122. H. B. W. Joseph to Harrod , 11 November 1926 [a]
[Answered by 123 ]
New Coll[ege, Oxford]
11 November 1926
My dear Harrod,
I'm writing in pencil so as to get a better copy.
I've been thinking about your paper, & want to try to put my points more clearly than I did yesterday on the spur of the moment. 
You start by assuming that at any moment there is something I ought to do rather than anything else; but if that were done, & I still had time, there would be something I ought to do next, & so on. Hence the actions open to me can be arranged in an order in which they ought to be selected for doing. 
I will call this a scale of precedency. It is what you called a scale of benefit. You professed not to mean more by saying that the benefit of an action a 1 [b] was greater than that of a 2 , than that if I have not time for both, I ought to do a 1 & omit a 2 . If you really mean no more, it seems to me unfortunate to express that by saying that the benefit of a 1 is greater, because inevitably that is liable to be taken as a reason why a 1 ought to be chosen. In calling the scale one of precedency I think I express what you profess to mean (but I still think, l ahÑn seaután , do not mean) by calling it a scale of benefit. And plainly I do not suggest that to stand higher on a scale of precedency is a reason why an act ought to be done rather, a low precedence is being chosen; it is but the tautology which you said your statement was.  But it differs from the other phrase in this way. When I say I ought to do a 1 before a 2 , my language ascribes no character to them, in respect of which a 1 can be ranked first. When I say a 1 has a higher degree of precedency, it does. But there isn't really any character therefore in the action, to be called precedency, of which one has more than another, & is therefore to be preferred, & which constitutes something quantitative, to be taken account of in morals.
There may be divers factors, as I said after we broke up, that are quantitative or numerical, involved in action, a change in which would affect the flow of an action open to me on this scale of precedency. It may be that a reduction of 10% in the time that a 2 would occupy should place it in the m th place & relegate a 1 to the n th . I think the use of m and n here is bad,  because it suggests places on a continuous scale, including all actions open at any time; where as in point of fact we make no such single scale, & there are independent scales for each occasion to include the acts open to me on that occasion; though it may be that certain acts frequently open to me always have the same relative positions on their several scales. But waiving that, I want to ask you to what that is quantitative in the acts a 1 and a 2 or in my obligation in respect of them this reduction of 10% in the time that a 2 would occupy can correspond? Surely it can't produce or correspond to an "increase of precedency" in a 2 ? And if "increased benefit" means the same, it can't correspond to that.
I could understand you saying that the benefit of a 2 is twice that of a 1 , but that so long as you would have to spend 40 min. in doing a 2 against 15 in doing a 1 , you ought to put a 1 before a 2 on your scale; but that if a 2 came to require only 20 min., the order should be reversed. Here however the benefit is something which is the ground of preference, & must be ascertained before the position on the scale of precedency can be known; & though the benefits may be measurable & perhaps actions may be capable of differing continuously in amount of benefits, the position on a scale of precedency that includes only the actions open to me at a given moment are neither continuous nor measurably related. But you preferred not to mean by "benefit" anything of this kind.
I might say with regard to the economic doctrine of marginal value that the subjects of value stand correspondingly on a scale of precession. I use this word to mark the difference between an order in which alternatives ought to be chosen, and one in which they actually are chosen. Similarly here, no one would suppose that to have a higher place on a scale of precession is to have any character that is a ground of being chosen; whereas to say that something has greater value would give rise to such a supposition. And, pace tua, I think all economists mean by greater value something that, on the supposition of which, in a thing makes us prefer it--not just being preferred.
But I think that if they have been <corrupted> by a bad philosopher of mathematics, they might say that they define having greater marginal value as being preferred: mixing together herein the very different senses which definition has in philosophical & in mathematical writing. A philosopher means by "defining" [c] expressing in words that indicate them the distinguishable factors in the being of what he defines; a mathematician means expressing the relations, quantitative or numerical, which what he says that he defines, but whose own nature he makes no attempt to elucidate, bears constancy to certain other things, whose nature is also supposed to be familiar, & in terms of which he is said to define it. Thus energy = ; but that tells us nothing of what energy is. Now a mathematician doesn't offer us definitions of anything which he has not some other reason to believe in that his familiarity with those things "in terms of which" he defines it. There is some other reason for talking about energy than familiarity with mass & velocity. And if the thing defined were not supposed to be other than those in terms of which it is defined, it could not be supposed to stand in quantitative or numerical relations to them. Only he omits the task of elucidating its nature, though assuming it to be something capable of variation in quantity or degree (which <last> he often does not distinguish from quantity). If Marshall really meant no more than that he defined "marginal value" in the mathematical sense as that which was always just greater in what was preferred than in the next thing rejected, he still meant that it was something in what was to be preferred connected with that distinct from its being preferred: else it couldn't be "defined" by relation thereto; nothing can be "defined" or fixed, by its relation to itself. But an enquirer may ask what is this "value" or "utility" whose varying amounts determine our choices, & so affect mankind in much profound ways. The economist must not then say that he is content to define it in the language already used for defining in the mathematician's sense. That is no answer to the enquirer, who wants a definition in the philosopher's sense. To offer the mathematician's definition also as a philosopher's definition does make the whole doctrine a tautology, as you said,  but as I can't satisfy myself that any mathematician or economist or philosopher intends.
H. W. B. Joseph
2. "Morals and Arithmetic", essay 3 , [jump to page] - [jump to page] .
3. "Morals and Arithmetic", essay 3 , [jump to page] and [jump to page] . Some notes taken by Harrod at the back of the last sheet of his paper, summarizing questions and points raised, indicate that Joseph had already raised some objections "on tautology in relation to quantitative object" (HP V-107-1/23).
4. Refers to "Morals and Arithmetic", essay 3 , [jump to page] .
- a. ALS, four pages on four leaves, in pencil, in HP IV-582. Copy in HBWJ, box 9 folder 48.
b. In the manuscript Joseph used superscripts instead of subscripts.
c. The inverted commas have been added to facilitate the understanding.
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