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 arbitrary p and q, [(p ∨ q)] will count as part of the content of both p (...) and q. In other words, any arbitrary p and q share some common content. This notion of content has disastrous effects on, for instance, Carnap's attempts to explicate the notion of confirmation in terms of probabilistic favorable relevance, and Popper's 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. (shrink)

The following is an essay on the notion of scientific explanation as unification. In it a new notion of content is used to explicate Michael Friedman's notion of "k-atomicity," and to explicate the notion of the surplus content of hypothesis h relative to evidence e. From this basis an analysis of unification as theoretical reduction is advanced. A second notion of unification, unification as reconciling prima facie incompatible statements, is introduced again with the aid of this new notion of content. (...) More generally, it is argued that rather than seek the essence of scientific explanation we should carefully catalog the various distinct explanatory virtues. Finally it is argue that in particular philosophical explanations put a high premium on the quality of unification through showing how to make compatible seemingly irreconcilable claims. (shrink)

In his paper, "Explanations of Irrelevance" (1983), Paul Horwich proposes an amended version of hypothetico-deductivism, (H-D * ). In this discussion note it is shown that (H-D * ) has the consequence that "A is a non-black raven" confirms "All ravens are black" relative to any tautology! It is noted that Horwich's (H-D * ) bears a strong resemblance to Hempel's prediction criterion of confirmation and that the prediction criterion faces the same obstacle. A related problem for hypothetico-deductivism in its (...) simplest form--that is, E confirms H iff E is an (observational) consequence of H--is displayed. The discussion concludes with a suggestion about how (H-D * ) and simple hypothetico-deductivism might be amended in order to avoid these results. (shrink)

: Any precise version of H-D needs to handle various problems, most notably, the problem of selective confirmation: Precise formulations of H-D should not have the consequence that where S confirms T, for any T', S confirms T&T'. It is the perceived failure of H-D to solve such problems that has lead John Earman to recently conclude that H-D is "very nearly a dead horse". This suggests the following state of play: H-D is an intuitively plausible idea that breaks down (...) in the attempt to give it a precise formulation. Indeed I think that fairly captures the view among specialists in the field of confirmation theory. Here I argue that the truth about H-D is largely the reverse: H-D can be given a precise formulation that avoids the longstanding technical problems, however, it relies on a fundamentally unsound philosophical intuition. The bulk of this paper involves reviewing the problems affecting previous attempts at giving precise formulations of H-D and displaying some recent versions that can handle these problems. It then briefly explains why the basic intuition behind H-D is itself unsound, namely, because H-D involves a tacit assumption of inductive scepticism. Finally, the historical relation between H-D and the positivists' quest for a criterion of empirical significance will be reconsidered with the surprising result that having glossed H-D as fundamentally unsound it is concluded that a sound version of the criterion of empirical significance is now available. The demarcation criterion, the positivists' philosopher's stone that serves to separate claims with empirical significance from claims lacking empirical significance having finally been found, it is argued that we should regard empirical significance as just one among a variety of virtues and not follow the positivists in taking it to be a sin qua non for all meaningful statements. (shrink)

Christensen [Philosophy of Science, 50: 471–481, 1983] and [Philosophy of Science, 57: 644–662, 1990] provides two sets of counter-examples to the versions of bootstrap confirmation for standard first-order languages presented in Glymour [Theory and Evidence, Princeton University Press, Princeton, 1980] and [Philosophy of Science, 50: 626–629, 1983]. This paper responds to the counter-examples of Christensen [Philosophy of Science, 50: 471–481, 1983] by utilizing a new notion of content introduced in Gemes [Journal of Philosophical Logic, 26, 449–476, 1997]. It is claimed (...) that this response is better motivated and more effective than that presented in Glymour [Philosophy of Science, 50: 626–629, 1983]. It is then argued that while this response meets some of the counter-examples of Christensen [Philosophy of Science, 57: 644–662, 1990] two of those counter-examples, though not unanswerable, suggest the need for a substantial reformulation of the formal versions of bootstrapping. The essay proceeds with such a reformulation, arguing that this new formulation better fits the philosophical insights that originally motivated bootstrapping than do Glymour’s earlier formulations. In the concluding sections some alternative solutions to the problem posed by the Christensen counter-examples are discussed. (shrink)

