Results

**1 - 3**of**3**### 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 ..."

Abstract
- Add to MetaCart

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, seemingly-irrelevant details of their presentation. For example, it would be unacceptable to deal with the paradox of the heap by invoking a multi-valued 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.

### Full text: 23,000 From Numerical Concepts to Concepts of Number

"... Abstract (Short version): Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe these abilities set the stage for later mathematics: the natural numbers and arithmetic. But the connection between these early and later skills is far from obv ..."

Abstract
- Add to MetaCart

Abstract (Short version): Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe these abilities set the stage for later mathematics: the natural numbers and arithmetic. But the connection between these early and later skills is far from obvious. We sketch what we think is the most likely model for infant abilities and argue that children could not extrapolate mature math concepts from these beginnings. We suggest instead that children may arrive at natural numbers by constructing mathematical schemas on the basis of innate abilities and math principles. Abstract (Long version): Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe these abilities set the stage for later mathematics: the natural numbers and arithmetic. But the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (a) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children’s understanding of number terms do not necessarily tap these concepts. (b) True