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.But it was classes that first engendered not mere unplausibilities butseemingly disastrous logical contradictions not merely peripheral logicalcontradictions but contradictions at the heart of the very principles onwhich Russell and Frege had taken mathematics to depend.We can collectinto classes not only ordinary objects like playing-cards and bachelors, butalso such things as classes themselves.I can ask how many shoes there arein a room and also how many pairs of shoes, and a pair of shoes is alreadya class.So now suppose I construct a class of all the classes that are not, asanyhow most classes are not, members of themselves.Will this class beone of its own members or not? If it embraces itself, this disqualifies itfrom being one of the things it is characterized as embracing; if it is notone of the things it embraces, this is just what qualifies it to be one amongits own members.So simple logic itself forbids certain ostensibly denoting expressions todenote.It is at least unplausible to say that there exist objects denoted bythe phrase round squares ; there is self-contradiction in saying that thereexists a class which is a member of itself on condition that it is not, andvice versa.Russell had already found himself forced to say of some expressionswhich had previously been supposed to name or denote, that they had tobe given exceptional treatment.They were not names but what he called incomplete symbols , expressions, that is, which have no meaning, in thesense of denotation, by themselves; their business was to be auxiliary toexpressions which do, as a whole, denote.(This was what Mill had said ofthe syncategorematic words.) The very treatment which had since theMiddle Ages been given to such little words as and , not , the , someand is was now given to some other kinds of expressions as well.Ineffect, though not explicitly, Russell was saying that, e.g., descriptivephrases were as syncategorematic as not , and and is had always beenallowed to be.Here Russell was on the brink of allowing that the meanings 376 COLLECTED PAPERS: VOLUME 2or significations of many kinds of expressions are matters not of namingthings but of saying things.But he was, I think, still held up by the idea thatsaying is itself just another variety of naming, i.e.naming a complex or an objective or a proposition or a fact some sort of postulated Fido rationis.He took a new and most important further step to cope with the para-doxes, like that of the class of classes that are not members of themselves.For he now wielded a distinction, which Mill had seen but left inert, thedistinction between sentences which are either true or false, on the onehand, and on the other hand sentences which, though proper in vocabu-lary and syntax, are none the less nonsensical, meaningless or absurd;and therefore neither true nor false.To assert them and to deny them areto assert and deny nothing.For reasons of a sort which are the properconcern of logic, certain sorts of concatenations of words and phrases intosentences produce things which cannot be significantly said.For example,the very question Is the class of all classes which are not members ofthemselves a member of itself or not? has no answer.Russell s famous Theory of Types was an attempt to formulate the reasons of logic whichmake it an improper question.We need not consider whether he wassuccessful.What matters for us, and what made the big difference tosubsequent philosophy, is the fact that at long last the notion of meaningwas realized to be, at least in certain crucial contexts, the obverse of thenotion of the nonsensical what can be said, truly or falsely, is at lastcontrasted with what cannot be significantly said.The notion of meaninghad been, at long last, partly detached from the notion of naming andreattached to the notion of saying.It was recognized to belong to, or evento constitute, the domain which had always been the province of logic;and as it is at least part of the official business of logic to establish andcodify rules, the notion of meaning came now to be seen as somehowcompact of rules.To know what an expression means involves knowingwhat can (logically) be said with it and what cannot (logically) be saidwith it.It involves knowing a set of bans, fiats and obligations, or, in aword, it is to know the rules of the employment of that expression.It was, however, not Russell but Wittgenstein who first generalized orhalf-generalized this crucial point.In the Tractatus Logico-Philosophicus, whichcould be described as the first book to be written on the philosophy oflogic, Wittgenstein still had one foot in the denotationist camp, but hisother foot was already free [ Pobierz całość w formacie PDF ]
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.But it was classes that first engendered not mere unplausibilities butseemingly disastrous logical contradictions not merely peripheral logicalcontradictions but contradictions at the heart of the very principles onwhich Russell and Frege had taken mathematics to depend.We can collectinto classes not only ordinary objects like playing-cards and bachelors, butalso such things as classes themselves.I can ask how many shoes there arein a room and also how many pairs of shoes, and a pair of shoes is alreadya class.So now suppose I construct a class of all the classes that are not, asanyhow most classes are not, members of themselves.Will this class beone of its own members or not? If it embraces itself, this disqualifies itfrom being one of the things it is characterized as embracing; if it is notone of the things it embraces, this is just what qualifies it to be one amongits own members.So simple logic itself forbids certain ostensibly denoting expressions todenote.It is at least unplausible to say that there exist objects denoted bythe phrase round squares ; there is self-contradiction in saying that thereexists a class which is a member of itself on condition that it is not, andvice versa.Russell had already found himself forced to say of some expressionswhich had previously been supposed to name or denote, that they had tobe given exceptional treatment.They were not names but what he called incomplete symbols , expressions, that is, which have no meaning, in thesense of denotation, by themselves; their business was to be auxiliary toexpressions which do, as a whole, denote.(This was what Mill had said ofthe syncategorematic words.) The very treatment which had since theMiddle Ages been given to such little words as and , not , the , someand is was now given to some other kinds of expressions as well.Ineffect, though not explicitly, Russell was saying that, e.g., descriptivephrases were as syncategorematic as not , and and is had always beenallowed to be.Here Russell was on the brink of allowing that the meanings 376 COLLECTED PAPERS: VOLUME 2or significations of many kinds of expressions are matters not of namingthings but of saying things.But he was, I think, still held up by the idea thatsaying is itself just another variety of naming, i.e.naming a complex or an objective or a proposition or a fact some sort of postulated Fido rationis.He took a new and most important further step to cope with the para-doxes, like that of the class of classes that are not members of themselves.For he now wielded a distinction, which Mill had seen but left inert, thedistinction between sentences which are either true or false, on the onehand, and on the other hand sentences which, though proper in vocabu-lary and syntax, are none the less nonsensical, meaningless or absurd;and therefore neither true nor false.To assert them and to deny them areto assert and deny nothing.For reasons of a sort which are the properconcern of logic, certain sorts of concatenations of words and phrases intosentences produce things which cannot be significantly said.For example,the very question Is the class of all classes which are not members ofthemselves a member of itself or not? has no answer.Russell s famous Theory of Types was an attempt to formulate the reasons of logic whichmake it an improper question.We need not consider whether he wassuccessful.What matters for us, and what made the big difference tosubsequent philosophy, is the fact that at long last the notion of meaningwas realized to be, at least in certain crucial contexts, the obverse of thenotion of the nonsensical what can be said, truly or falsely, is at lastcontrasted with what cannot be significantly said.The notion of meaninghad been, at long last, partly detached from the notion of naming andreattached to the notion of saying.It was recognized to belong to, or evento constitute, the domain which had always been the province of logic;and as it is at least part of the official business of logic to establish andcodify rules, the notion of meaning came now to be seen as somehowcompact of rules.To know what an expression means involves knowingwhat can (logically) be said with it and what cannot (logically) be saidwith it.It involves knowing a set of bans, fiats and obligations, or, in aword, it is to know the rules of the employment of that expression.It was, however, not Russell but Wittgenstein who first generalized orhalf-generalized this crucial point.In the Tractatus Logico-Philosophicus, whichcould be described as the first book to be written on the philosophy oflogic, Wittgenstein still had one foot in the denotationist camp, but hisother foot was already free [ Pobierz całość w formacie PDF ]