Why Carroll's logic is often so confusing

[ermete22]

Carroll’s logic, the advanced one in particular, is hard to read (I refer to “The symbolic logic by Lewis Carroll” by W. W. Bartley,III in 1977). Often you are lost as you can hardly follow Carroll due to its language. Why?
One of the fundamental reasons is for sure the fact that Carroll often touch problems which are at the limits of logic, as, for example the sentences stating the laws of logical inference. To properly make clear his points, Carroll would have needed a meta-language, that is a language which could contain logical sentences between “ “. It looks funny but it is like that. When you can put a logical sentence between “ “ you can obtain strange things, as you refer to the sentence as a pure string of symbols. The famous (“The snow is white “ only if the snow is white), by Tarski is one of the possible tricks. It is evident that if you have a meta-language you can reason ABOUT your logical system, while, not having it, you are CLOSED INSIDE the logical language you use, you cannot talk about it. At Carroll’s times meta-language concept had still to come in definite form, so Carroll, willing to discuss truth and its definition, was closed inside the language: he made terrible efforts to express his intuitions (The Achille and Tortoise dialogue) and he almost reached the point while remaining inside the logical system, by inserting an additional general law of inference as a internal language sentence. He could go no more ahead. The major critics of Carroll about his B.S. argument were Ryle and Toulmin, who were actually wrong by choosing to forbid in logic statement about the logical inference itself.
If the absence of a clearly conceived concept of meta- language makes some times Carroll hard to understand, it is evident that he was grasping some real need of it for real advances in logics; but what seems more important, contributed to create the most fascinating situations in Alice's Books and in Sylvie and Bruno. as you can feel the problem he talks about in his amusing funny style. A man who correctly understood the existence of problems like "how can I justify the validity of inference in logics?" and the need of semantic to talk about truth was for sure a relevant actor of the logic studies of his epoch. He missed to identify the need of a logic with a meta-language as many others. Also Boole would have solved many of his deepest conceptual problems if he had introduced a meta- language.
Carlo

[johntufail]

(One day a child of six will teach me how to use a computer. This my second attempt to reply to you Carlo - the first (unfinished and raw) is now floating in hyperspace.).

There is so much in your presentation that I'm not quite sure how to begin. Much of it is technical such as your mention of the laws of logical inference. This in itself is a huge minefield as, it raises issues between Aristotolean and Platonic philosophical and mathematical descriptions of reality that would take a compendium of books for any observer to comprehend.

I think your key phrase is 'Can I justify the validity of inference in logics?' And of course it all comes down to semantics.

Although Carroll was, of course interested in developing ways of eliminating fallacies in all foms of formal language, His main problem was always about how to bridge the gap between formal and'informal' (existential) truths.

I suspect that Carroll was intuitively aware of the need for metalanguages but also suspected that that there could never be such a thing as a 'pure' metalanguage - a metalanguage that is wholly external to the subject language.

It is quite clear that Carroll's passions were about what is language, how does it work and how can we command it to discover 'Truth'. And by Truth I believe he meant material, existential and spiritual truths. Just as Einstein searched all his life for a unifying theory of the physical universe, Carroll searched all his life for a unifying theory of the spiritual universe.




`

[ami]

