The negation of this
sentence
would be 'The idea B is not formed through something affecting the ego' if we assume that B is an idea.
Gottlob-Frege-Posthumous-Writings
that B doesn't obtain without A; 3.
the judgement that this is so.
I Iere too the combination is given the honour of a simple designation, while the constituent elements have to be content with complex expressions.
As the affirmation of the first case, Boole's logical product 'A? B' means the denial of the last three of our cases, and so is very rich in content. llowever this designation is more convenient than the others, since we ohtain a simple content by mere denial of such a product.
If one wishes to avoid the defect in the Boolean signs we have just
? Der Operationskreis des Logikkalkuls. Leipzig 1877. ? ? Vierteljahrsschriftfiir wissenschqftl. Phi/os. I, p. 456.
1
means the denial of A.
? 50 BooZe's logical Formula-language and my Concept-script
emphasized, one must introduce a special designation for the denial of one of the four cases set out above. It is enough for this purpose to select a single one of tliose cases for by using a negation sign one can obtain from each of the four cases any other. If, for instance, we put r for the denial of A those four cases then run:
not rand B,
not rand not B,
randB, rand notB;
that is the first case has assumed the form of the third, the second that of the fourth, and conversely the third that of the first, the fourth that of the second. If now it is possible to manage with one single sign which denies one of the four cases, we ought to do so, for the fewer primitive signs one introduces, the fewer primitive laws one needs, and the easier it will be to master the formulae.
Now, I have chosen the third case 'not A and B' as the one whose denial receives a special sign:
To form the denials of the remaining cases, I make use of the negation- stroke, a small vertical stroke attached beneath one of the horizontal strokes. So
means the denial of 'not not A and B', i. e. of 'A and B',
the denial of the case 'A and not B',
the denial of the case 'not A and not B'.
If the cases are to be affirmed, instead of denied, this is done by means of
a negation-stroke attached to the left hand end of the uppermost horizontal stroke. Accordingly
means 'not A and B',
? r
BooZe's logical Formula-language and my Concept-script 51
'A and B',
? A and not B', and finally
'not A and not B'. It is easy to see that you can translate
by 'A orB' in the inclusive sense, and
by 'neither A nor B'.
Nothing is yet asserted, no judgement is made, by all these designations;
only a new content of possible judgement is formed from given ones. Now in order to put a content forward as true, I make use of a small vertical stroke, the judgement stroke, as in
whereby the truth of the equation is asserted, whereas in - 3 2 = 9 no judgement has been made. Hence since the judgement stroke is lacking, we can even write down - 3 2 = 4 without saying anything untrue. If we include the negation-stroke, we can add the judgement stroke too without falling into error
means: 32 is not equal to 4 By
l2=4 t1+3=5
the fact that the case that 12 is not equal to 4 and that 1 + 3 = 5 does not obtain is asserted; and this rightly, since 1 + 3 simply is not equal to 5. Like- wise it is correct to put the judgement stroke in
22 = 4 t2+3=5
because the case that 22 is not equal to 4 and 2 + 3 = 5, does not obtain; for, of course 22 = 4. Similarly
? 52 Boole's logical Formula-language and my Concept-script
is right for two reasons: because (-2)2 = 4, and because -2 + 3 does not
equal 5. Whatever number you may put in the place of the 1 in
12=4 T1+3=s
the content is always correct. To express this general assertion, I use a roman letter:
Youcanalsorenderthis:ifx+3= 5,thenx2= 4. Andsowehaveherea hypothetical judgement. And the outstanding importance of this judgement has persuaded me to give the sign
precisely the meaning of the denial of the case 'not A and B'. Of course this alone doesn't yet give us a genuine hypothetical judgement: that arises only when A and B have in common an indefinite component which makes the situation described general.
I believe I have now adequately shown, that, as is proper, I divide the different tasks with which Boole burdens the one sign among several signs, without thereby increasing the total number of signs. The signs which I have also introduced elsewhere may be ignored in this context, since I am restricting myself to what corresponds to Boole's secondary propositions. As against his addition, subtraction, multiplication and equals signs, and his 0 and 1, we have:
1. The horizontal 'content-stroke',
2. The negation-stroke,
3. The vertical stroke that combines two content-strokes, 'the
conditional-stroke',
4. Theverticaljudgement-stroke.
Here, I haven't counted Boole's division sign and other numbers besides 0 and 1, since these are easier to dispense with.
