Abstract
Moorean validities are any in-general invalid inferences such as: “P; therefore I believe that P”. While these are prima facie invalid, they have no counterexamples, since any assertion of the truth of the premise pragmatically forces the conclusion to be true. I first show that Dummettian anti-realists have a seemingly impossible time explaining why Moorean validities are not valid. Then I argue that the anti-realist could restrict applications of Moorean validities to inferential situations outside of the scope of things assumed hypothetically for further discharge. In conclusion, I show how Brogaard and Salerno’s argument against Neil Tennant runs afoul of this restriction and also suggest that famous arguments by Berkeley and Davidson do as well.
Phil.: How say you, Hylas, can you see a thing which is at the same time unseen?
Hyl.: No, that were a contradiction.
Phil.: Is it not as great a contradiction to talk of conceiving a thing which is unconceived?
Hyl.: It is.
Phil.: The tree or house therefore which you think of, is conceived by you.
Hyl.: How should it be otherwise?
Phil.: Without question, that which is conceived is in the mind.
Phil.: How then came you to say, you conceived a house or tree existing independent and out of all minds whatsoever?
George Berkeley—“Three Dialogues Between Hylas and Philonous” [1].
And the criterion of a conceptual scheme different from our own now becomes: largely true but untranslatable.
The question whether this is a useful criterion
is just the question how well we understand the notion of truth,
as applied to language, independent of the notion of translation.
The answer is, I think, that we do not understand it independently at all
Donald Davidson—“On the Very Idea of a Conceptual Scheme” [6]
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Notes
- 1.
See [14] for the most sophisticated, and I think promising, approach to this strategy.
- 2.
The anti-realist needs to say something like this for second-order logic as well, which I think is probably the beginning of an explanation for our use of the soundness and completeness terminology, which apply to axiomatizable logics, albeit this issue needs to be investigated in light of the proposals in [14].
- 3.
For an argument to the conclusion that the quantified version of Tonk rather surprisingly undermines Christopher Peacocke’s anti-Dummettian views, see [4].
- 4.
Moore is reputed to have raised this in a lecture.
- 5.
These clauses have been taken, with minor modifications, from [7].
- 6.
Utilizing these clauses, of course, requires standard use of alphabetic variants.
- 7.
- 8.
In the body of this text I stick to the orthodox view (called by Tennant [15] passive manifestationism) that Dummettian anti-realists only charge understanders with being able to recognize canonical verifications of propositions when presented with them. For this position it is easy to establish the inadvisability of biting the bullet. However, in [8] the author argues for a more radical anti-realism where the understander must actually be able to discover the verifier (this, called by Tennant active manifestationism). Such a view is much more congenial to the unrestricted validity of Moorean inferences. Dubucs argues that his position requires further revision than mere intuitionism. If biting the bullet is more plausible for the feasibilist anti-realist, then it might be a test case for feasibilist revision that it prohibit the validity of the arguments in this section.
- 9.
At first blush, this argument does not run afoul of the revisionary strictures of Dubucs’ feasibilism. Nothing is assumed for vacuous discharge, and nothing assumed for further discharge is used more than once inside the scope of that thing’s subproof. However, a radical feasibilist might refuse to assert that a sentence is provable or disprovable just because that sentence is in a decidable theory. For it is such an assertion that forces an intuitionist to countenance proofs such that it is not feasible that any human could construct them.
- 10.
- 11.
Intuitionists might reject the transition from line 13. to 14., as \(P\rightarrow \mathit{KP}\) only really follows from \(\neg(P \wedge \neg \mathit{KP})\) with the help of a classical negation rule such as the law of excluded middle or double negation elimination. In [16], the author suggests that this might be thought of as providing evidence for intuitionism, albeit not very much. The denial that any claim can be both true and unknown, as stated schematically in line (13), is problematic enough.
- 12.
See the discussion in [3].
- 13.
Tennant [15] conclusively shows that Dummett’s own restriction strategy does not yield a verificationism strong enough to motivate the Dummettian program.
- 14.
See [5] for my regimentation of Dummett’s argument.
- 15.
Again, see [3] for an argument that Tennant’s solution is not ad hoc.
- 16.