Hi,
Thank you Carlo and John for your interesting posts. I am sorry to disagree once again. I find most of Carroll's logic work more technical and rarely philosophically profound. Let us take the example of the Achilles and Tortoise problem about the justification of inference, as you rightly wrote. Yes, this is a profound text, and it is now a classical text in philosophy which has been widely reprinted and commented by all the twentieth century most famous logicians and philosophers (Peirce, Russell, Ryle, Quine, etc). I agree with what you wrote about this text, but please keep in mind that this text is not representative at all of Carroll's logical work.
Most of Carroll's work is an invention of symbolic methods to find the solution which follow from a set of premises. That's almost what have done all the symbolists logicians of the time (Boole, Jevons, Venn, etc). This problem is known as the "Elimination problem". Almost all the content of Carroll's Symbolic Logic deals with this problem.
Contrary to Carlo, I found that Carroll's logic textbooks are not difficult to read at all. There might be difficult for an Alice reader of course, but in comparison to other nineteenth century logic works, it is not difficult at all. Carroll avoided all metaphysical questions, probably in order to make the book easy to read. Astonishingly, there is not even a definition of the word "logic' in his books! And of course, Carroll worked only on deductive logic while all other authors treated inductive logic and the logic of chances.
Carroll's two texts in Mind (The Barber shop problem in 1894, and the Achilles and the Tortoise problem in 1895) are very different from all his logic books. Russell wrote once that except for these two texts, almost all Carroll's work in logic was not important.
Let me now give a provocative hypothesis: What if it was not Carroll who wrote these two texts!!
Of course, he surely wrote the definitive version with his literary style, but maybe the original problem is not his own invention. We know that the two texts were the result of his dispute with John Cook Wilson, the very influential professor of logic in Oxford. We also already know that The Barber shop's original version is due to Wilson not to Carroll. Carroll himself wrote in his diaries (31 Mar. 94):
"Have just got printed, as a leaflet, A Disputed Point in Logic, the point Prof. Wilson and I have been arguing so long. This paper is wholly in his own words, and puts the point very clearly. I think of submitting it to all my logical friends."
What about The Achilles and the Tortoise problem? I have no definitive opinion. I know that the same argument with the same example in Euclidean Geometry appears in Wilson's notes which were published posthumously as "Statement and Inference" in 1926 (see page 444). Wilson made no reference to Carroll's paper. The problem is that we don't know exactly when did Wilson write that part of his work: before or after Carroll's version? According to the editor, Wilson's text is based on his logic lectures which he delivered since the 1880s. But Wilson changed his text often, and the final version is dated 1914.
All I wanted to say is that Carroll's two "philosophical" texts in logic for the journal Mind are not representative of all his work, and thus should be used with caution. All the other more technical but less profound (big) part of his work should not be neglected.

[ermete22]

Hi Ami,
first when I wrote that Carroll’s work are hard to read, I referred to a professional readers, who find themselves in front of a strange exotic language which is very far from the usual one. Often I had to write on a piece of paper some equivalence list between Carroll’s term and standard logical concepts, and that’s apart his strange reasoning about existence.
I would like to attempt some synthesis (which may be wrong) between our different point of view. The mass of correct data you cite must mean something after all and cannot be ignored when one tries to build up some non mythical vision of Carroll. On the other hand in some of its works something sees to emerge about certain intuitions about of the limits of logics and impress you. I do not know if some of these works were not an original invention by Carroll; I suppose they were in some sense, but I am aware that myths can play strange games. I do not agree with Bartley III enthusiasm about Carroll’s logic: you are right: most of the logical works by Carroll are rather irrelevant. The reason I believe is that Carroll had a quite split personality in logic: one side he had a excellent riddle making capability which he manifested in puzzles, games, etc. On the other hand, he was obsessed by the concept of truth since always; this aspiration attracted him towards the limits of the logics, its fundamental principles. He was not interested in what one can call the middle everyday work of a professional logician; so, in some sense, he faced the fundamental problems with the same tools which worked in riddle making.
This scarce interest for what I called middle logics is most probably the reason why many critics (Quine in particular, but you as well) classified Carroll as a second – rate logician. He had an extreme powerful capability in riddle-making and a deep feeling for the obscure concept of truth, this independently on how good a logician he was. In other words he was an extremely clever person with many important existential doubts about external reality and the nature of truth. It is also true that to work out some serious advances in logics, the everyday technical work is an essential part of the successful recipe; you cannot to demonstrate Godel’s theorems without continuous effort as, in logic, intuition is essential but not sufficient.
This state of affairs justify your judgements. At the same time however the intuitions that Carroll expresses in his books, more clearly in Sylvie and Bruno, shows, after me at least, that Carroll had understood the profound limits of logic respect to what was originally expected from it: it is nothing more than a computation, o formal system or if you prefer an algorithm, which cannot explain anything of human experience; after all Penrose suggested correctly that to explain consciousness you need a non-algorithmic physics and that Boole’s dream was good for computers but not for humans. As we cannot pretend that Carroll was a good academic logician (your point), we cannot also pretend he had not the intuitions he had and clearly expressed in his books possibly making use of his strange metaphoric language.
This is just an attempt of a beginning of a synthesis, probably wrong, in which however I am deeply interested.
Carlo

