How to be Rational about being Right
Lord (2017) has rigorously demonstrated that what we are rationally required to do is just what we Ought to do. This conclusion nonetheless raises the question as to what exactly counts as Rationality. Do normative judgements made on the basis of, for example, inconsistency-tolerant logic, count as rational? Timothy Williamson (forthcoming) argues that they do not, because by rejecting classical logic we also reject the most basic principles of mathematical logic. This in turn cuts at the basis of identity, a necessary condition of meaning and intentional action.
Lord (Ibid.) commits to Reasons Responsiveness account of rationality, according to which “rationality consists in correctly responding to the normative reasons you possess, where the reasons you possess are the facts that count in favour of acts and attitudes that are within your ken.” While Reasons Responsiveness presupposes normativity it does not explicitly restrict rationality just to classical logic, consisting in the law of non-contradiction ¬(P ∧ ¬P), excluded middle (P ∨ ¬P), and identity (∃!P = P). Paraconsistent logic rejects the law of non-contradiction while many-valued logic rejects the law of excluded middle. In this article I consider whether these formal concession are compatible with Lord’s normative judgement about rationality.
In non-classical logic it may be that P = P is both true AND false (or perhaps takes some intermediate truth-value), in which case P is indefinite and the law of identity is implicitly rejected. In other words, some things are no longer unambiguously themselves. This result, which I call identity-nihilism, obtains irrespective of whether the principle of explosion applies or not. In practical terms, imagine the case where the defendant in legal proceedings is both guilty and not-guilty (or neither) of the same charge. While many-valued logic may possess the means of provisionally accomodating such problems on the basis of probabilistic truth-value or preponderance of evidence, paraconsistency precludes the possibility of persistent normalisation of truth and therefore of practical reasoning. As David Enoch (2015, 50) has noted, “normative truths [are] indispensable for the project of deliberating and deciding what to do", and deciding what to do is a constitutive condition of just being an agent.
This brings us to a serious, albeit less obvious, practical consideration: do normative claims based on feeling, intuition, desire, or more generally, on anything that relies on the premise of First Person Authority (FPA) count as rational? For example, when I say ‘I feel sad’, this may reflect a true belief of mine iff I really do feel sad, irrespective of how I may appear to be feeling from the perspective of others and irrespective of what the others feel. A true FPA belief seems intuitively rational in the classical sense, as it does not violate the classical laws of logic; it merely describes how I feel, or what I think, or what I want etc. On the other hand, the normative claim ‘it is cold (and therefore we should increase the temperature)’ does not follow from the purely descriptive statement ‘I feel cold (and I would like to increase the temperature)’. The inconsistency-tolerant Discursive Logic developed by Jaskowski (1969) maintains that contradictory subjective beliefs can be regarded as equally true in a discourse if they are independently true (modally) in different possible worlds. This construction does nothing to show that contradictory beliefs can be true in the same world, specifically, in the world where the discourse takes place. FPA kind of claims can never be normative (in any world) according to classical logic, because my FPA judgement may be contradicted by FPA judgement of another. FPA beliefs may also be incompatible with the ‘sense’ of normativity, as has been rigorously argued by Douglas Lavin (2004): “There is no normativity if you cannot be wrong.” Another way, my judgement cannot be subject to a principle if the principle is subject to my judgement.
Paraconsistent logic, on the other hand, aims to tolerate contradictions. If I feel hot and you feel cold then we are both (paraconsistently) right, therefore the room is simultaneously too hot and too cold, and we both have equality valid reasons to turn the heating down and up, respectively. This does not leave any logical space for deliberation and rational agreement about what to do. The claim of universal ‘validity’ of personal experience, feelings, preferences or desires invokes paraconsistency if the asserted ‘validity’ becomes the basis of normative judgement. If trans-gender self-identification, for example, is ‘valid’ in the sense that it grants the entitlement (and, reciprocally, the obligation) to be indetified and treated objectively as such, it also implicitly negates the normative authority of gender as an objective property, and thus the claim about validity of the original normative judgement is self-negating. The same objection can be directed at subjective ethical judgements: if a subjective ethical judgement can be normative irrespective of any external facts, then there are no normative ethical facts, therefore ethics is not normative, therefore contradiction. Normative claims based on subjective judgement entail paraconsistency in case of objective disagreement, which in turn entails non-sense. Bob Beddor (2018, 25) summarises the distinction between subjective and objective disagreement as follows: “whereas there are objective facts about objective disagreement, there are no objective facts about subjective disagreement, only objective facts about subjective disagreement ascriptions” which are not normative, because “there are no objective [FPA] facts over and above facts about the truth conditions for [FPA] ascriptions.”
The above considerations suggest that without classical rationality (apart perhaps from some well-structured exemptions from the law of excluded middle) there can be no objectivity and therefore no normative truths. Since we need normative truths about action in order to be agents (Ibid. Enoch), and we already are agents, then there are normative truths about action. It follows that we do have normative reasons to adhere to classical rationality if we intend to act for any reason and aim to reliably get what we want out of action. If classical rationality is the highest normative principle (there may be other normative principles, for example, empathy) then Truth consists of all possible propositions that are simultaneously coherent within a consistent conceptual system.
Beddor, Bob. Subjective Disagreement. Nous, 2018.
Enoch, David. Taking Morality Seriously. Oxford: Oxford University Press, 2011.
Jaskowski, S. Propositional Calculus for Contradictory Deductive Systems. Studia Logica, 1969.
Lavin, Douglas. Practical Reason and the Possibility of Error. Ethics, 2004.
Lord, Errol. What You’re Rationally Required to Do and What You Ought to Do (Are the Same Thing!). Mind, 2017.
Williamson, Timothy. Alternative Logics and Applied Mathematics. (Forthcoming)