? I. Piinjer:
2. Frege: J. P. 4. F.
5. P.
6. F.
7. P. H. F.
Y. P. 10. P.
11. F. 12. P.
1
[Dialogue with Piinjer on Existence] 1 [Before 1884]
[I. The Dialogue]
'Something does not have the characteristic of flying, but does fall under the concept "bird'": does this have the same meaning as 'Among what is, is something that does not have the characteristic of flying, but does fall under the concept "bird"'? What does is mean?
It means can be experienced (by us).
Is it not pleonastic to say of something that it can be experienced?
No, since by manipulating at will the ideas derived from experience, we are able to form ideas to which nothing that can be experienced corresponds.
Is it A or the idea ofA that is the real, as opposed to the grammatical, subject in the sentence 'A is something that can be experienced'.
A.
'The statement "A cannot be experienced" is the negation of the statement "A can be experienced"'. Is that correct?
Yes, if by 'A cannot be experienced' is understood: the sentence 'A can be experienced' is false.
The statement 'A cannot be experienced' is not possible. Therefore the question is nonsensical. Neither does it make sense to deny that a thing can be experienced.
In that case it seems to me pleonastic to say of something that it can be experienced.
'There are men' means 'To the concept man there corresponds something that can be experienced'. Or 'One of the things that
Frege's partner in the dialogue is the protestant theologian Bernard Piinjer ( IHS0-1885), who held a chair at Jena from 1880. Both the parenthetical remark at K4 and the style of Piinjer's contributions leave no doubt that what we have in I is the record of a dialogue which actually took place. According to comments on the copies that have been preserved, the manuscript to 11 was found in an envelope together with the transcript of the dialogue.
Frcge's own more rigorous treatment of the theme in the Grundlagen (? 53) provides a clue for dating the two manuscripts. In any case the date of Piinjer's death sets an upper limit to the time of composition (ed. ).
? 54
[Dialogue with Piinjer on Existence]
13. F. 14. P.
15. F. 16. P. 17. F.
18. P.
19. F. 20. P.
21. F.
22. P.
23. F.
can be experienced falls under the concept man'. 'There are no centaurs' means 'To the idea or concept centaur there corresponds nothing that can be experienced'.
Here the negation goes with the 'corresponds'.
Yes. Or none of the things which can be experienced fall under the concept centaur.
To say of a thing that it can be experienced is not to characterize it in any way.
No. That is the difference between this statement and the others.
It still seems to me therefore as if it is pleonastic to say of something that it can be experienced, because by saying this we learn nothing new about the subject. You just explained 'There are' and why such judgements are not pleonastic, but you did not explain why the judgement 'This can be experienced' is not pleonastic.
'This can be experienced' means 'The idea of the "this" is not an hallucination, it is not something which originates from myself alone; but the idea has been formed as a result of the ego's being affected by the this'.
So you distinguish two kinds of ideas?
Yes; there are two kinds of idea: those that originate from the ego alone, and those that are formed through something affecting the ego. In order to distinguish these I say: the objects of ideas of the latter kind can be experienced; to ideas of the former kind there do not correspond any objects that can be experienced.
It seems to me then as if the real subject on your way of thinking is the idea. Do you not admit that in every substantive statement the real subject is assigned to a class and is thereby distinguished from other things that do not belong to that class?
I admit that; but a statement of existence is not a substantive one. I do not admit it if by 'substantive' is understood 'not self- evident', 'not containing a purely logical law'.
When you say 'There are men' and 'There are no centaurs' you are also making a classification. But you are not classifying things, which in one case are not there at all, and in the other case are not being assigned to one of two classes, but you are classifying the concepts 'man' and 'centaur' by assigning one to the class of concepts under which something falls, and excluding the other from this class. This is why I hold that in these sentences the concepts are the real subjects. If you say 'This can be experienced', where this has the sense 'This idea of mine is not something originating from myself alone', then you
? ? 24. P.
25. F.
26. P.
are classifying the idea. You are assigning it to one of the two kinds that you distinguished earlier. This is why I maintain that it is here the idea that is the real subject. Another way of putting the same thing is to say: The idea has the property that something corresponds to it.
A t this point the question arises o f what negation is. Negation is possible only when something has already been posited. Hence if we say 'Centaurs do not exist', this is possible only because we first think of them as being outside ourselves. We have a twofold ground for denying existence: I. a logical contradiction, 2. outside the concept or idea in experience. 1 So properly speaking the real subject is neither the concept nor the idea.
In saying this you are only citing the ground on which we base a judgement about existence. One can also derive a judgement like 'There are square roots of 4' from the concept of the square root of 4.