[ami]

Dear Carlo,
We agree on much more than you might expect and your synthesis is not that wrong.
Our misunderstanding is due to the fact that you always talk about Carroll, the person, while I am always talking about his work (as it appears in his published texts). The reason is probably that I am not acquainted enough with Carroll's personality and his non-logical works. Thus, I cannot say about Carroll the logician more than what I find in his logical works. Of course, my view is limited but that's all I can guarantee.
What I said is that his book "Symbolic Logic" do not treat deep philosophical issues but is more technical. That doesn't mean that Carroll was not aware of those philosophical difficulties (about existence, judgment, inference, etc). As you said, his literary works show that he was aware of these. My explanation is simply that he avoided all philosophical issues to make his book accessible to a wide audience.
I didn't said that Carroll was not a good logician. As you know, nineteenth century logic swings between philosophy and mathematics (or at least symbolic approaches). Carroll choose the symbolic approach and avoided (or at least postponed) philosophical ones. This is why his (published) work is an important contribution to Symbolic Logic (or the so-called Algebra of Logic), but an almost unimportant one to philosophical logic (except of course the Mind papers).
It's nice to read you.

[johntufail]

Hi Carlo and Ami,

I was about to write a reply to Ami's mail that was so close to Carlos's that I have been saved the trouble, thank goodness!

However, I think that I have to re-affirm Carlos's point that the only way one can learn from Carroll's insights is to take an holistic approach to his works and his methods.

There is nothing schizophrenic about Carroll. He merely does what any successful communicator does. He tailors his delivery to suit the audience he is attempting to addess. Thus, as you rightly point out Ami, he does not address deep metaphysical, epistemological or ontolgical issues in either symbolic logic or Game of Logic. Mind you, the approach he takes is very symbolic in itself. Much of Symbolic Logic has to do with semantics and the relationship between Formal and Informal language processes.

Mind you, even in technical mattes I am informed by logicians far more adept than I that his critique of Venn and his alternative reveals a high level of technical competence.

There is also of course the damnably elusive fact hat Lewis Carroll will not lay down. If we compartmentalise Carroll (as many have done) we can make statements such as 'he was a good but not original mathematician'; 'he was a competent logician but not in the first class';
'He was a writer of children's literature so really has no place in the adult literary cannon'.

Isn't it intereting that, when you compartmentalise carroll like this, he appears to be a jack of all trades, master of none! But the reality is that he ranks along Shakespeare as one of the most influential Literary minds (no small feat) and goes far beyond Shakespeare by reaching into areas of conceptuality in various areas of maths that Shakespeare couldn't even come close to.

And, on top of this, or perhaps underpinning it, he remains one of the most important writers on relativity and contiguity in morality and justice - yet he never wrote a single formal paper on these issues!

So, Whwre do we go from here?




The question is. How do we take this very interesting discussion forward in a way that is both rewarding to the participants and accessible and stimulating to any others who would like to cointribute to this learning process.

[otherprofessor]

Might I suggest (if I dare as a very new newcomer) that posting individual logical problems of Carroll's and taking us through them, showing his reasoning , might be very interesting?

Perhaps a new thread for every new 'knot' just to aid clarity?

[mahendra]

I would like to second that, it would be very useful. Also, if possible, if the problems could be briefly put into context, for example, how do they relate to the thinking of his era, both mathematical & philosophical, etc.

[johntufail]

Hmm, Interesting.

I hope that Carlo and Ami (and others) will give their own responses to this. My feeling is that, as stated, the suggestion will reveal little more than has already been covered. However there is much merit in explaining why certain logical propositions (or interpretations of the limits of logic) of Carroll have caused controversy. This has been complicated by Ami's proposition regarding regarding the Wilson Carroll debate. It is a valid and important point point however.

