Online research in philosophy

Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell’s Paradox, Burali-Forti’s Paradox, Mirimanoff’s Paradox, König’s Paradox, Berry’s Paradox, Richard’s Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell’s Schema: there is a property φ and function δ such that..

The paradox of analysis has been a problem for analytic philosophers at least since Moore’s time, and it is especially significant for those who seek an account of analysis along classical lines. The present paper offers a new solution to the paradox, where a theory of analysis is given where (1) analysandum and analysans are distinct concepts, due to their failing to share the same conceptual form, yet (2) they are related in virtue of satisfying various semantic constraints on the analysis relation. Rather than distinguish between analysandum and analysans by appeal to epistemic considerations, the paper appeals to semantic considerations in giving a candidate account of the identity conditions for concepts. The distinctness of analysandum and analysans then serves to block the paradox in a straightforward way.

The epistemological problems of unification of two distinct theories are discussed. An approach related to the work of Soviet authors (Stepin, Podgoretzky and Smorodinsky) is used and developed. The notion of ‘crossbred objects’—theoretical objects with contradictory properties which are part of the domain of application of two independent theories—is introduced which helps to describe the dynamics of revolutionary theory change. The occurrence of the cross-contradiction of two theories is reconstructed and the reductionistic and the synthetic means of its elimination are proposed. The results of the methodological analysis are applied to the paradox of equivalence.

We identify a class of paradoxes that are neither set-theoretical or semantical, but that seem to depend on intensionality. In particular, these paradoxes arise out of plausible properties of propositional attitudes and their objects. We try to explain why logicians have neglected these paradoxes, and to show that, like the Russell Paradox and the direct discourse Liar Paradox, these intensional paradoxes are recalcitrant and challenge logical analysis. Indeed, when we take these paradoxes seriously, we may need to rethink the commonly accepted methods for dealing with the logical paradoxes.

To solve the highly counterintuitive paradox of confirmation represented by the statement, “A pair of red shoes confirms that all ravens are black,” Hempel employed a strategy that retained the equivalence condition but abandoned Nicod’s irrelevance condition. However, his use of the equivalence condition is fairly ad hoc, raising doubts about its applicability to this problem. Furthermore, applying the irrelevance condition from Nicod’s criterion does not necessarily lead to paradoxes, nor does discarding it prevent the emergence of paradoxes. Hempel’s approach fails to adequately resolve the paradox.

We prove the following algebraic characterization of elementary equivalence: $\equiv$ restricted to countable structures of finite type is minimal among the equivalence relations, other than isomorphism, which are preserved under reduct and renaming and which have the Robinson property; the latter is a faithful adaptation for equivalence relations of the familiar model theoretical notion. We apply this result to Friedman's fourth problem by proving that if L = L ωω (Q i ) i ∈ ω 1 is an (ω 1 , ω)-compact logic satisfying both the Robinson consistency theorem on countable structures of finite type and the Löwenheim-Skolem theorem for some $\lambda for theories having ω 1 many sentences, then $\equiv_L = \equiv$ on such structures.

The very idea of informative analysis gives rise to a well-known paradox. Yet a parallel puzzle, herein called the paradox of synonymy, arises for statements which do not express analyses. The paradox of synonymy has a straightforward metalinguistic solution: certain words are referring to themselves. Likewise, the paradox of analysis can be solved by recognizing that certain expressions in an analysis statement are referring to their own semantic structures.

An attempt is made to provide a statement of the sufficient conditions for the functional equivalence of observable events in Psychology. Without a statement of those conditions, no explanation of functional equivalence in empirical situations can be achieved. A characterization of functional equivalence strictly in terms of the traditional S-R language is examined. This characterization is found to be inappropriate in that it entails vacuous mediators. A revision of S-R language is attempted in order to characterize functional equivalence. While this account does not entail vacuous mediators, it is unsatisfactory since it cannot be stated naturally in terms of the S-R language. It is argued that the degree to which the conditions for functional equivalence can be appropriately and naturally stated in theoretical languages provides a criterion for choosing among them as theoretical languages for psychology. A statement of the conditions for functional equivalence in terms of a TOTE analysis (see [5]) is then given. This is found to be more satisfactory than both the traditional and modified S-R analyses in that it does not entail vacuous mediators and in that a natural characterization of functional equivalence can be achieved.

The thesis of 3D/4D equivalence states that every three-dimensional description of the world is translatable without remainder into a four-dimensional description, and vice versa. In representing an object in 3D or in 4D terms we are giving alternative descriptions of one and the same thing, and debates over whether the ontology of the physical world is "really" 3D or 4D are pointless. The twins paradox is shown to rest, in relativistic 4D geometry, on a reversed law of triangle inequality. But considering the twins as 3D beings who age through time, the paradox implies that time passes at different rates in different reference frames, and therefore that the concept of a single global or Absolute time is unsustainable.