'There are square roots of 4' does not mean 'there is something that can be experienced which falls under the concept square root of 4', if we understand by what can be experienced something self-subsistent, something existing in its own right. Numbers exist only in something. Hence this judgement is essentially different from the judgement 'there are men'. I shall never say '4 exists'. And equally I shall not say 'a square root of 4 exists'. Here the 'there is' is used in a different sense. It means: it is a property of 4 that it can result from multiplying a number by itself, that one can find a number which yields 4 when multiplied by itself. We can only make the judgement after we have formed the proposition 22 = 4 (or (-2)2 = 4). This is what it has in common with the other existential judgements such as 'there are men'.
It was earlier objected to me with the example 'there are square roots of 4' that this is an existential judgement. Now you seem not to count it as such, because you do not want to say 'A square root of 4 exists'.
'There are square roots of 4' is an existential judgement.
(on 18) The proposition 'The idea of the this has been formed as a result of the ego's being affected by the this' is self-evident, if it is possible without absurdity to formulate its content at all; for we cannot use the expression 'The idea of this' before we have made the judgement 'Something corresponds to this idea of mine' or 'This idea of mine has been formed as a result of
27. F.
28. P. 29. F.
[Dialogue with Piinjer on Existence] 55
1 These are the words as they occur in the manuscript (ed. ).
? 56
[Dialogue with Piinjer on Existence]
30. P.
31. F.
32. P. 33. F.
something affecting the ego'. Only then can we assign the name 'this' to what has done the affecting, to what corresponds to my idea.
'The idea of the this has been formed as a result of the ego's being affected by the this' is only another way of saying 'To this idea of mine there corresponds something that can be experienced'.
I understand your remark (20) in the following way: If you want to say that B is an idea that does not originate from the ego alone, but is formed through something affecting the ego, then you use the words 'The object of B can be experienced'. The two sentences are synonymous. Is that right?
Instead of 'B is an idea that etc. ' I should say 'The idea B is etc. ', assuming straight off that B is an idea.
I grant that it is not self-evident and pleonastic to say 'The idea B does not originate from the ego alone, but is formed through something affecting the ego'; for not every idea is formed through something affecting the ego; at least the point is a debatable one.
The negation of this sentence would be 'The idea B is not formed through something affecting the ego' if we assume that B is an idea. In that case the negation has a perfectly good sense and hence it is not pleonastic and self- evident to utter the sentence 'The idea B is formed through something affecting the ego' or the sentence 'The object of B can be experienced', which you maintain to have the same meaning. But if these sentences have the same meaning, then in the judgement 'The negation of the sentence "The idea B is formed through something affecting the ego" has a good sense' we may replace 'The idea B is formed through something affecting the ego' by 'The object of B can be experienced'. We then obtain the judgement: The negation of the sentence 'The object of B can be experienced' has a good sense. This contradicts your earlier position.
There is no contradiction in calling the negation of the statement 'The object of the idea B can be experienced' legitimate, but the negation of the statement 'The object B can be experienced' illegitimate.
If I understand you rightly, the contradiction is resolved as follows: In the expression 'The object of the idea' the word 'object' is used in a different sense from in 'The object A can be experienced'.
No. The word 'object' has the same meaning, but 'object of an idea' means something different from 'object'.
Does adding 'of an idea' merely serve to restrict the sense? 'Object' by itself means object that is not merely object of an
34. P.
35. F.
36. P. 37. F.
38. P.
? ? . W. P. 40. F.
41. P.
42. F. 43. P. -14. F.
45. P. 4h. F.
47. P. 4H. F.
41). P. 50. F. 51. P. 52. F.
53. P.
54. F. 55. P. 5o. F.
57. P. 5H. F.
[Dialogue with Piinjer on Existence] 57 idea, but of experience. The contrast to draw should really be
that between object of an idea and object of experience.
(referring to 26 & 27) Number cannot be experienced in the same sense as Paul.
So you distinguish two senses of'can be experienced'?
No. Number can be experienced in the same general sense. The concept of that which can be experienced is in both cases the same; it is the same whether I say number, thing or colour can be experienced.
You do not always understand by 'can be experienced' something that can be experienced on its own?
What cannot be experienced on its own can still be experienced, as e. g. a colour, which can only be experienced in something. You said (26) that you would not say '4 exists'. Are you here using 'exist' in the same sense as 'capable of being ex- perienced'?
Yes, I take it back that I would not say '4 exists', 'a square root of 4 exists'.
The difference between the judgements 'There are men' and 'There are square roots of 4' does not lie in the 'there are' but in the difference between the concepts 'man' and 'square root of 4'. We understand by a man something that exists in its own right, but we do not understand this by a square root of 4.
