The conference is hosted by the ERC-Starting Grant ‘Truth and Semantics’ (TRUST 803684) at the University of Bristol directed by Johannes Stern. It centers around two themes: truth and indeterminacy/vagueness (broadly construed). We investigate paradoxes related to these notions, non-classical logics or semantic frameworks that have been proposed for handling them, as well as the interconnections between theories of truth and theories of indeterminacy.
9.30: Conference opening and coffee.
9.45 - 11.00: Ken Akiba (Virginia Commonwealth University): The Boolean many-valued solution to the fission problem for personal identity.
11.00 - 11.15 Coffee.
11.15 - 12.30: Xinhe Wu (University of Bristol): Vague Identity: A Uniform Approach.
12.30 - 13.45: Lunch.
13.45 - 15.00: Andrea Iacona (University of Turin): Quantitative Supervaluationism.
15.00 - 15.15: Break.
15.15 - 16.30: Tedy Nenu (University of Bristol): The Practical-Fuzzy View of Vagueness.
16.30 - 16.45: Coffee.
16.45 - 18.00: Lavinia Picollo (National University of Singapore): Indeterminacy and Quantification.
It is simply mathematically incorrect to think that classical logic (in the deductive sense) must be bivalent (i.e., 2-valued) semantically, for there are various many-element Boolean algebras such as the 4-, 8-, 16-, …, infinite-element Boolean algebra, and any of those Boolean algebras can be a model for classical logic. Thus, we can combine classical logic with Boolean many-valued semantics to solve various philosophical problems. As an instance of this general strategy, I will present the Boolean many-valued solution to the fission problem for personal identity. I will offer a many-valued Boolean model that makes the following statement true: Person A (who goes into surgery) is identical with one of B, C, D, … (who come out of the surgery with A’s memory), but it is indeterminate which one.
There are numerous apparent examples of vague identity, i.e. examples where two objects appear to be neither determinately identical nor determinately distinct. Philosophers disagree on whether the source of vagueness in identity is semantic or ontic/metaphysical. In this talk, I explore the use of Boolean-valued models as a many-valued semantic framework for identity. I argue that this semantics works well with both a semantic and ontic conception of vague identity. I also discuss, in the context of Boolean-valued logic, responses to the Evans’ argument under the two conceptions.
So far the method of supervaluations has been mainly employed to provide an account of truth, understood as a non-gradable property. But it is also possible, and arguably at least as plausible, to define a gradable property in terms of the same method. In my talk I will presents a supervaluationist semantics that is quantitative rather than qualitative. As I will show, there are at least two distinct interpretations of the semantics — one alethic, the other epistemic — which can coherently be applied to key issues such as vagueness and future contingents.
The phenomenon of vagueness contaminates each and every proposal advanced by formal semanticists. My aims for this talk are threefold. First, I want to advance a modest hypothesis based on Kahneman’s (1973, 2011) dual-process theory of thought that sets out to explain the psychological appeal of the soritical premisses. Second, I want to present some shortcomings of classical approaches to vagueness in light of the special sciences. Both classical and non-classical approaches will turn out to be particularly vulnerable to Michael Tye’s (2021) recent vagueness-related paradox of phenomenality. Lastly, I want to make the case that, despite the usual philosophical objections, there are strong practical reasons for carrying out the formal semantics of natural languages in fuzzy frameworks.
A folk argument purports to establish the determinacy of a universal claim about the natural numbers from the determinacy of each of its instances. I argue that this reasoning is misguided by noting that, on plausible semantic and metasemantic assumptions, general statements have neither substitutional nor objectual truth-conditions — their truth-values do not supervene on the truth-values of their instances. I then point out that the gap between a generalization and its instances simply cannot be bridged, from which I conclude that arithmetic is essentially indeterminate.
The notion of metainference and of metainferential validity gained popularity in the discussion in Philosophical Logic in the last decade. Part of the interest relies on the study of Strong Kleene logics and their application to paradoxes. The aim of this talk is highlighting the proper way to understand metainferential validity and also showing the usefulness of semantic tableaux, aka. analytic trees, in the study of these logics both at the inferential and metainferential level.
I introduce a form of non-classical supervaluation in which the set of admissible precisifications are partial models to provide truth-conditions for restricted quantifiers and a conditional expressing (a form of) material implication. This semantics can be used to construct naive truth models, but can also be applied to the Sorites paradox.
Knowing a proposition’s semantic status can give us a useful guide to what to believe. There are a number of views that make this connection. A prominent view is that belief aims at truth. Another, stronger, view is that truth is internal to the power of belief. It’s less clear what one ought to believe towards indeterminate propositions, and whether we should treat indeterminacy as a semantic status or as capturing some distinct phenomena. Williams (2012) presents a wide range of examples of indeterminacy, and it is unclear whether they are all latching onto the same semantic status. Paradigmatic examples of vagueness can illustrate this tension. Consider a patch of paint which I will call “Patchy”, where it is indeterminate whether Patchy is red or orange. Is Patchy red? On some accounts of vagueness, it is true that Patchy is red (e.g. epistemicism). On other accounts of vagueness, it may fall into some third semantic category (e.g. on a many-valued logic approach), or on others, it may lack semantic status (e.g. supervaluationism). Yet all of these accounts agree that Patchy is an example of indeterminacy/ borderline colour. What ought one to believe towards the question of whether Patchy is red? If I ought to only believe what is true, how can I take an attitude towards “Patchy is red”? It seems we have a dilemma: Either “Patchy is red” is true (and the truth norm doesn’t provide guidance) or “Patchy is red” is neither true nor false (and the truth norm is not general). In this talk, I argue that regardless of one’s view on semantic status, we should look to the phenomena of indeterminacy to guide our belief. In particular, I argue that in some cases we ought to prescribe certain attitudes to have towards cases like Patchy, regardless of one’s preferred solution to vagueness. Thus, truth as a general guide to rational attitudes seems debunked, and the central importance of truth to belief seems undermined.
The semantic and property-theoretic paradoxes provide one motivation for restricting classical logic. Vagueness provides another. In both cases the motivation can be resisted, but if one goes along with it, then an initially attractive non-classical logic for both purposes is Lukasiewicz continuum-valued logic (“fuzzy logic”). But a deeper look shows that in neither case does this logic satisfy the motivations for going non-classical. The reason is similar in both cases. I’ll sketch a generalization of the logic that avoids the problem and seems like an attractive way to go non-classical.
For all further questions about the conference please contact Xinhe Wu.