On Denoting
职务层次
By a 'denoting phra' I mean a phra such as any one of the following: a man, some man, any man, every man, all men, the prent King of England, the prent King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phra is denoting solely in virtue of its form. We may distinguish three cas: (1) A phra may be denoting, and yet not denote anything; e.g., 'the prent King of France'. (2) A phra may denote one definite object; e.g., 'the prent King of England' denotes a certain man. (3) A phra may denote ambiguously; e.g. 'a man' denotes not many men, but an ambiguous man. The interpretation of such phras is a matter of considerable difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain.
The subject of denoting is of very great importance, not only in logic and mathematics, but also in the theory of knowledge. For example, we know that the center of mass of the solar system at a definite instant is some definite point, and we can affirm a number of propositions about it; but we have no immediate acquaintance with this point, which is only known to us by description. The distinction between acquaintance and knowledge about is the distinction between the things we have prentatio
ns of, and the things we only reach by means of denoting phras. It often happens that we know that a certain phra denotes unambiguously, although we have no acquaintance with what it denotes; this occurs in the above ca of the center of mass. In perception we have acquaintance with objects of perception, and in thought we have acquaintance with objects of a more abstract logical character; but we do not necessarily have acquaintance with the objects denoted by phras compod of words with who meanings we are acquainted. To take a very important instance: there ems no reason to believe that we are ever acquainted with other people's minds, eing that the are not directly perceived; hence what we know about them is obtained through denoting. All thinking has to start from acquaintance; but it succeeds in thinking about many things with which we have no acquaintance.
The cour of my argument will be as follows. I shall begin by stating the theory I intend to advocate[[#endnote_1|[1]]]; I shall then discuss the theories of Frege and Meinong, showing why neither of them satisfies me; then I shall give the grounds in favor of my theory; and finally I shall briefly indicate the philosophical conquences of my theory.
韩国男歌手My theory, briefly, is as follows. I take the notion of the variable as fundamental; I u 'C(x)' to mean a proposition[[#endnote_2|[2]]] in which x is a constituent, where x, the variable, is esntially and w
holly undetermined. Then we can consider the two notions 'C(x) is always true' and 'C(x) is sometimes true'[[#endnote_3|[3]]]. Then everything and nothing and something (which are the most primitive of denoting phras) are to be interpreted as follows: C(everything) means 'C(x) is always true';
C(nothing) means ' "C(x) is fal" is always true';
C(something) means 'It is fal that "C(x) is fal" is always true.'[[#endnote_4|[4]]]
Here the notion 'C(x) is always true' is taken as ultimate and indefinable, and the others are defined by means of it. Everything, nothing, and something are not assumed to have any meaning in isolation, but a meaning is assigned to every proposition in which they occur. This is the principle of the theory of denoting I wish to advocate: that denoting phras never have any meaning in themlves, but that every proposition in who verbal expression they occur has a meaning. The difficulties concerning denoting are, I believe, all the result of a wrong analysis of propositions who verbal expressions contain denoting phras. The proper analysis, if I am not mistaken, may be further t forth as follows.
Suppo now we wish to interpret the proposition, 'I met a man'. If this is true, I met some definite m
an; but that is not what I affirm. What I affirm is, according to the theory I advocate:
' "I met x, and x is human" is not always fal'.
Generally, defining the class of men as the class of objects having the predicate human, we say that:
'C(a man)' means ' "C(x) and x is human" is not always fal'.高中排列组合公式
This leaves 'a man', by itlf, wholly destitute of meaning, but gives a meaning to every proposition in who verbal expression 'a man' occurs.
Consider next the proposition 'all men are mortal'. This proposition is really hypothetical[[#endnote_5|[5]]] and states that if anything is a man, it is mortal. That is, it states that if x is a man, x is mortal, whatever x may be. Hence, substituting 'x is human' for 'x is a man', we find:
'All men are mortal' means ' "If x is human, x is mortal" is always true.'
This is what is expresd in symbolic logic by saying that 'all men are mortal' means ' "x is human" implies "x is mortal" for all values of x'. More generally, we say:
'C(all men)' means ' "If x is human, then C(x) is true" is always true'.个人心得体会300字
墨鱼怎么做好吃>雷锋心得体会Similarly
'C(no men)' means ' "If x is human, then C(x) is fal" is always true'.