I agree with that.
Is the sentence 'A can be experienced' right, if A is taken to be an idea?
Yes. An idea can be experienced.
Is there an idea of an idea?
There are ideas of ideas.
You once referred to an idea as a fluctuating image, a series of inner perceptions. What are the inner perceptions out of which the idea of the idea A is formed?
They are the particular mental acts performed in having the idea A.
Do 'act of forming an idea' and 'idea' mean the same?
Yes.
So we are wrong to distinguish the act of forming an idea from an idea.
Yes.
From your remarks (18) and (20) it follows that 'This can be experienced' has the same meaning as 'To this idea of mine there corresponds something that can be experienced'. Here 'can be experienced' is defined in terms of itself.
? ? ? 58
[Dialogue with Piinjer on Existence]
59. P.
60. F. 61. P.
62. F. 63. P.
64. F. 65. P. 66. F.
67. F. 68. P.
69. F. 70. P.
71. F. 72. P. 73. F.
74. P. 75. F.
But it isn't meant to be a definition. I still maintain that the expression 'The idea of the this' can always be used.
Has every idea an object?
Yes. Every idea has of necessity an object. 'object of an idea' is the same as 'content of an idea'.
Is the content of the idea A the same as A?
No. What is represented in the idea is the fluctuating image. To
be exact, it should be distinguished from the idea. What is represented does not include the mental act.
Is the object of an idea different from what is represented in it? Y es.
If you see a Fata morgana or have an hallucination, what then is the object of your idea? 1 (no reply).
Do you admit that the negation of the sentence 'The object of B can be experienced' has a good sense?
Y es.
Do you admit that one can give the name A to the object of the ideaB?
Y es.
Then you admit that the negation of the sentence 'A can be experienced' has a good sense.
Yes. But in your question (8) A was understood not as an object of an idea, but as an object of experience.
I didn't say of A that it was meant to be an object of an idea or an object of experience; I left the matter quite open. That is why I understood your answer (10) more generally that you now seem to understand it. However, since I had used the expression 'idea ofA' in (6), the suggestion was rather that A be understood as an object of an idea.
But surely A was there expressly understood to be an object of experience.
I don't see that. Perhaps we can take things further by asking: Do you admit that there are objects of ideas, where these ideas have not been caused by something affecting the ego?
1 This part of the dialogue-from 52 onwards-is particularly obscure. Because there are clear Kantian overtones in the use here of 'Vorstellung' ('idea') and 'Anschauung' ('inner perception'), it might be thought better to have translated the former by 'representation' and the latter by 'intuition'. It is, however, doubtful whether the use of overt Kantian terminology would have made things any clearer. Fortunately, we do not need to understand Piinjer at this point in order to follow the objections that Frege later brings against him (trans. ).
? 76. P.
77. F.
78. P.
7l). F.
Yes.
Do you admit that objects of ideas which have not been caused by something affecting the ego do not exist?
Yes.
Then it follows that there are objects of ideas-ideas which have not been caused by something affecting the ego-which do not exist. Now if you are using the word 'exists' in the same sense as the expression 'there is', then you have at the same time both asserted and denied the same predicate of the same subject. The inference is valid; for the concept 'objects of ideas which have not been caused by something affecting the ego' is exactly the same in both premises, and is exactly the same as it is in the conclusion. Do you grant this?
Yes. But the word 'there is' is wrongly used in this context.
Then put in its place another expression that will express the matter better.
We can't: any other expression would again fail to say what is meant to be expressed.
So in your opinion we have here a contradiction in the nature of things-one to which reason is necessarily captive; for we cannot get rid of it by merely changing the mode of expression. Before we deny the existence of anything whatever, we have to represent it as existing in order to go on to deny existence of it. But I don't think that we shall get any further along these lines. How do you explain 'there are men'?
(What follows this is left out, because we went round in a circle, coming back again to the question:)
How do you explain 'There are living beings'?
As follows: the statement that A, no matter what I take A to be, does not fall under the concept 'living being' is false.
What are we supposed to have in mind by A?
The meaning I assign to A is not meant to be subject to any restriction at all. If I am meant to say anything about it, it can only be something self-evident, such as A= A.
The mistake rests on the fact that you continue to think ofA as a thing that has being, with the consequence that you are simply presupposing the 'there is'.
A is not subject to the restriction that it is something that has being, unless we understand by has being something that goes without saying, in which case the restriction is no restriction. What is 'going without saying'?
I say a statement goes without saying if it does nothing to qualify the thing it is made about.
