Conditional proof

About: Conditional proof is a research topic. Over the lifetime, 18 publications have been published within this topic receiving 424 citations.

Another Blow to Knowledge from Knowledge

Abstract: A novel argument is offered against the following popular condition on inferential knowledge: a person inferentially knows a conclusion only if they know each of the claims from which they essentially inferred that conclusion. The epistemology of conditional proof reveals that we sometimes come to know conditionals by inferring them from assumptions rather than beliefs. Since knowledge requires belief, cases of knowing via conditional proof refute the popular knowledge from knowledge condition. It also suggests more radical cases against the condition and it brings to light the underrecognized category of inferential basic knowledge.

On the function of consciousness

Abstract: In this paper I try to establish a conditional: if consciousness has a function then that function is not performed by any brain mechanism. As the reader will often find me making the assumption that consciousness has a function, I emphasize now that this is simply for conditional proof. In the first section I derive a principle of functional explanation which is the mainstay of my argument. This principle is a consequence of a familiar account of evolutionary function which I shall have to present. But, for the sake of brevity, I will simply state what is needed here, give an illustrative example and make comparative reference to the literature. In the second section I derive my main conclusion, in the final section I do so again but in the context of the Functionalist philosophy of mind.

Supervaluationism and good reasoning

Abstract: This paper is a tribute to Delia Graff Fara. It extends her work on failures of meta-rules (conditional proof, RAA, contraposition, disjunction elimination) for validity as truth-preservation under a supervaluationist identification of truth with supertruth. She showed that such failures occur even in languages without special vagueness-related operators, for standards of deductive reasoning as materially rather than purely logically good, depending on a context-dependent background. This paper extends her argument to: quantifier meta-rules like existential elimination; ambiguity; deliberately vague standard mathematical notation. Supervaluationist attempts to qualify the meta-rules impose unreasonable cognitive demands on reasoning and underestimate her challenge.

Liar-Like Paradox and Object-Language Features

Abstract: The key rules, T-elimination and T-introduc tion, play an important role in this reasoning. These (or similar rules, and/or conditional statements) are often taken to be character izing features of truth (or at least, of truth predicates). There are other ways to derive this contradiction from the Liar sentence given those key rules and standard logical principles: excluded middle provides another way, and going from (3) via conditional proof to "if s is true then s is not true," and then to "s is not true" by clavius is another way, and there are others still. Notice that the proof of the contradiction rests on no undischarged assumptions: if the rules are allowed in full generality with a strong enough logic, the inconsistent theorems are generated. Two features of object languages that tend to be blamed for Liar-like paradoxes are: (A) the object language's containing (some of) its own semantic predicate(s), and (B) the language's containing the means to refer to truth-bearers (sentences or propositions). However, it turns out to be far from clear that either of these (or their interaction) is straightforwardly to blame for Liar-like paradox. It is the purpose of this paper to show that Liar-like paradox can occur without either feature being present. Here is a classic motivating passage from Tarski (1944):

Conditionals and Curry

Abstract: Curry’s paradox for “if.. then..” concerns the paradoxical features of sentences of the form “If this very sentence is true, then 2 + 2 = 5”. Standard inference principles lead us to the conclusion that such conditionals have true consequents: so, for example, 2 + 2 = 5 after all. There has been a lot of technical work done on formal options for blocking Curry paradoxes while only compromising a little on the various central principles of logic and meaning that are under threat. Once we have a sense of the technical options, though, a philosophical choice remains. When dealing with puzzles in the logic of conditionals, a natural place to turn is independently motivated semantic theories of the behaviour of “if... then...”. This paper argues that a closest-worlds approach outlined in previous work offers a philosophically satisfying reason to deny conditional proof and so block the paradoxical Curry reasoning, and can give the verdict that standard Curry conditionals are false, along with related “contraction conditionals”.