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Selfreference and Logic
 Phi News
, 2002
"... Tarski's schema T plays a central role in each of these formalizations. a In particular, we show that each of the classical paradoxes of selfreference can be reduced to lIf the sentence is true, what it states must be the case. But it states that it itself is not true. Thus, if it is true, it is no ..."
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Tarski's schema T plays a central role in each of these formalizations. a In particular, we show that each of the classical paradoxes of selfreference can be reduced to lIf the sentence is true, what it states must be the case. But it states that it itself is not true. Thus, if it is true, it is not true. On the contrary assumption, if the sentence is not true, then what it states must not be the case and, thus, it is true. Therefore, the sentence is true iff it is not true. 2 Often cases of selfreference will fit into more than one of these categories. aTarski's schema T is the set of all firstorder logical equivalences T(rg TM)  g where g is any sentence and rg is a term denoting g. schema T. This leads us to a discussion of schema T, the problems it gives rise to, and how to circumvent these problems. The first part of the essay does not require any training in mathematical logic. Part I: SelfReference We start out by taking a closer look at paradoxes related to selfr
Vagueness and Truth
"... In philosophy of logic and elsewhere, it is generally thought that similar problems should be solved by similar means. This advice is sometimes elevated to the status of a principle: the principle of uniform solution. In this paper I will explore the question of what counts as a similar problem and ..."
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In philosophy of logic and elsewhere, it is generally thought that similar problems should be solved by similar means. This advice is sometimes elevated to the status of a principle: the principle of uniform solution. In this paper I will explore the question of what counts as a similar problem and consider reasons for subscribing to the principle of uniform solution. 1 Introducing the Principle of Uniform Solution It would be very odd to give different responses to two paradoxes depending on minor, seeminglyirrelevant details of their presentation. For example, it would be unacceptable to deal with the paradox of the heap by invoking a multivalued logic, ̷L∞, say, and yet, when faced with the paradox of the bald man, invoke a supervaluational logic. Clearly these two paradoxes are of a kind—they are both instances of the sorites paradox. And whether the sorites paradox is couched in terms of heaps and grains of sand, or in terms of baldness and the number of hairs on the head, it is essentially the same problem and therefore must be solved by the same means. More generally, we might suggest that similar paradoxes should be resolved by similar means. This advice is sometimes elevated to the status of a principle, which usually goes by the name of the principle of uniform solution. This principle and its motivation will occupy us for much of the discussion in this paper. In particular, I will defend a rather general form of this principle. I will argue that two paradoxes can be thought to be of the same kind because (at a suitable level of abstraction) they share a similar internal structure, or because of external considerations such as the relationships of the paradoxes in question to other paradoxes in the vicinity, or the way they respond to proposed solutions. I will then use this reading of the principle of uniform solution to make a case for the sorites and the liar paradox being of a kind.