You only recognize statements that are made about something? 'There are statements which are not made about anything'
KO. P. Kl.
I Iere too the combination is given the honour of a simple designation, while the constituent elements have to be content with complex expressions.
As the affirmation of the first case, Boole's logical product 'A? B' means the denial of the last three of our cases, and so is very rich in content. llowever this designation is more convenient than the others, since we ohtain a simple content by mere denial of such a product.
If one wishes to avoid the defect in the Boolean signs we have just
? Der Operationskreis des Logikkalkuls. Leipzig 1877. ? ? Vierteljahrsschriftfiir wissenschqftl. Phi/os. I, p. 456.
1
means the denial of A.
? 50 BooZe's logical Formula-language and my Concept-script
emphasized, one must introduce a special designation for the denial of one of the four cases set out above. It is enough for this purpose to select a single one of tliose cases for by using a negation sign one can obtain from each of the four cases any other. If, for instance, we put r for the denial of A those four cases then run:
not rand B,
not rand not B,
randB, rand notB;
that is the first case has assumed the form of the third, the second that of the fourth, and conversely the third that of the first, the fourth that of the second. If now it is possible to manage with one single sign which denies one of the four cases, we ought to do so, for the fewer primitive signs one introduces, the fewer primitive laws one needs, and the easier it will be to master the formulae.
Now, I have chosen the third case 'not A and B' as the one whose denial receives a special sign:
To form the denials of the remaining cases, I make use of the negation- stroke, a small vertical stroke attached beneath one of the horizontal strokes. So
means the denial of 'not not A and B', i. e. of 'A and B',
the denial of the case 'A and not B',
the denial of the case 'not A and not B'.
If the cases are to be affirmed, instead of denied, this is done by means of
a negation-stroke attached to the left hand end of the uppermost horizontal stroke. Accordingly
means 'not A and B',
? r
BooZe's logical Formula-language and my Concept-script 51
'A and B',
? A and not B', and finally
'not A and not B'. It is easy to see that you can translate
by 'A orB' in the inclusive sense, and
by 'neither A nor B'.
Nothing is yet asserted, no judgement is made, by all these designations;
only a new content of possible judgement is formed from given ones. Now in order to put a content forward as true, I make use of a small vertical stroke, the judgement stroke, as in
whereby the truth of the equation is asserted, whereas in - 3 2 = 9 no judgement has been made. Hence since the judgement stroke is lacking, we can even write down - 3 2 = 4 without saying anything untrue. If we include the negation-stroke, we can add the judgement stroke too without falling into error
means: 32 is not equal to 4 By
l2=4 t1+3=5
the fact that the case that 12 is not equal to 4 and that 1 + 3 = 5 does not obtain is asserted; and this rightly, since 1 + 3 simply is not equal to 5. Like- wise it is correct to put the judgement stroke in
22 = 4 t2+3=5
because the case that 22 is not equal to 4 and 2 + 3 = 5, does not obtain; for, of course 22 = 4. Similarly
? 52 Boole's logical Formula-language and my Concept-script
is right for two reasons: because (-2)2 = 4, and because -2 + 3 does not
equal 5. Whatever number you may put in the place of the 1 in
12=4 T1+3=s
the content is always correct. To express this general assertion, I use a roman letter:
Youcanalsorenderthis:ifx+3= 5,thenx2= 4. Andsowehaveherea hypothetical judgement. And the outstanding importance of this judgement has persuaded me to give the sign
precisely the meaning of the denial of the case 'not A and B'. Of course this alone doesn't yet give us a genuine hypothetical judgement: that arises only when A and B have in common an indefinite component which makes the situation described general.
I believe I have now adequately shown, that, as is proper, I divide the different tasks with which Boole burdens the one sign among several signs, without thereby increasing the total number of signs. The signs which I have also introduced elsewhere may be ignored in this context, since I am restricting myself to what corresponds to Boole's secondary propositions. As against his addition, subtraction, multiplication and equals signs, and his 0 and 1, we have:
1. The horizontal 'content-stroke',
2. The negation-stroke,
3. The vertical stroke that combines two content-strokes, 'the
conditional-stroke',
4. Theverticaljudgement-stroke.
Here, I haven't counted Boole's division sign and other numbers besides 0 and 1, since these are easier to dispense with.
? I. Piinjer:
2. Frege: J. P. 4. F.
5. P.
6. F.
7. P. H. F.
Y. P. 10. P.
11. F. 12. P.
1
[Dialogue with Piinjer on Existence] 1 [Before 1884]
[I. The Dialogue]
'Something does not have the characteristic of flying, but does fall under the concept "bird'": does this have the same meaning as 'Among what is, is something that does not have the characteristic of flying, but does fall under the concept "bird"'? What does is mean?
