human Feeling (1967-1982)(Vol 1)(Vol. 2)(Vol. 3).
She primarily dealt with various forms of artistic communication and symbolism
and was able to express very complex ideas in terms understood by people in
other fields.
In 1960, she was elected to the Academy of Arts and Sciences. Susanne Katherina
Knauth Langer died on July 17, 1985 in Old Lyme, Connecticut.
Moufang Loop
>
> On Sun, 2 Mar 2003 14:38:36 +0000 (UTC), Moufang Loop
> <Moufan...@btinternet.com> wrote:
>
> >
> > Is that Susan K Langer?
> >
> Sure... :-)
>
> >
> > If so, I was about to remark that the book is rather old.
> >
> So what?
>
> Ok... the first edition of Langer's book "Introduction in Symbolic Logic" was
> published in 1937, hence it's actually "rather old". :-)
>
> On the other hand, I REALLY can't understand all that talking about "old books".
"Is that Susan K Langer? If so, I was about to remark that the book is
rather old. But that might be construed as an un-gallant remark about a
lady's age!"
As I wrote, I was _about_ to remark that the book is rather old; but I
didn't. You'll be familar with the use/mention distinction :-)
ML
G. Frege
<Moufan...@btinternet.com> wrote:
> > >
> > > If so, I was about to remark that the book is rather old.
> > >
> > So what?
> >
> > Ok... the first edition of Langer's book "Introduction in Symbolic Logic" was
> > published in 1937, hence it's actually "rather old". :-)
> >
> > On the other hand, I REALLY can't understand all that talking about "old books".
> >
>
> "...I was about to remark that the book is rather old [...]"
>
> As I wrote, I was _about_ to remark that the book is rather old; but I
> didn't. You'll be familiar with the use/mention distinction :-)
>
Ehrr... I DIDN'T say/express (not even suggest) that _you_ complained about the
age of Langer's book, did I? :-)
On the other hand, one MIGHT conclude that from the fact that you were "about to
remark that the book is rather old" thoughts of that nature are not completely
alien to you..., no?
Anyway, it didn't mean YOU here when stating: "I REALLY can't understand all
that talking about 'old books'" - this was a _general_ remark. :-)
F.
The remarks at Amazon are quite interesting:
"This is the book that introduced me to logic. It enthused me so much that I
became a professional logician, a career that I have pursued for 35 years.
Langer points out that, once one becomes acquainted with modern symbolic logic,
one can go on to do groundbreaking research. This is true."
"A truly wonderful introduction to symbolic logic. One of the best. // It covers
boolean algebra, propositional calculus, and Russell and Whitehead's logistic.
// A charming and delightful book."
Moufang Loop
>
> On Sun, 2 Mar 2003 18:17:49 +0000 (UTC), Moufang Loop
> <Moufan...@btinternet.com> wrote:
>
> > > >
> > > > If so, I was about to remark that the book is rather old.
> > > >
> > > So what?
> > >
> > > Ok... the first edition of Langer's book "Introduction in Symbolic Logic" was
> > > published in 1937, hence it's actually "rather old". :-)
> > >
> > > On the other hand, I REALLY can't understand all that talking about "old books".
> > >
> >
> > "...I was about to remark that the book is rather old [...]"
> >
> > As I wrote, I was _about_ to remark that the book is rather old; but I
> > didn't. You'll be familiar with the use/mention distinction :-)
> >
> Ehrr... I DIDN'T say/express (not even suggest) that _you_ complained about the
> age of Langer's book, did I? :-)
>
> On the other hand, one MIGHT conclude that from the fact that you were "about to
> remark that the book is rather old" thoughts of that nature are not completely
> alien to you..., no?
Being a gentleman I held back for fear of offending a lady, not
realizing that said lady was beyond being offended and had been for some
years.
ML
Chris Menzel
> This may be true. But ACTUALLY quoting the dependencies at the left is
> one of the main (and distinctive) features of Lemmon's system!
>
> Hence it has been retained in modern approaches to Lemmon's system.
> See Allan Hand's "Logic Primer", for example:
> http://logic.tamu.edu/Primer/
That would be (Colin) Allen and (Michael) Hand, two of my fine
colleagues. Allen and I have been working on more intelligent support
for the web-based proof checker based on information gleaned from logs
of actual student performance; I'd welcome comments and suggestions from
sci.logic denizens interested in logic pedagogy:
http://logic.tamu.edu/daemon.html.
> They write:
>
> "We prefer systems of natural deduction to other ways of
> representing arguments, and we have adopted Lemmon's technique of
> explicitly tracking assumptions on each line of a proof. We find
> that this technique illuminates the relation between conclusions
> and premises better than other devices for managing assumptions.
> Besides that, it allows for shorter, more elegant proofs."
Perhaps, but experience has led me to the view that students on the
whole find Fitch-style systems with subproofs easier to master. That
said, I prefer Allen and Hand for honors courses, as it is a very
rigorous and elegant system with minimal commentary. This tends to
lead to fruitful interaction with bright students in small classes.
Chris Menzel
G. Frege
> >
> > [...] ACTUALLY quoting the dependencies at the left is
> > one of the main (and distinctive) features of Lemmon's system!
> >
> > Hence it has been retained in modern approaches to Lemmon's system.
> > See Allan _&_ Hand's "Logic Primer", for example.
> >
Sorry, I forgot the ampersand. :-/
>
> That would be (Colin) Allen and (Michael) Hand, two of my fine
> colleagues. Allen and I have been working on more intelligent support
> for the web-based proof checker based on information gleaned from logs
> of actual student performance; I'd welcome comments and suggestions from
> sci.logic denizens interested in logic pedagogy:
> http://logic.tamu.edu/daemon.html.
>
Actually, I am quite impressed by your Logic Deamon - it's a fine piece of
(educational) software!
> >
> > "We prefer systems of natural deduction to other ways of
> > representing arguments, and we have adopted Lemmon's technique of
> > explicitly tracking assumptions on each line of a proof. We find
> > that this technique illuminates the relation between conclusions
> > and premises better than other devices for managing assumptions.
> > Besides that, it allows for shorter, more elegant proofs."
> >
> Perhaps, but experience has led me to the view that students on the
> whole find Fitch-style systems with subproofs easier to master.
>
I see. In fact, Fitch-style seems actually quite natural. And it's surely a very
"handy" tool.
"Lemmon style" is probably more appropriate for more "mathematical oriented"
minds, I would guess.
>
> That said, I prefer Allen and Hand for honors courses, as it is a very
> rigorous and elegant system with minimal commentary. This tends to
> lead to fruitful interaction with bright students in small classes.
>
I'm n o t surprised. ;-)
F.