2026-08-31
Agenda
Agenda
Agenda
\[x + y = 4\]
\[x + y < x\]
\[x = x\]
\[x \text{ is in Normal, Illinois}\]
\[x \text{ is a round square}\]
\[x \text{ is in Normal}\]
Words like ‘everything’, ‘something’, and ‘nothing’ are devices for quantification. They do not express senses which determine referents. Instead, they offer answers to questions about the formula they quantify over.
Both definite and indefinite descriptions imply existence; a definite description also implies uniqueness.
Again, the key point is that this analysis does not assign a sense to the denoting phrase which determines a referent.
Agenda
[Meinong’s] theory regards any grammatically correct denoting phrase as standing for an object. Thus “the present King of France,” “the round square,” etc., are supposed to be genuine objects. It is admitted that such objects do not subsist, but nevertheless they are supposed to be objects. (482–83)
This is in itself a difficult view; but the chief objection is that such objects, admittedly, are apt to infringe the law of contradiction. It is contended, for example, that the existent present King of France exists, and also does not exist; that the round square is round, and also not round; etc. But this is intolerable; and if any theory can be found to avoid this result, it is surely to be preferred. (483)
Agenda
A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science. (484–85)
If \(a\) is identical with \(b\), whatever is true of the one is true of the other, and either may be substituted for the other in any proposition without altering the truth or falsehood of that proposition. Now George IV. wished to know whether Scott was the author of Waverley; and in fact Scott was the author of Waverley. Hence we may substitute Scott for the author of “Waverley,” and thereby prove that George IV. wished to know whether Scott was Scott. Yet an interest in the law of identity can hardly be attributed to the first gentleman of Europe.
Argument
By the law of excluded middle, either “A is B” or “A is not B” must be true. Hence either “the present King of France is bald” or “the present King of France is not bald” must be true. Yet if we enumerated the things that are bald, and then the things that are not bald, we should not find the present King of France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig.
Consider the proposition “A differs from B”. If this is true, there is a difference between A and B, which fact may be expressed in the form “the difference between A and B subsists”. But if it is false that A differs from B, then there is no difference between A and B, which fact may be expressed in the form “the difference between A and B does not subsist”. But how can a non-entity be the subject of a proposition? “I think, therefore I am” is no more evident than “I am the subject of a proposition, therefore I am,” provided “I am” is taken to assert subsistence or being, not existence. Hence, it would appear, it must always be self-contradictory to deny the being of anything; but we have seen, in connexion with Meinong, that to admit being also sometimes leads to contradictions. Thus if A and B do not differ, to suppose either that there is, or that there is not, such an object as “the difference between A and B” seems equally impossible.
Agenda
When we say: “George IV. wished to know whether so-and-so,” [and] “so-and-so” contains a denoting phrase. We may either eliminate this denoting phrase from the subordinate proposition ” so-and-so,” or from the whole proposition in which “so-and-so” is a mere constituent. Different propositions result according to which we do. (489)
When we say, “George IV. wished to know whether Scott was the author of Waverley,” we normally mean “George IV. wished to know whether one and only one man wrote Waverley and Scott was that man”; but we may also mean: “One and only one man wrote Waverley, and George IV. wished to know whether Scott was that man”. In the latter, “the author of Waverley” has a primary occurrence; in the former, a secondary. (489)
Argument
Argument
“The King of France is not bald” is false if the occurrence of “the King of France” is primary, and true if it is secondary. Thus all propositions in which “the King of France” has a primary occurrence are false; the denials of such propositions are true, but in them “the King of France” has a secondary occurrence. Thus we escape the conclusion that the King of France has a wig. (490)
Russell’s example,
is weird. Happily, he offers other examples that are easier to follow, like:
The whole realm of non-entities, such as “the round square,” “the even prime other than 2,” “Apollo,” “Hamlet,” etc., can now be satisfactorily dealt with. All these are denoting phrases which do not denote anything. A proposition about Apollo means what we get by substituting what the classical dictionary tells us is meant by Apollo, say “the sun-god”. All propositions in which Apollo occurs are to be interpreted by the above rules for denoting phrases. If “Apollo” has a primary occurrence, the proposition containing the occurrence is false; if the occurrence is secondary, the proposition may be true. (491)
Argument
Russell claims that, on his analysis (OA1) begs the question.