Moore's paradoxes

G.E. Moore is associated with three paradoxes:

(1) the "paradox of analysis" - that the explication of a conceptual equivalence can be either correct or informative, but not both;
(2) "Moore's paradox" - that some well-formed sentence functions can produce nonsensical sentences when certain variables are given the value of present indexicals;
(3) the "naturalistic fallacy" which is a particular case of an open question paradox.

(1) and (3) directly bear on the limitations of the analytic programme (as traditionally conceived). (2), I think, rescues a productive conception of analysis from this catastrophe.

Here's a summary:

'Analysis' was (informally?) conceived as being about rendering a concept in terms of others independent of it (to avoid circularity), in a way which was informative - which elucidated the concept under examination. Paradox (1) arises because it seemed that additional information only arose if the analysis introduced things which were not part of the analysand. Moore compared 'A brother is a male sibling' with 'A brother is a brother'. If the concept 'male sibling' contains nothing not already included in concept 'brother', the statements should be equivalent - but the first is clearly an analysis, while the second is not.

(The paradox depends upon the concepts being taken to be independent of the words used to articualate them - a presumption that might now be challenged.)

"Moore's paradox" is associated with the peculiarity of saying "It is raining, but I do not believe that it is raining".  It is sometimes taken to be about the logic of 'believe', but is more correctly understood as the problem that a properly formulated sentence function should produce sentences that are either true or false as its variables are given values, but should not produce nonsense.

Here are two well formed sentence functions, which will evaluate as true or false, depending on the  values given to x and y:

(a) "x believes that y"
(b) "it is not true that y"

Their conjunction "(a) and (b)" is also, therefore, a well formed function, and some substitutions seem unproblematic:

"Mary believes that it is raining, and it is not true that it is raining."

The paradox is that "I believe that it is raining, and it is not true that it is raining" seems to be nonsensical, or at least unintelligible, rather than false. It is not a move that could ever be made in a playable language game.

Open queston paradoxes, which I've talked about at length, arise when a normative category - e.g. "Truth", "Goodness" - adjudicates over any account that can be given of it. Is it true that telling the truth requires us to X? Is it good to define goodness as Y?

OQ paradoxes are pervasive.  They might be said to delimit the analytic tradition, as they arise when we try to give reductive accounts of the foundations of knowledge, truth, meaning, goodness, and arithmetic. Gödel's incompleteness theorems and Russell's paradox are both examples - one to do with valid computations of validity, and the other with distinguishing the membership of 'set'. Even the Kripke/Goodman paradox arises when we try to render the rules for distinguishing rule-following.

It seems natural, now, to replace our naive conceptions of analysis with a more language oriented approach. I have argued that certain questions about the possibility of sense-making have a Moorean peculiarity: We may say that John and Mary completely fail to  understand one other, but I cannot say to you that you and I do. The switch from third to first person generates nonsense, not falsehood. And this saves us from the catastrophic effects of the OQ problems - which must arise in, are indeed the distinguishing mark of, the most general philosophical enquiries. The apparent systematic ambiguities of truth, validity, knowledge are largely neutralised when we consider the way that type (2) paradoxes constrain our normative claims. That truth is 'unanalysable' does not make the possibility that we cannot tell the truth intelligible.

So. Good for Moore?