Published February 3, 2024 | Version v1
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# An Easy Refutation of Ramsey's Attacks on Keynes's relational, propositional logic for academicians

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F P Ramsey, RB Braithwaite, and all of their many supporters over the last 103 years, never read Keynes’s A Treatise on Probability. It is easy to show this simply by studying pp.4-6 of chapter I of the A Treatise on Probability and comparing Keynes’s analysis to page 3 of Ramsey’s 1922 review that was published in Cambridge Magazine and republished in 1989 in The British Journal for the Philosophy of Science. Pages 4-6 provide an excellent introduction to Keynes’s formal analysis contained in Part II of the A Treatise on Probability.

All of Keynes’s analysis is based on the work of G Boole. Consider Boole’s basic, introductory statements in chapter I of his 1854 The Laws of Thought: “Instead, then, of saying that Logic is conversant with relations among things and relations among facts, we are permitted to say that it is concerned with relations among things and relations among propositions.… Among such relations I suppose to be included those which affirm or deny existence with respect to things, and those which affirm or deny truth with respect to propositions. Now let those things or those propositions among which relation is expressed be termed the elements of the propositions by which such relation is expressed. Proceeding from this definition, we may then say that the premises of any logical argument express given relations among certain elements, and that the conclusion must express an implied relation among those elements, or among a part of them, i.e. a relation implied by or inferentially involved in the premises… As the conclusion must express a relation among the whole or among a part of the elements involved in the premises, it is requisite that we should possess the means of eliminating those elements which we desire not to appear in the conclusion, and of determining the whole amount of relation implied by the premises among the elements which we wish to retain. Those elements which do not present themselves in the conclusion are, in the language of the common Logic, called middle terms; and the species of elimination exemplified in treatises on Logic consists in deducing from two propositions, containing a common element or middle term, a conclusion connecting the two remaining terms.”(Boole,1854 ,pp.7-8;underline and italics added). Now there is one conclusion that we can derive from Boole, which is that  in an argument form, the conclusion  must be related to the premises .Other terms besides related that one could use , would be the words  relevant, similar or like .Keynes, in fact, uses all four terms -related ,like similar, and relevant.

It is impossible to deploy Boole’s relational, propositional logic in the case where the propositions, premises and conclusion, are unrelated, irrelevant, dissimilar or unlike each other. This is, however, exactly what Ramsey did .Ramsey presented a series of argument forms where the premises and conclusion are unrelated to each other, unlike each other, irrelevant to each other, or dissimilar to each other, so that it would be impossible to compare the premises and conclusion to each other.

Note that Keynes explicitly rejects this explicitly in 1921 by arguing that the premises and conclusion must be logically connected to each other (Keynes, A Treatise on Probability, p.5 ) or must always be comparable to each other (Keynes,ibid.,pp.137-138): “We can only be interested in our final results when they deal with actually existent and intelligible probabilities—for our object is, always, to compare one probability with another—and we are not incommoded, therefore, in our symbolic operations by the circumstance that sums and products do not exist between every pair of probabilities.” (Keynes,1921, pp.137-138). Ransey does exactly the opposite. Ramsey chooses to deal with actually non existent and unintelligible probabilities so that it is impossible to compare one probability with another. Ramsey makes the absurd, idiotic, preposterous, and incomprehensible claim that Keynes’s logical theory of probability is based on propositions which are completely unrelated to each other. An example of this is   C. Misak’s favorite, cited example taken from Ramsey’s 1922 revoew(Misak,2020,p.114)  ,that “…My carpet is blue, Napoleon was a great general…” (Ramsey,1922,p.3) Bertrand Russell, unfortunately without explicitly identifying Ramsey by name in his 1922 review, gave the following nonsensical type of Ramsey example: “2+2 =4, Napoleon disliked poodles.” (Russell,1922,p.120,*ft.). It is a great ,100 plus year mystery how thousands of economists, philosophers ,historians and other academicians could have fallen for Ramsey’s baseless and bewildering  argument .

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