Martin Gardner, in his utterly invaluable work, The Annotated Alice: The Definitive Edition, provides an exegesis of the passage quoted in the drawing above:
Lewis Carroll was fully aware of the profundity in Humpty Dumpty's whimsical discourse on semantics. Humpty takes the point of view known in the Middle Ages as nominalism; the view that universal terms do not refer to objective existences but are nothing more than flatus vocis, verbal utterances. The view was skillfully defended by William of Occam and is now held by almost all contemporary logical empiricists.One wonders what Mr Dumpty would have made of the terminological debate between the Cappadocian Fathers and Aetius and Eunomius.
Even in logic and mathematics, where terms are usually more precise than in other subject matters, enormous confusion often results from a failure to realize that words often mean "neither less nor more" than what they are intended to mean. In Carroll's time a lively controversy in formal logic concerned the "existential import" of Aristotle's four basic propositions. Do the universal statements "All A is B" and "No A is B" imply that A is a set that actually contains members? Is it implied in the particular statements "Some A is B" and "Some A is not B"?
Carroll answers these questions at some length on page 165 of his Symbolic Logic. The passage is worth quoting, for it is straight from the broad mouth of Humpty Dumpty.The writers, and editors, of the Logical textbooks which run in the ordinary grooves – to whom I shall hereafter refer to by the (I hope inoffensive) title "The Logicians" – take, on this subject, what seems to me to be a more humble position than is at all necessary. They speak of the Copula of a Proposition "with bated breath"; almost as if it were a living, conscious Entity, capable of declaring for itself what it chose to mean, and that we, poor human creatures, had nothing to do but to ascertain what was its sovereign will and pleasure, and submit to it.The view adopted by Carroll (that both "all" and "some" imply existence but that "no" leaves the question open) did not finally win out. In modern logic only the "some" propositions are taken to imply that a class is not a null class. This does not, of course, invalidate the nominalistic attitude of Carroll and his egg. The current point of view was adopted solely because logicians believed it to be the most useful.
In opposition to this view, I maintain that any writer of a book is fully authorised in attaching any meaning he likes to any word or phrase he intends to use. If I find an author saying, at the beginning of his book. "Let it be understood that by the word 'black' I shall always mean 'white', and that by the word 'white' I shall always mean 'black', " I meekly accept his ruling, however injudicious I may think it.
And so, with regard to the question whether a Proposition is or is not to be understood as asserting the existence of its Subject, I maintain that every writer may adopt his own rule, provided of course that it is consistent with itself and with the accepted facts of Logic.
Let us consider certain views that may logically be held, and thus settle which of them may conveniently be held; after which I shall hold myself free to declare which of them I intend to hold.
When logicians shifted their interest from the class logic of Aristotle to the propositional or truth-value calculus, another furious and funny debate (though mostly among non-logicians) raged over the meaning of "material implication." Most of the confusion sprang from a failure to realize that "implies" in the statement "A implies B" has a restricted meaning peculiar to the calculus and does not refer to any casual relation between A and B. A similar confusion still persists in regard to the multivalued logics in which terms such as and, not and implies have no common-sense or intuitive meaning; in fact, they have no meaning whatsoever other than that which is exactly defined by the matrix tables, which generate these "connective" terms. Once this is fully understood, most of the mystery surrounding these queer logics evaporates.
In mathematics equal amounts of energy have been dissipated in useless argumentation over the "meaning" of such phrases as "imaginary number," transfinite number," and so on; useless because such words mean precisely what they are defined to mean; no more, no less.
On the other hand, if we wish to communicate accurately we are under a kind of moral obligation to avoid Humpty's practice of giving private meanings to commonly used words. "May we... make our words mean whatever we chose them to mean?" asks Roger W. Holmes in his article, "The Philosopher's Alice in Wonderland," (Antioch Review, Summer 1959). "One thinks of a Soviet delegate using 'democracy' in a UN debate. May we pay our words extra, or is this the stuff that propaganda is made of? Do we have an obligation to past usage? In one sense words are our masters, or communication would be impossible. In another we are the masters; otherwise there could be no poetry."
The Eunomians relied on a strictly logical method of speaking of God, Whom they regarded above all as ungenerated (not-born). Ingeneracy was made the primary and defining character of God, such that the Son and the Holy Spirit (as well as other generated beings) were clearly not God. Words were seen as having essentially revelatory force: names revealed essences. To which point St Basil argued that there is no direct correspondence between name and nature; St Gregory the Theologian argues that the human mind can never comprehend God or name His essence; and St Gregory of Nyssa argues that the name "God" describes His activity, not His being. So, while the Fathers certainly wouldn't go as far as Humpty Dumpty in relativizing language, they would look at language as being, so to speak, relational rather than definitive.
That is, while the Fathers base their theological language on that of revealed Scripture, they are aware, nonetheless, that our theological jargon, however carefully defined and delimited, can in no way describe the reality of God's being (whereas the Eunomians would claim that the term "ungenerated" named, defined, and disclosed the Godhead. The Cappadocians preferred mystical insight and apophatic (negative) language as the primary mode of theology. If we were to place the Fathers in one linguistic camp, I'd place them nearer the nominalists, albeit not quite next to Humpty Dumpty (if anything, I'd put them closer to Wittgenstein's box).