Arguably, the greatest contemporary task facing semantic anti-realists is discerning a plausible anti-realistically acceptable theory of modality. Timothy Williamson’s [17] paper remains canonical. For further philosophical discussions, see especially [2, 13], and Salerno’s dissertation. My own view, still being worked out in light of Dummettian dialectical pressures and reasonable success conditions on any theory of modality, is a development of the Humean idea that impossibility is projected on the world via our own experience of not being able to fulfill all of our desires, and that “objective” possibility and necessity are parasitic on this projection. Unlike Hume, but like Schopenhauer, I take it that phenomenology shows us that the experience of frustrated desire is objective. I also do not think that this renders modal claims about the universe, math, and logic to be devoid of truth values, albeit bivalence does fail.
- 17.
In what follows, the following correspondences of lines with numbered propositions in Brogaard and Salerno’s proof hold: lines 1–5 with propositions 1–5; lines 6–9 with propositions 5.1–5.4; lines 10–21 with propositions 6–6.92; lines 22–23 with propositions 7–8; lines 24–26 with propositions 9–9.2; lines 27–28 with propositions 10–11. In footnotes I give their justification for each numbered proposition.
- 18.
“Let us suppose (for our primary reductio) that there is an undecided statement:” [2, p. 147].
- 19.
“If line 1 is true, then some instance of it is true:” [2, p. 147].
- 20.
“Since line 2 does not violate Tennant’s restriction (that is, \(K(\neg \mathit{KA} \wedge \neg K\neg A)\) is not self-contradictory), we may apply anti-realism to it. It follows from anti-realism that it is possible to know 2:” [2, p. 147].
- 21.
“Now let the anti-realist suppose for reductio that it is known that A is undecided.” [2, p. 147].
- 22.
“Knowing a conjunction entails knowing each of the conjuncts. Therefore,” [2, p. 147].
- 23.
“Applying principle (*) to each of the conjuncts gives us” [2, p. 147].
- 24.
“Given the assumption of anti-realism, we derive a contradiction \((\neg A \wedge \neg\neg A)\). So the anti-realist must reject our assumption at line 4.” [2, p. 148]. Note that one can craft a shorter proof if one just deletes line 16, allows lines 17 to follow from 15 by V.′, removes the discharge bars from 17 and 18 deletes 19 and 20, and has absurdity in 21 follow from 17 and 18. That is, starting another subproof on line 16 is superfluous, as we already have \(\neg A\) on line 15. I’ve presented it with the superfluous subproof only to make clear that I really am regimenting the proof Brogaard and Salerno had in mind.
- 25.
“Resting only on the assumption of anti-realism, which the anti-realist takes to be known, line 7 [22] is now known” [2, p. 148].
- 26.
“But then, by (*), it is epistemically impossible to know that A is undecided:” [2, p. 148].
- 27.
“But this contradicts line 3, which rests merely upon anti-realism and line 2. Line 2 is the instance of the undecidedness claim at line 1. A contradiction then rests on anti-realism conjoined with undecidedness. The anti-realist must reject the claim of undecidedness:” [2, p. 148].
- 28.
“Since anti-realism is taken to be a necessary thesis, it must be admitted by the anti-realist that, necessarily, there are no undecided statements:” [2, p. 148].
- 29.
One could argue, on historical and philosophical grounds, that Dummettian anti-realism is really the most plausible current form of neo-Kantianism.
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Acknowledgments
I would like to thank Berit Brogaard, Emily Beck Cogburn, Jacques Dubucs, Jeff Roland, Joe Salerno, Mark Silcox, and Neil Tennant for conversation and inspiration. This paper arose out of sustained reflection on [2, 8]. I would have liked to further discuss the parts of Brogaard and Salerno’s piece that strike me as both non-trivial and true (i.e. the important restrictions on various options for an anti-realist account of modality), as well as to have explored a Dubucsian reaction to Moorean validities in more detail. However, space-time constraints, combined with the internal logic of the paper, prohibited this.
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Cogburn, J. (2012). Moore’s Paradox as an Argument Against Anti-realism. In: Rahman, S., Primiero, G., Marion, M. (eds) The Realism-Antirealism Debate in the Age of Alternative Logics. Logic, Epistemology, and the Unity of Science, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1923-1_4
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