Equality of ordinal vs. cardinal utility under transformations - who made the distinction first? In the context of preferences among items or choices under certainty, we can consider ordinal value function (viz., utility functions) to be equivalent under monotonously increasing transformations $u(x)\equiv F(u(x))$ for strictly increasing function $F$, but cardinal value functions only under linear transformations, i.e., $u(x)\equiv a u(x)+b$ for positive $a$ and constant $b$.

For adding a reference to an article in the philosophy of economics, I'd like to know who showed this the first time and where? Von Neumann and Morgenstern (1947)? Debreu (1960)? Or is this just "folklore"?

I'm aware of the history of utility in economics, the cardinal approaches of 19th century and the switch to ordinal representations by Pareto, Samuelson, etc. But I can't find a good "first" reference for the above distinction.
It appears to be the Theory of Games and Economic Behavior (1944) by John von Neumann &amp; Oskar Morgenstern. I have the 1953 edition which is counted as "3d", but by reading the included introductions to the 2nd and to the 3d editions, it appears that nothing of substance has been changed in chapter 3, where I locate the issue of equivalence up to linear transformations.  

In sub-chapter 3.4 the authors discuss in general the issue of equivalence under transformations for any system of quantities, mainly from physics. They end this sub-chapter by writing (bold my emphasis)


  "One may take the attitude that the only "natural" datum in this domain (utility) is the relation "greater," i.e. the concept of
  preference. In this case utilities are numerical up to a monotone
  transformation. This is, indeed, the generally accepted standpoint in
  economic literature, best expressed in the technique of indifference
  curves. To narrow the system of transformations it would be
  necessary to discover further "natural" operations or relations in the
  domain of utility. Thus it was pointed out by Pareto (in V. Pareto, Manuel d'Economie Politique, Paris, 1907, p. 264) that an equality
  relation for utility differences would suffice; in our terminology it
  would reduce the transformation system to the linear
  transformations. However, since it does not seem that this relation is
  really a "natural" one—i.e. one which can be interpreted by
  reproducible observations—the suggestion does not achieve the
  purpose."


In sub-chapter 3.5 they start by writing 


  "The failure of one particular device need not exclude the possibility  of achieving the same end by another device. Our
  contention is that the  domain of utility contains a "natural"
  operation which narrows the system  of transformations to precisely
  the same extent as the other device would  have done(*). This is the
  combination of two utilities with two given  alternative probabilities
  $a, 1 — a, (0 &lt; a &lt; 1)$ as described in 3.3.2. The  process is so
  similar to the formation of centers of gravity mentioned in 
  3.4.3. that it may be advantageous to use the same terminology."


(*) Note: The "failure of one particular device" refers to the suggestion of Pareto mentioned in the previous passage. So what they are saying here, is that, apart from ordinal preference, there is another "natural operation" related to utility (but not the one suggested by Pareto), that will nevertheless achieve the same purpose as Pareto's suggestion, i.e. to narrow the admissible transformations to linear ones only.  

And which is this "natural operation"?


  "...The combination of two utilities with two given  alternative probabilities $a, 1 — a, (0 &lt; a &lt; 1)$"


which ushers us into the world of expected utility.

The details come next, together with Appendix "The Axiomatic Treatment of Utility" at the end of the book.

PS: By rejecting Pareto's suggestion, the authors make clear that expected utility is not cardinal utility, since what they reject is the existence of "an equality relation between utility differences". This rejection preserves fundamentally the ordinal nature of expected utility.