'C(some men)' will mean the same as 'C(a man)[[#endnote_6|[6]]]', and
经营营运资本'C(a man)' means 'It is fal that "C(x) and x is human" is always fal'.
'C(every man)' will mean the same as 'C(all men)'.
It remains to interpret phras containing the. The are by far the most interesting and difficult of denoting phras. Take as an instance 'the father of Charles II was executed'. This asrts that there was an x who was the father of Charles II and was executed. Now the, when it is strictly ud, involves uniqueness; we do, it is true, speak of 'the son of So-and-so' even when So-and-so has veral sons, but it would be more correct to say 'a son of So-and-so'. Thus for our purpos we take the as involving uniqueness. Thus when we say 'x was the father of Charles II' we not only asrt that x had a certain relation to Charles II, but also that nothing el had this relation. The relation in question, without the assumption of uniqueness, and without any denoting phras, is expresd by 'x begat Charles II'. To get an equivalent of 'x was the father of Charles II', we must ad
d 'If y is other than x, y did not beget Charles II', or, what is equivalent, 'If y begat Charles II, y is identical with x'. Hence 'x is the father of Charles II' becomes: 'x begat Charles II; and "If y begat Charles II, y is identical with x" is always true of y'.
Thus 'the father of Charles II was executed' becomes: 'It is not always fal of x that x begat Charles II and that x was executed and that "if y begat Charles II, y is identical with x is always true of y'.
小儿夏季热This may em a somewhat incredible interpretation; but I am not at prent giving reasons, I am merely stating the theory.
To interpret 'C(the father of Charles II)', where C stands for any statement about him, we have only to substitute C(x) for 'x was executed' in the above. Obrve that, according to the above interpretation, whatever statement C may be, 'C(the father of Charles II)' implies:
'It is not always fal of x that "if y begat Charles II, y is identical with x is always true of y',
which is what is expresd in common language by 'Charles II had one father and no more'. Conquently if this condition fails, every proposition of the form 'C(the father of Charles II)' is fal. every proposition of the form 'C(the prent King of France)' is fal. This is a great advant
age to the prent theory. I shall show later that it is not contrary to the law of contradiction, as might be at first suppod.
The above gives a reduction of all propositions in which denoting phras occur to forms in which no such phras occur. Why it is imperative to effect such a reduction, the subquent discussion will endeavor to show.
The evidence for the above theory is derived from the difficulties which em unavoidable if we regard denoting phras as standing for genuine constituents of the propositions in who verbal expressions they occur. Of the possible theories which admit such constituents the simplest is that of Meinong[[#endnote_7|[7]]]. This theory regards any grammatically correct denoting phra as standing for an object. Thus 'the prent King of France', 'the round square', etc., are suppod to be genuine objects. It is admitted that such objects do not subsist, but nevertheless they are
suppod to be objects. This is in itlf 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 prent 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.
The above breach of the law of contradiction is avoided by Frege's theory. He distinguishes, in a denoting phra, two elements, which we may call the meaning and the denotation[[#endnote_8|[8]]].Thus 'the center of mass of the solar system at the beginning of the twentieth century' is highly complex in meaning, but its denotation is a certain point, which is simple. The solar system, the twentieth century, etc., are constituents of the meaning; but the denotation has no constituents at all[[#endnote_9|[9]]]. One advantage of this distinction is that it shows why it is often worth while to asrt identity. If we say 'Scott is the author of Waverley,' we asrt an identity of denotation with a difference of meaning. I shall, however, not repeat the grounds in favor of this theory, as I have urged its claims elwhere (loc. cit.), and am now concerned to dispute tho claims.
One of the first difficulties that confront us, when we adopt the view that denoting phras express a meaning and denote a denotation,[[#endnote_10|[10]]] concerns the cas in which the denotation appears to be abnt. If we say 'the King of England is bald', that is, it would em, not a statement about the complex meaning 'the King of England', but about the actual man denoted by the meaning. But now consider 'the king of France is bald'. By parity of form, this also ought to be about the denotation of the phra 'the King of France'. But this phra, though it has a meaning provided 'the King of England' has a meaning, has certainly no denotation, at least in any obvious n. Hence o
ne would suppo that 'the King of France is bald' ought to be nonn; but it is not nonn, since it is plainly fal. Or again consider such a proposition as the following: 'If u is a class which has only one member, then that one member is a member of u', or as we may state it, 'If u is a unit class, the u is a u'. This proposition ought to be always true, since the conclusion is true whenever the hypothesis is true. But 'the u' is a denoting phra, and it is the denotation, not the meaning, that is said to be a u. Now if u is not a unit class, 'the u' ems to denote nothing; hence our proposition would em to become nonn as soon as u is not a unit class.