It means can be experienced (by us).
Is it not pleonastic to say of something that it can be experienced?
No, since by manipulating at will the ideas derived from experience, we are able to form ideas to which nothing that can be experienced corresponds.
Is it A or the idea ofA that is the real, as opposed to the grammatical, subject in the sentence 'A is something that can be experienced'.
A.
'The statement "A cannot be experienced" is the negation of the statement "A can be experienced"'. Is that correct?
Yes, if by 'A cannot be experienced' is understood: the sentence 'A can be experienced' is false.
The statement 'A cannot be experienced' is not possible. Therefore the question is nonsensical. Neither does it make sense to deny that a thing can be experienced.
In that case it seems to me pleonastic to say of something that it can be experienced.
'There are men' means 'To the concept man there corresponds something that can be experienced'. Or 'One of the things that
Frege's partner in the dialogue is the protestant theologian Bernard Piinjer ( IHS0-1885), who held a chair at Jena from 1880. Both the parenthetical remark at K4 and the style of Piinjer's contributions leave no doubt that what we have in I is the record of a dialogue which actually took place. According to comments on the copies that have been preserved, the manuscript to 11 was found in an envelope together with the transcript of the dialogue.
Frcge's own more rigorous treatment of the theme in the Grundlagen (? 53) provides a clue for dating the two manuscripts. In any case the date of Piinjer's death sets an upper limit to the time of composition (ed. ).
? 54
[Dialogue with Piinjer on Existence]
13. F. 14. P.
15. F. 16. P. 17. F.
18. P.
19. F. 20. P.
21. F.
22. P.
23. F.
can be experienced falls under the concept man'. 'There are no centaurs' means 'To the idea or concept centaur there corresponds nothing that can be experienced'.
Here the negation goes with the 'corresponds'.
Yes. Or none of the things which can be experienced fall under the concept centaur.
To say of a thing that it can be experienced is not to characterize it in any way.
No. That is the difference between this statement and the others.
It still seems to me therefore as if it is pleonastic to say of something that it can be experienced, because by saying this we learn nothing new about the subject. You just explained 'There are' and why such judgements are not pleonastic, but you did not explain why the judgement 'This can be experienced' is not pleonastic.
'This can be experienced' means 'The idea of the "this" is not an hallucination, it is not something which originates from myself alone; but the idea has been formed as a result of the ego's being affected by the this'.
So you distinguish two kinds of ideas?
Yes; there are two kinds of idea: those that originate from the ego alone, and those that are formed through something affecting the ego. In order to distinguish these I say: the objects of ideas of the latter kind can be experienced; to ideas of the former kind there do not correspond any objects that can be experienced.
It seems to me then as if the real subject on your way of thinking is the idea. Do you not admit that in every substantive statement the real subject is assigned to a class and is thereby distinguished from other things that do not belong to that class?
I admit that; but a statement of existence is not a substantive one. I do not admit it if by 'substantive' is understood 'not self- evident', 'not containing a purely logical law'.
When you say 'There are men' and 'There are no centaurs' you are also making a classification. But you are not classifying things, which in one case are not there at all, and in the other case are not being assigned to one of two classes, but you are classifying the concepts 'man' and 'centaur' by assigning one to the class of concepts under which something falls, and excluding the other from this class. This is why I hold that in these sentences the concepts are the real subjects. If you say 'This can be experienced', where this has the sense 'This idea of mine is not something originating from myself alone', then you
? ? 24. P.
25. F.
26. P.
are classifying the idea. You are assigning it to one of the two kinds that you distinguished earlier. This is why I maintain that it is here the idea that is the real subject. Another way of putting the same thing is to say: The idea has the property that something corresponds to it.
A t this point the question arises o f what negation is. Negation is possible only when something has already been posited. Hence if we say 'Centaurs do not exist', this is possible only because we first think of them as being outside ourselves. We have a twofold ground for denying existence: I. a logical contradiction, 2. outside the concept or idea in experience. 1 So properly speaking the real subject is neither the concept nor the idea.
In saying this you are only citing the ground on which we base a judgement about existence. One can also derive a judgement like 'There are square roots of 4' from the concept of the square root of 4.
