123. Harrod to H. B. W. Joseph , [26 November 1926] [a]

[Attached to a letter not found, replies to 122 , answered by 129 ]

[26 November 1926] [1]

1. Your comments on my use of definition were well deserved. The language of my paper was undoubtedly misleading. Where I said "I define benefit as ..." I ought to have said "I intend to use the word benefit for ...". [2] It would then have been plain that I was not attempting to define anything in the proper sense of that word, but was simply introducing my audience to some new notation. When you complain of Energy =   [b] it is because you suspect, probably rightly, that the physicist is doing more than he pretends to be doing, that he is making a "synthetic" proposition. [3]

You suspect me of practicing the same sort of deception. I do not think you would have done so had you seen as well as heard my paper.

2. You not only claim that I was meaning something different by benefit and utility from what I pretended to be meaning, but you deny that my account of utility is true of current, e.g. Marshallian, usage. The relevant passage in Marshall is on p. 92 of the Principles (8th Ed.). [4] Here he makes utility correlative to desire, which is nearer the sense in which I claim than he uses it, viz. as correlative to will or choice, that it is to the sense in which you claim that he uses it, viz. as equivalent to satisfaction. On the same page there is an obscure footnote which might be interpreted as modifying his explanation of what he means in such a way as to make his sense equivalent to mine. (It might be interpreted otherwise). When there is doubt about the use of a word by a man who is a great master in his own subject but has inadequate philosophical training, I think it is right to assume that he uses the word in the sense which makes sense of the most important passages in which it occurs rather than in the sense proposed in his formal account of it, if there is a conflict. It is true that sometimes he uses it in an undoubtedly different sense as when he says that £1 has more utility to a poor man than to a rich. [5] This makes utility equivalent to satisfaction. But it is more likely that he uses it in two senses than that he always uses it in a sense which makes nonsense of most of the reasonings of the Principles. Since most of his arguments require it to be taken in my sense and since one interpretation of the footnote implies that he meant it in my sense, I think it is only fair and reasonable to assume that he was in most cases using it in my sense. Similarly with the writers of his school. He cannot of course be exempted from the charge of being confused.

3. You say that there is no single scale of all possible actions, [6] but that there are independent scales for each occasion which include the acts open to that occasion. No doubt there are various independent scales. But I do not see how it can be denied that all actions are always open to us. We do not, of course, survey all possible actions on every occasion. We decide, gradually, by trial and error, a general scheme, which only leaves matters of detail to be settled on each afternoon. But our plan of life is always liable to be overthrown. Something may suggest to us that it is faulty and we may have to begin ab initio to draw up our scale of duties, considering all actions as open. This is not inconsistent with the undoubted fact that my past conduct has in a way committed me. My past conduct is part of the whole condition of things which I shall have to take into account in reconstructing my scale of duties.

4. The term "beneficial" of my paper was no doubt grossly misleading. [7] The word "obligacious" might carry my meaning better. [8] A is obligatory if it ought to be done in the circumstances. A is obligacious if it ought to be done supposing that it does not take up any time.

A is more obligacious than B means that if there is mutual exclusiveness A ought to be done. [9]

Only compare equi-lasting actions. Suppose that A and B stand not for lengths of time spent in an activity, but for amounts achieved (i.e. so many acres ploughed). If the rate of A varies we may have to compare ths of A with B, ths of A with B, ths of A with B etc. Suppose that anything less than ths of A is less obligacious than B and that anything more than ths is more obligacious. It is clear that at some point as we compare increasing fractions of A with B that there is a transition from less to more obligacious than B. Suppose that ths of A is as obligacious as B.

Suppose that we are dealing with small parts so that any th of A may be regarded as equally obligacious with any other. (Obligaciousness being of course measured by comparison with the same increment of something else).

In my paper I contended, and I begin to think your criticism is justified, that to say that O(mpths of A)=O(B) was the same as to say that {O(A)}=O(B). [10] (on the assumption of course that mpth of A is constant for successive tenths of A). It appears that the two equations which I have written down are not absolutely equivalent as I tried to make them in my paper.

What I now submit that it is impossible to think the former and disbelieve the latter. It is not a question of formal proof. It merely seems to me impossible honestly to say that you believe that mpths of an action (A) has the same obligaciousness as another action (B) and yet not think that ths of A has ths of the obligaciousness of B. (It being assumed that of the mpths of A and th has the same obligaciousness as any other).

5. If I understand your views aright your only objection to this is your general objection to applying arithmetic to things which cannot be divided into parts.

i. If you are right certain branches of mathematics could still be used in morals, provided that it is true, as claimed, that mathematicians can tell us a lot if we give them only greaters and lesses and nothing more precise. I do not know that we have any reason to deny this claim.

ii. But I cannot convince myself that you are right. For instance, how do you view the following rather different sort of moral scale? Let A, B, C be three obligacious actions. It does often seem quite clear that O(A) exceeds O(B) by more than O(B) exceeds O(C). E.g. saving a drowning man, being in time for a private hour and catching the post with a business letter. I ought to do each of these if the other two were not competing. It would be absurd to deny that the obligaciousness of saving the drowning man exceeds that of being punctual for my pupil by more than being punctual exceeds in obligaciousness the posting of the letter. O(A) - O(B) > O(B) - O(C). But if this is possible it must in principle be also possible for there to be three actions such that O(A) - O(B) = O(B) - O(C). From which it follows that O(A) - O(C) = 2{O(B) - O(C)}. [11] Etc.

  1. 1. The date is read from Joseph's reply (letter 129 R).

    2. In "Morals and Arithmetic" (essay 3 ) Harrod does not use this specific wording; the notion of "benefit" is introduced on [jump to page] .

    3. This paragraph substitutes the following paragraph in the draft:

    • You suspect me of practicing the same sort of deception. Certainly in my paper I always thought I was using the word in such a way that the longer expression to which I regarded it as absolutely equivalent could be substituted for it. I deliberately gave this pseudo-definition of benefit and it never left my mind, I hope, that I had only given such a definition.

    4. Reference is to A. Marshall, Principles of Economics (1920). In the draft, the opening passage of section 2 runs as follows: "Similarly with regard to utility. I also claimed that this was how economists generally use utility. Marshall explains utility (by explain I mean describes how he proposes to use the word) on p. 92 of the Princs (8th ed.)"

    5. "Morals and Arithmetic", essay 3 , [jump to page] .

    6. Letter 122 , [jump to page] . In the draft, Harrod specified at this point: "open at any one time".

    7. "Beneficial" is defined in "Morals and Arithmetic", essay 3 , [jump to page] . Joseph criticized Harrod's terminology in letter 122 , [jump to page] .

    8. In the draft, Harrod thought at first of the word "obligable" and its derivatives. This was later substituted with "obligacious" throughout the draft.

    9. In the draft, Harrod specified: "I think obligaciousness is better than precedency since the latter suggests temporal considerations." "Precedency" was the term suggested by Joseph: letter 122 , [jump to page] .

    10. "Morals and Arithmetic", essay 3 , [jump to page] .

    11. This replies to a criticism raised by Joseph a year earlier, in an exchange stimulated by a paper Joseph read before the Political Economy Club: see letter 96 , [jump to page] .

    1. a. AN, four pages on four leaves, in HBWJ, Box 9, folder 48. A draft AN, four pages on four numbered leaves is preserved in HP V-107-2. Harrod later noted on top of the first page of the draft: "Is this a reply to Joseph?" The relevant differences between the two versions are indicated in the endnotes.

      b. Ms: «Energy = mV2». In the draft, however, the formula was written correctly.

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