Now it is plain that such propositions do not become nonn merely becau their hypothes are fal. The King in The Tempest might say, 'If Ferdinand is not drowned, Ferdinand is my only son'.' Now 'my only son' is a denoting phra, which, on the face of it, has a denotation when, and only when, I have exactly one son. But the above statement would nevertheless have remained true if Ferdinand had been in fact drowned. Thus we must either provide a denotation in cas in which it is at first sight abnt, or we must abandon the view that denotation is what is concerned in propositions which contain denoting phras. The latter is the cour that I advocate. The former cour may be taken, as Meinong, by admitting objects which do not subsist, and denying that they obey the law of contradiction; this, however, is to be avoided if possible. Another way of taking the sa
me cour (so far as our prent alternative is concerned) is adopted by Frege, who provides by definition some purely conventional denotation for the cas in which otherwi there would be none. Thus 'the King of France', is to denote the null-class; 'the only son of Mr. So-and-so' (who has a fine family of ten), is to denote the class of all his sons; and so on. But this procedure, though it may not lead to actual logical error, is plainly artificial, and does not give an exact analysis of the matter. Thus if we allow that denoting phras, in general, have the two sides of meaning and denotation, the cas where there ems to be no denotation cau difficulties both on the assumption that there really is a denotation and on the assumption that there really is none.
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 the rve much the same purpo as is rved by experiments in physical science. I shall therefore state three puzzles which a theory as to denoting ought to be able to solve; and I shall show later that my theory solves them.
(1) 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 falhood 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.
(2) By the law of the excluded middle, either 'A is B' or 'A is not B' must be true. Hence either 'the prent King of France is bald' or 'the prent 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 prent King of France in either list. Hegelians, who love
a synthesis, will probably conclude that he wears a wig.
(3) Consider the proposition 'A differs from B'. If this is true, there is a difference between A and B, which fact may be expresd in the form 'the difference between A and B subsists'. But if it is fal that A differs from B, then there is no difference between A and B, which fact may be expresd 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 asrt subsistence or being,[[#endnote_11|[11]]] not existe
nce. Hence, it would appear, it must always be lf-contradictory to deny the being of anything; but we have en, in connexion with Meinong, that to admit being also sometimes leads to contradictions. Thus if A and B do not differ, to suppo either that there is, or that there is not, such an object as 'the difference between A and B' ems equally impossible.
The relation of the meaning to the denotation involves certain rather curious difficulties, which em in themlves sufficient to prove that the theory which leads to such difficulties must be wrong.
When we wish to speak about the meaning of a denoting phra, as oppod to its denotation, the natural mode of doing so is by inverted commas. Thus we say:
The center of mass of the solar system is a point, not a denoting complex;
'The center of mass of the solar system' is a denoting complex, not a point.
Or again,
The first line of Gray's Elegy states a proposition.
'The first line of Gray's Elegy' does not state a proposition.
Thus taking any denoting phra, say C, we wish to consider the relation between C and 'C', where the difference of the two is of the kind exemplified in the above two instances.
We say, to begin with, that when C occurs it is the denotation that we are speaking about; but when 'C' occurs, it is the meaning. Now the relation of meaning and denotation is not merely linguistic through the phra: there must be a logical relation involved, which we express by saying that the meaning denotes the denotation. But the difficulty which confronts us is that we cannot succeed in both prerving the connexion of meaning and denotation and preventing them from being one and the same; also that the meaning cannot be got at except by means of denoting phras. This happens as follows.
The one phra C was to have both meaning and denotation. But if we speak of 'the meaning of C', that gives us the meaning (if any) of the denotation. 'The meaning of the first line of Gray's Elegy' is the same as 'The meaning of "The curfew tolls the knell of parting day",' and is not the same as 'The meaning of "the first line of Gray's Elegy".' Thus in order to get the meaning we want, we must speak not of 'the meaning of C', but 'the meaning of "C",' which is the same as 'C' by itlf. Similarly 'the denotation of C' does not mean the denotation we want, but means something which, if it denotes at all, denotes what is denoted by the denotation we want. For example, let 'C' be 'the denoting comple
x occurring in the cond of the above instances'. Then
C = 'the first line of Gray's Elegy', and
the denotation of C = The curfew tolls the knell of parting day. But what we meant to have as the denotation was 'the first line of Gray's Elegy'. Thus we have failed to get what we wanted.