'There are square roots of 4' does not mean 'there is something that can be experienced which falls under the concept square root of 4', if we understand by what can be experienced something self-subsistent, something existing in its own right. Numbers exist only in something. Hence this judgement is essentially different from the judgement 'there are men'. I shall never say '4 exists'. And equally I shall not say 'a square root of 4 exists'. Here the 'there is' is used in a different sense. It means: it is a property of 4 that it can result from multiplying a number by itself, that one can find a number which yields 4 when multiplied by itself. We can only make the judgement after we have formed the proposition 22 = 4 (or (-2)2 = 4). This is what it has in common with the other existential judgements such as 'there are men'.
It was earlier objected to me with the example 'there are square roots of 4' that this is an existential judgement. Now you seem not to count it as such, because you do not want to say 'A square root of 4 exists'.
'There are square roots of 4' is an existential judgement.
(on 18) The proposition 'The idea of the this has been formed as a result of the ego's being affected by the this' is self-evident, if it is possible without absurdity to formulate its content at all; for we cannot use the expression 'The idea of this' before we have made the judgement 'Something corresponds to this idea of mine' or 'This idea of mine has been formed as a result of
27. F.
28. P. 29. F.
[Dialogue with Piinjer on Existence] 55
1 These are the words as they occur in the manuscript (ed. ).
? 56
[Dialogue with Piinjer on Existence]
30. P.
31. F.
32. P. 33. F.
something affecting the ego'. Only then can we assign the name 'this' to what has done the affecting, to what corresponds to my idea.
'The idea of the this has been formed as a result of the ego's being affected by the this' is only another way of saying 'To this idea of mine there corresponds something that can be experienced'.
I understand your remark (20) in the following way: If you want to say that B is an idea that does not originate from the ego alone, but is formed through something affecting the ego, then you use the words 'The object of B can be experienced'. The two sentences are synonymous. Is that right?
Instead of 'B is an idea that etc. ' I should say 'The idea B is etc. ', assuming straight off that B is an idea.
I grant that it is not self-evident and pleonastic to say 'The idea B does not originate from the ego alone, but is formed through something affecting the ego'; for not every idea is formed through something affecting the ego; at least the point is a debatable one.
The negation of this sentence would be 'The idea B is not formed through something affecting the ego' if we assume that B is an idea. In that case the negation has a perfectly good sense and hence it is not pleonastic and self- evident to utter the sentence 'The idea B is formed through something affecting the ego' or the sentence 'The object of B can be experienced', which you maintain to have the same meaning. But if these sentences have the same meaning, then in the judgement 'The negation of the sentence "The idea B is formed through something affecting the ego" has a good sense' we may replace 'The idea B is formed through something affecting the ego' by 'The object of B can be experienced'. We then obtain the judgement: The negation of the sentence 'The object of B can be experienced' has a good sense. This contradicts your earlier position.
There is no contradiction in calling the negation of the statement 'The object of the idea B can be experienced' legitimate, but the negation of the statement 'The object B can be experienced' illegitimate.
If I understand you rightly, the contradiction is resolved as follows: In the expression 'The object of the idea' the word 'object' is used in a different sense from in 'The object A can be experienced'.
No. The word 'object' has the same meaning, but 'object of an idea' means something different from 'object'.
Does adding 'of an idea' merely serve to restrict the sense? 'Object' by itself means object that is not merely object of an
34. P.
35. F.
36. P. 37. F.
38. P.
? ? . W. P. 40. F.
41. P.
42. F. 43. P. -14. F.
45. P. 4h. F.
47. P. 4H. F.
41). P. 50. F. 51. P. 52. F.
53. P.
54. F. 55. P. 5o. F.
57. P. 5H. F.
[Dialogue with Piinjer on Existence] 57 idea, but of experience. The contrast to draw should really be
that between object of an idea and object of experience.
(referring to 26 & 27) Number cannot be experienced in the same sense as Paul.
So you distinguish two senses of'can be experienced'?
No. Number can be experienced in the same general sense. The concept of that which can be experienced is in both cases the same; it is the same whether I say number, thing or colour can be experienced.
You do not always understand by 'can be experienced' something that can be experienced on its own?
What cannot be experienced on its own can still be experienced, as e. g. a colour, which can only be experienced in something. You said (26) that you would not say '4 exists'. Are you here using 'exist' in the same sense as 'capable of being ex- perienced'?
Yes, I take it back that I would not say '4 exists', 'a square root of 4 exists'.
The difference between the judgements 'There are men' and 'There are square roots of 4' does not lie in the 'there are' but in the difference between the concepts 'man' and 'square root of 4'. We understand by a man something that exists in its own right, but we do not understand this by a square root of 4.
I agree with that.
