Phæd. It seems such.
X. And, therefore, the argument from which it flows, I presume, is false?
Phæd. Scavenger of bad logic! I confess that it looks so.
Phil. You confess? So do not I. You die "soft," Phædrus; give me the cudgels, and I'll die "game," at least. The flaw in your argument, X., is this: you summoned Phædrus to invert his proposition, and then you extorted an absurdity from this inversion. But that absurdity follows only from the particular form of expression into which you threw the original proposition. I will express the same proposition in other terms, unexceptionable terms, which shall evade the absurdity. Observe. A and B are at this time equal in value; that is, they now exchange quantity for quantity. Or, if you prefer your own case, I say that one barouche exchanges for six hundred thousand besoms. I choose, however, to express this proposition thus: A (one barouche) and B (six hundred thousand besoms) are severally equal in value to C. When, therefore, A doubles its value, I say that it shall command a double quantity of C. Now, mark how I will express the inverted case. When B doubles its value, I say that it shall command a double quantity of C. But these two cases are very reconcilable with each other. A may command a double quantity of C at the same time that B commands a double quantity of C, without involving any absurdity at all. And, if so, the disputed doctrine is established, that a double value implies a double command of quantity; and reciprocally, that from a doubled command of quantity we may infer a doubled value.
X. A, and B, you say, may simultaneously command a double quantity of C, in consequence of doubling their value; and this they may do without absurdity. But how shall I know that, until I know what you cloak under the symbol of C? For if the same thing shall have happened to C which my argument assumes to have happened to B (namely, that its value has altered), then the same demonstration will hold; and the very same absurdity will follow any attempt to infer the quantity from the value, or the value from the quantity.
Phil. Yes, but I have provided against that; for by C I mean any assignable thing which has not altered its own value. I assume C to be stationary in value.
X. In that case, Philebus, it is undoubtedly true that no absurdity follows from the inversion of the proposition as it is expressed by you. But then the short answer which I return is this: your thesis avoids the absurdity by avoiding the entire question in dispute. Your thesis is not only not the same as that which we are now discussing; not only different in essence from the thesis which is now disputed; but moreover it affirms only what never was disputed by any man. No man has ever denied that A, by doubling its own value, will command a double quantity of all things which have been stationary in value. Of things in that predicament, it is self-evident that A will command a double quantity. But the question is, whether universally, from doubling its value, A will command a double quantity: and inversely, whether universally, from the command of a double quantity, it is lawful to infer a double value. This is asserted by Adam Smith, and is essential to his distinction of nominal and real value; this is peremptorily denied by us. We offer to produce cases in which from double value it shall not be lawful to infer double quantity. We offer to produce cases in which from double quantity it shall not be lawful to infer double value. And thence we argue, that until the value is discovered in some other way, it will be impossible to discover whether it be high or low from any consideration of the quantity commanded; and again, with respect to the quantity commanded—that, until known in some other way, it shall never be known from any consideration of the value commanding. This is what we say; now, your "C" contradicts the conditions; "until the value is discovered in some other way, it shall never be learned from the quantity commanded." But in your "C" the value is already discovered; for you assume it; you postulate that C is stationary in value: and hence it is easy indeed to infer that, because A commands double quantity of "C," it shall therefore be of double value; but this inference is not obtained from the single consideration of double quantity, but from that combined with the assumption of unaltered value in C, without which assumption you shall never obtain that inference.
Phæd. The matter is clear beyond what I require; yet, X., for the satisfaction of my "game" friend Philebus, give us a proof or two ex abundanti by applying what you have said to cases in Adam Smith or others.
X. In general it is clear that, if the value of A increases in a duplicate ratio, yet if the value of B increases in a triplicate ratio, so far from commanding a greater quantity of B, A shall command a smaller quantity; and if A continually goes on squaring its former value, yet if B continually goes on cubing its former value, then, though A will continually augment in value, yet the quantity which it will command of B shall be continually less, until at length it shall become practically equal to nothing. [Footnote: The reader may imagine that there is one exception to this case: namely, if the values of A and B were assumed at starting to be = 1; because, in that case, the squares, cubes, and all other powers alike, would be = I; and thus, under any apparent alteration, the real relations of A and B would always remain the same. But this is an impossible and unmeaning case in Political Economy, as might easily be shown.] Hence, therefore, I deduce,
1. That when I am told by Adam Smith that the money which I can obtain for my hat expresses only its nominal value, but that the labor which I can obtain for it expresses its real value—I reply, that the quantity of labor is no more any expression of the real value than the quantity of money; both are equally fallacious expressions, because equally equivocal. My hat, it is true, now buys me x quantity of labor, and some years ago it bought x/2 quantity of labor. But this no more proves that my hat has advanced in real value according to that proportion, than a double money price will prove it. For how will Adam Smith reply to him who urges the double money value as an argument of a double real value? He will say—No; non valet consequentia. Your proof is equivocal; for a double quantity of money will as inevitably arise from the sinking of money as from the rising of hats. And supposing money to have sunk to one fourth of its former value, in that case a double money value—so far from proving hats to have risen in real value—will prove that hats have absolutely fallen in real value by one half; and they will be seen to have done so by comparison with all things which have remained stationary; otherwise they would obtain not double merely, but four times the quantity of money price. This is what Adam Smith will reply in effect. Now, the very same objection I make to labor as any test of real value. My hat now obtains x labor; formerly it obtained only one half of x. Be it so; but the whole real change may be in the labor; labor may now be at one half its former value; in which case my hat obtains the same real price; double the quantity of labor being now required to express the same value. Nay, if labor has fallen to one tenth of its former value, so far from being proved to have risen one hundred per cent. in real value by now purchasing a double quantity of labor, my hat is proved to have fallen to one fifth of its former value; else, instead of buying me only x labor, which is but the double of its former value (x/2), it would buy me 5 x, or ten times its former value.