This paper presents an outline of a new theory of relevant deduction which arose from the purpose of solving paradoxes in various fields of analytic philosophy. In distinction to relevance logics, this approach does not replace classical logic by a new one, but distinguishes between relevance and validity. It is argued that irrelevant arguments are, although formally valid, nonsensical and even harmful in practical applications. The basic idea is this: a valid deduction is relevant iff no subformula of the conclusion (...) is replaceable on some of its occurrences by any other formula salva validitate of the deduction. The paper first motivates the approach by showing that four paradoxes seemingly very distant from each other have a common source. Then the exact definition of relevant deduction is given and its logical properties are investigated. An extension to relevance of premises is discussed. Finally the paper presents an overview of its applications in philosophy of science, ethics, cognitive psychology and artificial intelligence. (shrink)

After presenting the major objections raised against standard formulations of the H-D method of theory testing, I identify what seems to be an important element of truth underlying the method. I then draw upon this element in an effort to develop a plausible formulation of the H-D method which avoids the various objections.

In Gemes (1990) I examined certain formal versions of hypothetico-deductivism (H-D) showing that they have the unacceptable consequence that "Abe is a white raven" confirms "All ravens are black"! In Gemes (1992) I developed a new notion of content that could save H-D from this bizarre consequence. In this paper, I argue that more traditional formulations of H-D also need recourse to this new notion of content. I present a new account of the vexing notion of the natural axiomatization of (...) a theory. The notion is used to construct a form of H-D that allows for the type of selective confirmation without which Glymour (1980a,b) claims H-D is hopeless. (shrink)

Alleged counter-examples deployed in Park [Erkenntnis 60: 229–240] against the account of selective hypothetico-deductive confirmation offered in Gemes [Erkenntnis 49: 1–20] are shown to be ineffective. Furthermore, the reservations expressed in Gemes [ibid] and [Philosophy of Science 62: 477–487] about hypothetico-deductivism are retracted and replaced with the conclusion that H-D is a viable account of confirmation that captures much of the practice of working scientists. However, because it cannot capture cases of inference to the best explanation and cases of the (...) observational confirmation of statistical hypotheses, it is concluded that H-D cannot supply a complete theory of confirmation. (shrink)

Philosophers of science, including the inductivist Carnap and the deductivist Popper, share the notion that the content of a proposition is given by its consequence class. I argue that this notion of content is unintuitive and inappropriate for many of the formal needs of philosophers of science. The basic problem is that given this notion of content, for any arbitrary p and q, $\lceil$p v q$\rceil$ will count as part of the content of both p and q. So any arbitrary (...) p and q share some common content! I present an alternative notion of content which better fits our intuitions about content and better serves the formal needs of philosophers of science. Essentially, this new notion of content demands that for p$\prime$ to be part of the content of q, p must not simply be a consequence of q, but that there must be no stronger consequence of q constructible in the vocabulary of p$\prime$. This, for instance, rules out $\lceil$p v q$\rceil$ as being part of the content of p, since p itself is a consequence of p stronger than q and constructible using only the vocabulary of $\lceil$p v q$\rceil$. In Chapter I the details of this account are developed for a series of formal languages. In Chapter II this new notion of content is used to define a new notion of confirmation called real confirmation. E really confirms h if and only if e is favorably relevant to every content part of h. It is argued that it is this notion of real confirmation, rather than mere Carnapian favorable relevance, that provides an appropriate explicandum for the notion of inductive confirmation. The remaining chapters examine other applications of this new notion of content; III, to the problem of giving a precise formulation of inductive scepticism; IV, to improving standard versions of hypothetico-deductivism and Glymour's bootstrapping account of confirmation; V, to an analysis of the alleged asymmetry of verification and falsification and Popper's early attempts to define verisimilitude; and VI, to Michael Friedman's attempts to explain explanation in terms of unification. (shrink)