Is the sentence 'A can be experienced' right, if A is taken to be an idea?
Yes. An idea can be experienced.
Is there an idea of an idea?
There are ideas of ideas.
You once referred to an idea as a fluctuating image, a series of inner perceptions. What are the inner perceptions out of which the idea of the idea A is formed?
They are the particular mental acts performed in having the idea A.
Do 'act of forming an idea' and 'idea' mean the same?
Yes.
So we are wrong to distinguish the act of forming an idea from an idea.
Yes.
From your remarks (18) and (20) it follows that 'This can be experienced' has the same meaning as 'To this idea of mine there corresponds something that can be experienced'. Here 'can be experienced' is defined in terms of itself.
? ? ? 58
[Dialogue with Piinjer on Existence]
59. P.
60. F. 61. P.
62. F. 63. P.
64. F. 65. P. 66. F.
67. F. 68. P.
69. F. 70. P.
71. F. 72. P. 73. F.
74. P. 75. F.
But it isn't meant to be a definition. I still maintain that the expression 'The idea of the this' can always be used.
Has every idea an object?
Yes. Every idea has of necessity an object. 'object of an idea' is the same as 'content of an idea'.
Is the content of the idea A the same as A?
No. What is represented in the idea is the fluctuating image. To
be exact, it should be distinguished from the idea. What is represented does not include the mental act.
Is the object of an idea different from what is represented in it? Y es.
If you see a Fata morgana or have an hallucination, what then is the object of your idea? 1 (no reply).
Do you admit that the negation of the sentence 'The object of B can be experienced' has a good sense?
Y es.
Do you admit that one can give the name A to the object of the ideaB?
Y es.
Then you admit that the negation of the sentence 'A can be experienced' has a good sense.
Yes. But in your question (8) A was understood not as an object of an idea, but as an object of experience.
I didn't say of A that it was meant to be an object of an idea or an object of experience; I left the matter quite open. That is why I understood your answer (10) more generally that you now seem to understand it. However, since I had used the expression 'idea ofA' in (6), the suggestion was rather that A be understood as an object of an idea.
But surely A was there expressly understood to be an object of experience.
I don't see that. Perhaps we can take things further by asking: Do you admit that there are objects of ideas, where these ideas have not been caused by something affecting the ego?
1 This part of the dialogue-from 52 onwards-is particularly obscure. Because there are clear Kantian overtones in the use here of 'Vorstellung' ('idea') and 'Anschauung' ('inner perception'), it might be thought better to have translated the former by 'representation' and the latter by 'intuition'. It is, however, doubtful whether the use of overt Kantian terminology would have made things any clearer. Fortunately, we do not need to understand Piinjer at this point in order to follow the objections that Frege later brings against him (trans. ).
? 76. P.
77. F.
78. P.
7l). F.
Yes.
Do you admit that objects of ideas which have not been caused by something affecting the ego do not exist?
Yes.
Then it follows that there are objects of ideas-ideas which have not been caused by something affecting the ego-which do not exist. Now if you are using the word 'exists' in the same sense as the expression 'there is', then you have at the same time both asserted and denied the same predicate of the same subject. The inference is valid; for the concept 'objects of ideas which have not been caused by something affecting the ego' is exactly the same in both premises, and is exactly the same as it is in the conclusion. Do you grant this?
Yes. But the word 'there is' is wrongly used in this context.
Then put in its place another expression that will express the matter better.
We can't: any other expression would again fail to say what is meant to be expressed.
So in your opinion we have here a contradiction in the nature of things-one to which reason is necessarily captive; for we cannot get rid of it by merely changing the mode of expression. Before we deny the existence of anything whatever, we have to represent it as existing in order to go on to deny existence of it. But I don't think that we shall get any further along these lines. How do you explain 'there are men'?
(What follows this is left out, because we went round in a circle, coming back again to the question:)
How do you explain 'There are living beings'?
As follows: the statement that A, no matter what I take A to be, does not fall under the concept 'living being' is false.
What are we supposed to have in mind by A?
The meaning I assign to A is not meant to be subject to any restriction at all. If I am meant to say anything about it, it can only be something self-evident, such as A= A.
The mistake rests on the fact that you continue to think ofA as a thing that has being, with the consequence that you are simply presupposing the 'there is'.
A is not subject to the restriction that it is something that has being, unless we understand by has being something that goes without saying, in which case the restriction is no restriction. What is 'going without saying'?
I say a statement goes without saying if it does nothing to qualify the thing it is made about.
You only recognize statements that are made about something? 'There are statements which are not made about anything'
KO. P. Kl.
