Ken Gemes

A NEW THEORY OF CONTENT I: BASIC CONTENT

Philosophers of science as divergent as the inductivist Carnap and the deductivist Popper share the notion that the (logical) content of a proposition is given by its consequence class. I claim that this notion of content is (a) unintuitive and (b) inappropriate for many of the formal needs of philosophers of science. The basic problem is that given this notion of content, for any arbitraryp andq, ⌈(p Vq)⌉ will count as part of the content of bothp andq. In other words, any arbitraryp andq share some common content. This notion of content has disastrous effects on, for instance, Carnaps attempts to explicate the notion of confirmation in terms of probabilistic favorable relevance, and Poppers attempts to define verisimilitude. After briefly reviewing some of the problems of the traditional notion of content I present an alternative notion of (basic) content which (a) better fits our intuitions about content and (b) better serves the formal needs of philosophers of science.

A New Theory of Content II: Model Theory and Some Alternatives

This paper develops a semantical model – theoretic account of (logical) content complementing the syntactically specified account of content developed in “A New Theory of Content I”, JPL 23: 596–620, 1994. Proofs of Completeness are given for both propositional and quantificational languages (without identity). Means for handling a quantificational language with identity are also explored. Finally, this new notion of content is compared, in respect of both logical properties and philosophical applications, to alternative partitions of the standard consequence class relation proposed by Stelzner, Schurz and Wiengartner.

Verisimilitude and content

Popper’s original definition of verisimilitude in terms of comparisons of truth content and falsity content has known counter-examples. More complicated approaches have met with mixed success. This paper uses a new account of logical content to develop a definition of verisimilitude that is close to Popper’s original account. It is claimed that Popper’s mistake was to couch his account of truth and falsity content in terms of true and false consequences. Comparison to a similar approach by Schurz and Wiengartner show certain advantages of this new approach.

Nietzsche’s Illusion

It is sometimes claimed that Nietzsche’s primary focus was the problem of suffering. Against this, the central contention of this chapter is that Nietzsche’s focus was on the existential lack of meaning, which he took to be particular apposite to modern times. Thus, in contrast to Schopenhauer, for Nietzsche suffering as such was never the fundamental objection to life. The authors locate this position in the third essay of the Genealogy where Nietzsche remarks that ‘the meaninglessness of suffering, not suffering itself, was the curse thus far stretched over humanity’ (GM, III, 28), and argue that this is also the position of Nietzsche’s first published work, The Birth of Tragedy. The continuity between the early and later Nietzsche’s view is thus constituted in the import he gives to the question of meaning.

Irrelevance: Strengthening the Bayesian requirements

Bayesians standardly identify irrelevance with probabilistic irrelevance. However, there are cases where e is probabilistically irrelevant to h but intuitively e is relevant to h. For instance, ‘Die A came up 1 and die B came up 1, 3, 5 or 6’ is probabilistically irrelevant to ‘Die A came up odd and die B came up even’, yet, intuitively, it is not, irrelevant to that claim, in the sense that ‘Sydney has a harbour Bridge’ is irrelevant to it. In the context of decision making this notion of irrelevance combined with such rules as ‘Do not expend resources on irrelevant evidence’ leads to bad results. A stronger notion of irrelevance fitting our intuitions and the contexts of decision making is proposed: e is irrelevant to h if and only if every part of e is probabilistically irrelevant to every part of h. However, we need to take care in determining what counts as part of a statement.