The difficulty in speaking of the meaning of a denoting complex may be stated thus: The moment we put the complex in a proposition, the proposition is about the denotation; and if we make a proposition in which the subject
is 'the meaning of C', then the subject is the meaning (if any) of the denotation, which was not intended. This leads us to say that, when we distinguish meaning and denotation, we must be dealing with the meaning: the meaning has denotation and is a complex, and there is not something other than the meaning, which can be called the complex, and be said to have both meaning and denotation. The right phra, on the view in question, is that some meanings have denotations.
But this only makes our difficulty in speaking of meanings more evident. For suppo that C is our complex; then we are to say that C is the meaning of the complex. Nevertheless, whenever C occurs
without inverted commas, what is said is not true of the meaning, but only of the denotation, as when we say: The center of mass of the solar system is a point. Thus to speak of C itlf, i.e. to make a proposition about the meaning, our subject must not be C, but something which denotes C. Thus 'C', which is what we u when we want to speak of the meaning, must not be the meaning, but must be something which denotes the meaning. And C must not be a constituent of this complex (as it is of 'the meaning of C'); for if C occurs in the complex, it will be its denotation, not its meaning, that will occur, and there is no backward road from denotations to meaning, becau every object can be denoted by an infinite number of different denoting phras.
Thus it would em that 'C' and C are different entities, such that 'C' denotes C; but this cannot be an explanation, becau the relation of 'C' to C remains wholly mysterious; and where are we to find the denoting complex 'C' which is to denote C? Moreover, when C occurs in a proposition, it is not only the denotation that occurs (as we shall e in the next paragraph); yet, on the view in question, C is only the denotation, the meaning being wholly relegated to 'C'. This is an inextricable tangle, and ems to prove that the whole distinction between meaning and denotation has been wrongly conceived.
That the meaning is relevant when a denoting phra occurs in a proposition is formally proved by th
e puzzle about the author of Waverley. The proposition 'Scott was the author of Waverley' has a property not possd by 'Scott was Scott', namely the property that George Iv wished to know whether it was true. Thus the two are not identical propositions; hence the meaning of 'the author of Waverley' must be relevant as well as the denotation, if we adhere to the point of view to which this distinction belongs. Yet, as we have just en, so long as we adhere to this point of view, we are compelled to hold that only the denotation is relevant. Thus the point of view in question must be abandoned.
It remains to show how all the puzzles we have been considering are solved by the theory explained at the beginning of this article.
According to the view which I advocate, a denoting phra is esntially part of a ntence, and does not, like most single words, have any significance on its own account. If I say 'Scott was a man', that is a statement of the form 'x was a man', and it has 'Scott' for its subject. But if I say 'the author of Waverley was a man', that is not a statement of the form 'x was a man', and does not have 'the author of Waverley' for its subject. Abbreviating the statement made at the beginning of this article, we may put, in place of 'the author of Waverley was a man', the following: 'One and only one entity wrote Waverley, and that one was a man'. (this is not so strictly what is meant as what was sai
d earlier; but it is easier to follow.) And speaking generally, suppo we wish to say that the author of Waverley had property phi, what we wish to say is equivalent to 'One and only one entity wrote Waverley, and that one had the property phi'.
The explanation of denotation is now as follows. Every proposition in which 'the author of Waverley' occurs being explained as above, the proposition 'Scott was the author of Waverley' (i.e. 'Scott was identical with the author of Waverley') becomes 'One and only one entity wrote Waverley, and Scott was identical with that one'; or, reverting to the wholly explicit form: 'It is not always fal of x that x wrote Waverley, that it is always true of y that if y wrote Waverley y is identical with x, and that Scott is identical with x.' Thus if 'C' is a denoting phra, it may happen that there is one entity x (there cannot be more than one) for which the proposition 'x is identical with C' is true, this proposition being interpreted as above. We may then say that the entity x is the denotation of the phra 'C'. Thus Scott is the denotation of 'the author of Waverley'. The 'C' in inverted commas will be merely the phra, not
