On Wyman’s Theory of the Meaninglessness of Contradictions: Cancellation View of Negation and Reductio ad Absurdum
(2025) 10th Workshop on Connexive Logics — Location: Tohoku University, Sendai (27.November.2025)
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- Abstract
- In this talk, I discuss a rarely commented passage from ‘On What There Is’. Quine 1948 credits the strawman Wyman with the idea that contradictions are meaningless, and makes two objections to this thesis. I will analyze Wyman’s position and Quine’s objections in turn, before concluding that these objections have no rea-son to bother Wyman. The key-idea to my interpretation is that Wyman not only supports a kind of (pseudo-)Meinongian ontology, but also defends non-classical views in logic (notably concerning the semantics of negation). In doing so, I hope to provide a better understanding of perhaps the most important paper in metaontolo-gy. * After having discussed Wyman’s (pseudo-)Meinongian ontological view (the tripartition: impossibilia aren’t and don’t exist, mere possibilia are but don’t exist, while actualia both are and exist), Quine 1948 adds a few comments on the logical alleged absurdities that follow from Wyman’s ‘lush’ ontology. Quine 1948: 4-5 attrib-utes to Wyman the following three claims: (1) Wyman thinks that contradictions are meaningless, i.e., they have a null content. (2) Wyman’s view (1) entails that proofs by reductio ad absurdum are invalid. (3) Wyman’s view (1) implies that there is not a procedure that is an effective test of meaningfulness, and that is worrying because every competent speaker thinks she always speaks meaningfully, and so without any strong self-reflection on what she says. After having succinctly presented Wyman’s meta-ontological background and the theoretical postulates of the apagogic way of reasoning, I will discuss in turn these three claims, especially I will discuss why and how (2) follows from (1). My main aim is to show how Wyman’s thesis (1) – albeit surely wrong (it is widely assumed amongst philosophers that contradictions are discriminable and convey some infor-mation, if so they probably should have some content) – is not a silly construction from Quine’s mind, but a philosophical position that is grounded on a cancellation view about negation (viz. not-A erases or cancels the semantic content of A). Why does Wyman – the caricatural ‘Meinongian strawman’ in Quine 1948 – think that all inconsistent sentences are meaningless? For ontological reasons: Wy-man takes it for granted that there are no impossibilia (in all senses of ‘there are’) for he thinks that every meaningful sentence or definite description must refer to something that is in some way (either as belonging to the realm of actualia, or to the ghostly realm of possibilia). Indeed, like McX but in a different fashion, Wyman sup-ports the Parmenidean-Platonic metaontology (Quine 1948: 1-2): every namelike syn-tagm – either a grammatical name like ‘Pegasus’ or a description that seems to be-have like a name as ‘the round square cupola on Berkeley College’ – functions as a referring or denoting term which needs to refer to something that exists in some sense (in a nutshell: meaning implies reference, reference implies existence, therefore meaning implies existence). So, if I can think or speak about something, then this thing must exist in some way or other. For Wyman, the conceivable, the meaningful and what is conflate as do the inconceivable, the meaningless and what is not. Impos-sibilia do not have any kind of being, so impossibilia are inconceivable and no mean-ingful thought or talk can be uttered about. Hence (1), impossible sentences (or sen-tences about impossibilia) must be meaningless. The worry is how (2) can be inferred from (1). Quine makes no explicit at-tempt to explain such an entailment. But an answer can be provided: Wyman is not only a heretic metaphysician (from Quine’s point of view) but also an unorthodox logician. My exegesis of the fictional position ascribed to Wyman by Quine 1948 is that the meaninglessness of contradictions (1) and the rejection of the proofs by re-ductio (2) are grounded on a particular view about negation: the cancellation view (see Routley & Routley 1985 on the three semantical views of negation). Indeed, the cancellation view of negation (<not> is an erasure-operation, viz. not-A cancels A) offers, first, an easy way to ostracize impossibilia, to exile them outside his ontological universe given that a contradiction A & not-A is void of se-mantic content, so says nothing; and, second, prima facie gives up the validity of reductio ad absurdum for nothing can be entailed by a contradiction (in virtue of a ‘Wittgensteinlike’ rule: “if an inferential move leads to content-collapse and nullifies contenthood, stop!”). So to speak, contradiction would be implosive (A & not-A en-tails nothing) rather than explosive (A & not-A entails everything). I shall discuss in length the relation between the cancellation view of negation and whether the reduc-tio ad absurdum is valid or not. The aim is to explain Quine’s objections and show that, in fine, they miss their target (Wyman can be a classical mathematician and agree with usual reductions ad absurdum, even if he understands reductio proofs in a non-classical way). If I have time, I will also discuss (3) and argue that Quine’s objection is un-successful for meaningfulness is not a syntactic property and cannot be reduced to a mechanical procedure (for this, I’ll borrow a lot from Routley and Goddard 1973’s logics of significance). * Insofar as the cancellation view of negation had been said to lead towards connexivism (see Routley 1978, 1989a; Routley et al. 1982; Routley & Routley 1985; and Priest 1999, but this point was criticized in Wansing & Skurt 2018 and, after-wards, Kapsner 2025), this talk shall offer a refinement in the history of connexivism, arguing that it was a logical position that, in fact, already appears in the most fa-mous paper on metaontology in contemporary philosophy. Throughout the talk, I’ll also want to show that Wyman’s conceptual scheme (composed of ontological claims about mere possibilia and logical non-classical views) was not merely fictional, but had some forerunners in past philosophy, namely in the Leibnizian-Wolffian tradition from the 17-18th centuries (especially, Baumgarten’s Metaphysics is ‘Wymanesque’ in many respects). Hence, interpreting Wyman’s view is not doing philosophical sci-fi, but shedding light on a real opposition between two philosophical positions that have had their defenders in the past, namely Quine’s extensionalist quantificational-ism and the ‘connexivist-friendly’ Leibnizian-Wolffian tradition.
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Marion, F. (2025). On Wyman’s Theory of the Meaninglessness of Contradictions: Cancellation View of Negation and Reductio ad Absurdum. 10th Workshop on Connexive Logics, Tohoku University, Sendai. https://hdl.handle.net/2078.5/260703