My reservations are around the way the question is put. It appears to restrict the debate to Carroll's formal writings on logic.

My own feeling is that you cannot separate Lewis Carroll from Charles Dodgson. Everything I have read about Charles Dodgson, everything I Have learned, is that the alto ego of Lewis Carroll enabled him to break free of the formal religious and academic boundaries within which he was enclosed.

Thus, although Charles Dodgson's mathematical and logical papers are certainly not without merit, Unless one can see these within the context of his arguments and challenges under the cloak of 'Lewis Carroll' we cannot really progress. The majority of Charles Dodgson's most challenging and profound ideas in logical and philosophical terms are embedded in his 'fictional works'.

So. In answer to the suggestion. I suggest that the idea be expanded to incluse key elelments of Carroll's fictional works that will more than answer the question of how Carroll's QUESTIONS and ideas related to his social, poliical , intelectual and spiritual environment.

Shrug!
JT

[johntufail]

Hmm, Interesting.

I hope that Carlo and Ami (and others) will give their own responses to this. My feeling is that, as stated, the suggestion will reveal little more than has already been covered. However there is much merit in explaining why certain logical propositions (or interpretations of the limits of logic) of Carroll have caused controversy. This has been complicated by Ami's proposition regarding regarding the Wilson Carroll debate. It is a valid and important point point however.

My reservations are around the way the question is put. It appears to restrict the debate to Carroll's formal writings on logic.

My own feeling is that you cannot separate Lewis Carroll from Charles Dodgson. Everything I have read about Charles Dodgson, everything I Have learned, is that the alto ego of Lewis Carroll enabled him to break free of the formal religious and academic boundaries within which he was enclosed.

Thus, although Charles Dodgson's mathematical and logical papers are certainly not without merit, Unless one can see these within the context of his arguments and challenges under the cloak of 'Lewis Carroll' we cannot really progress. The majority of Charles Dodgson's most challenging and profound ideas in logical and philosophical terms are embedded in his 'fictional works'.

So. In answer to the suggestion. I suggest that the idea be expanded to incluse key elelments of Carroll's fictional works that will more than answer the question of how Carroll's QUESTIONS and ideas related to his social, poliical , intelectual and spiritual environment.

Shrug!
JT

[johntufail]

Hmm, Interesting.

I hope that Carlo and Ami (and others) will give their own responses to this. My feeling is that, as stated, the suggestion will reveal little more than has already been covered. However there is much merit in explaining why certain logical propositions (or interpretations of the limits of logic) of Carroll have caused controversy. This has been complicated by Ami's proposition regarding regarding the Wilson Carroll debate. It is a valid and important point point however.

My reservations are around the way the question is put. It appears to restrict the debate to Carroll's formal writings on logic.

My own feeling is that you cannot separate Lewis Carroll from Charles Dodgson. Everything I have read about Charles Dodgson, everything I Have learned, is that the alto ego of Lewis Carroll enabled him to break free of the formal religious and academic boundaries within which he was enclosed.

Thus, although Charles Dodgson's mathematical and logical papers are certainly not without merit, Unless one can see these within the context of his arguments and challenges under the cloak of 'Lewis Carroll' we cannot really progress. The majority of Charles Dodgson's most challenging and profound ideas in logical and philosophical terms are embedded in his 'fictional works'.

So. In answer to the suggestion. I suggest that the idea be expanded to incluse key elelments of Carroll's fictional works that will more than answer the question of how Carroll's QUESTIONS and ideas related to his social, poliical , intelectual and spiritual environment.

