This book is dedicated to a classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal (...) logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics". (shrink)

KEY TO FOOTNOTE ABBREVIATIONS MM-P. Structure Phenomenology Sense Praise Signs Visible Themes Humanism Primacy Maurice Merleau-Ponty The Structure of ...

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.

Theories of Truth provides a clear, critical introduction to one of the most difficult areas of philosophy. It surveys all of the major philosophical theories of truth, presenting the crux of the issues involved at a level accessible to nonexperts yet in a manner sufficiently detailed and original to be of value to professional scholars. Kirkham's systematic treatment and meticulous explanations of terminology ensure that readers will come away from this book with a comprehensive general understanding of one of philosophy's (...) thorniest set of topics. -/- Included are discussions of the correspondence, coherence, pragmatic, semantic, performative, redundancy, appraisal, and truth-as-justification theories. There are also chapters or sections of chapters on the liar paradox, three-valued logic, Field's critique of Tarski, Davidson's program, Dummett's theory of linguistic competence, satisfaction, recursion, the extension/intension distinction, and an explanation of how theories of justification, properly understood, differ from theories of truth. -/- A persistent theme is that philosophers have too often failed to recognize that not all theories of truth are intended to answer the same question. When the various questions are made distinct, it is apparent that many of the "debates" in this field are really cases of philosophers talking past one another. There is much less disagreement within the field than has commonly been thought. (shrink)

In a number of essays published over the last decade or so, W. V. Quine has made some interesting suggestions concerning the ontology of theories. If I understand him correctly, one of his principal objects has been to formulate a criterion by means of which one can correctly decide what are the ontological commitments of any given theory. My aim in this paper is to reveal what I think are inadequacies in Quine's criterion and to indicate the direction in which (...) a proper formulation lies. (shrink)

The claim that visually masked, unidentifiable words are analyzed at the level of whole word meaning has been challenged by recent findings indicating that instead, analysis occurs mainly at the subword level. The present experiments examined possible limits on subword analysis. Experiment 1 obtained semantic priming from pleasant- and unpleasant-meaning subliminal words in which no individual letter contained diagnostic information about a word’s evaluative valence; thus analysis must operate on information more complex than that contained in individual letters. Experiments 2 (...) and 3 showed that analysis must operate on information more complex than that represented by individual bigrams or trigrams . These findings suggest that while subliminal priming is driven by subword analysis, the effective units of analysis are distributed widely across at least short words. (shrink)

Peter Geach has said that Russell's use of ‘propositional function’ is ‘hopelessly confused and inconsistent’. Geach is right, and attempts to say what exactly a Russellian propositional function is, or is supposed to be, are bound to end in frustration. Nevertheless, it may be worthwhile to pursue an account of propositional functions that accommodates a good deal of what Russell says about them and that can provide some of what he expected of them.

The critics of Schleiermacher's hermeneutic are legion and its defenders few – due, to a great extent, to the popularity of Gadamer's Truth and Method and its attack on Schleiermacher. I believe that the critics of Schleiermacher have not understood him very well and the failure of his hermeneutics to gain very much respect lies, at least partially, to a lack of understanding of what he had to say. Besides, if we look at contemporary scholars who focus on the study (...) of language and how it functions we will find that they often have views very much like those found in Schleiermacher's discussion of hermeneutics. (shrink)

I defend mereological nihilism, the view that there are no composite objects, against a challenge from ontological emergence, the view that some things have properties that are ‘something over and above’ the properties of their parts. As the nihilist does not believe in composite wholes, there is nothing in the nihilist's ontology to instantiate emergent properties – or so the challenge goes. However, I argue that some simples can collectively instantiate an emergent property, so the nihilist's ontology can in fact (...) accommodate emergent properties. Furthermore, I show that employing plural instantiation does not bloat the nihilist's ontology or ideology. (shrink)

In a recent book, J. R. Lucas presents an argument to show that if God has infallible knowledge of the future, our will is not free. Thus, Lucas concludes, like the medieval Jewish philosopher Gersonides, that God in creating beings with genuinely free will, abdicates some of his omniscience as well as some of his omnipotence. God could, but will not, determine our choices, since such an exercise of his power would rob us of free will. Similarly, Lucas holds, God (...) could but does not foreknow our future choices since this also would rob us of free will. This argument, from so formidable a foe of determinism as Lucas, merits our most serious attention. However, I believe that there is a way to evade its conclusion, a way which Lucas considers but rejects. (shrink)

In a recent paper in Psychological Science, Kouider and Dupoux reported obtaining unconscious Stroop priming only when subjects had partial awareness of the masked distractor words . Kouider and Dupoux conjectured that semantic priming occurs only when such partial awareness is present. The present experiments tested this conjecture in an affective categorization priming task that differed from Kouider and Dupoux’s in using masked distractors that subjects had practiced earlier as visible words. Experiment 1 showed priming from practiced words when subjects (...) had no partial awareness of those words. Experiment 2 showed that, in the absence of partial awareness, practiced words yielded priming but not-practiced words did not. Experiment 3 corroborated Experiment 1 and 2s results using a different test of partial awareness. These results suggest that unconscious processing of subword elements drives masked semantic priming by practiced words. (shrink)

This important volume explores alternative ways in which those involved in the field of speech communication have attempted to find a philosophical grounding for rhetoric. Recognizing that rhetoric can be supported in a wide variety of ways, this text examines eight different philosophies of rhetoric: realism, relativism, rationalism, idealism, materialism, existentialism, deconstructionism, and pragmatism. The value of this book lies in its pluralistic and comparative approach to rhetorical theory. Although rhetoric may be the more difficult road to philosophy, the fact (...) that it is being traversed by a group of authors largely from speech communication demonstrates important growth in this field. Ultimately, there is recognition that if different thinkers can have solid reasons to adhere to disparate philosophies, serious communication problems can be eliminated. _Rhetoric and Philosophy_ will assist scholars in choosing from among the many philosphical starting places for rhetoric. (shrink)