Shrug!
JT

[ermete22]

My impression is that Carroll loved so much to lead his readers on a wild-goose chase, that sometimes he could not but derail himself, at least in his fiction works; I mean that he, quite abruptly, changed of register under the sudden impression of an association (in many possible different senses: rhyme, metaphor, linguistic game,…) which appeared in his mind. The result is a baroque structure, made of a great number of diversions, which takes you up and down, here and there, until you get lost but with the unpleasant impression he meant something you have actually missed. This is one of the reasons he reminds me so much Laurence Stern, and why the interpretation of his fiction works is a never-ending process.
I mean I agree with John; if it exists something about the deepest truths about Carroll, they are surely hidden in his fictional works and many times into very sophisticated structures. I tell you about an example I discovered myself: when Alice falls into the rabbit hole, the are cupboards and bookshelf around, she takes a jar, but from a shelf (that is a bookshelf and not a cup board) and on it there is written ORANGE MARMELADE (that is marmalade in Dutch). JAR, in the English of Carroll’s time, meant also something not good, less than what was promised. So was such object a book about Orange family which was somehow a rip-off or a jar of marmalade?
I think not only that John is right, but that there is a lot of good work to be done.
Carlo

[ami]

Dear otherprofessor and mahendra.
I agree that it would be very useful to give particular examples of Carroll's logic problems and explain them. Of course, Carrollians are less acquainted with his logic work than with his Alice works. I will try to do some of the job in the forthcoming days, in the "logic" section (because we are currently in the "mathematics" one).
I agree with Carlo and John that it is necessary to discuss Carroll's work without dividing it and that we should not separate the scientific and fictional works. We should not however remain on general considerations and we need to discuss the details in order to understand the whole.

[johntufail]

I totally agree with you Ami. One of the greatest problems with Carroll biographies, most especially the Cohen biography, is that the authors really didn't understand their subject matter. Hudson's biography was totally distorted by the fact that he failed to understand that Carroll's 'squib' about the 'Jowett Controversy' actually supported Jowett's position. Hudson relied on prior biographies and interviews with the Dodgson family. Yet any objective sudy of this squib shows that Carrol is (at least) de-constructing Pusy's opposition to Jowett's appointment.

Similarly, and most disappointingly, in a very odd chapter in Cohen's book, He admits that Carroll was (at the very least) 'Broad Church' in his views. However, he confesses himself unable to understand the philosophy of Coleridge as expessed in 'Aids to Reflection' . He fails to mention Biographia Literaria' and makes no mention at all of Carroll's interest in Blake, his membership of the Spiritualist Society, His logical disputtions with Wilson, his interests in 'Esoteric Budhism' (Madame Blatavsky) and a ghost of other significant issues.

I could go on. Sigh!

It is the issues that Cohen failed to address that we should be concentratiing on. We need to be more precise and authorititative in constructing. however Fuzzy' our imagery of Caroll/Dodgson. Ands in this, we must be clear that we are not talking so much about his life as his thoughts and ideas.

I do like Ami's proposal as, at the very least, one way of building the body od information we all need.

Regards

JT

[ermete22]

I spent some time to study Carroll's spiritualism.
Some points seem clear to me even if I was compelled to read many books on american spiritualism, which sometimes are very hard to digest (I can pass a list if you want).
1) As many researchers already know, there were a lot of spiritualist books in possession of Carroll, so his interest is evident.
2) Probably the basic logical point influencing Carroll is that the existence of spirits is in a strange logical position: it is impossible to demonstrate they do not exist.
3) It does not contradict the fundamentals of Christian Religion; in facts there still exists a respectable spiritualist church in USA.
4) Also Swedenborg is, from many points of view, coherent with Christian doctrine (not in an orthodox sense)
5) Also some scientists were convinced spiritualists.
6) There existed many honest spiritualists.
7) The theological environment was rapidly taking new positions.

So I believe that it was not a "scandal in front of the reason" to be spiritualists, at least within in the context of SPR. The existence of the spirits, in the sense of Swedenborg, not ghosts walking with their head under the right harm, or vampires, was a comprehensible growing hope in the 19th century and a reaction to the materialist hypothesis that was no more than an ideological position then (I suspect it is still like that, but this has nothing to do with Carroll).
We then have many implicit elements to believe that Carroll was very keen to accept the spiritualist hypothesis,withou forgetting of course his tendency to doubt about everything. So one can say he was a problematic spiritualist.
As Cohen, I was not able to understand the spirit of Coleridge's philosophy; some concepts like "personal truth" looks to me as a contradiction of terms; so I cannot add anything on the subject.
Carlo