Gottlob Freg was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of languageand philosophical logic. He is generally seen as one of the fathers of the analytic method, which dominated philosophy in English-speaking (...) countries for most of the twentieth century. His work is studied today not just for its historical importance, but also because many of his ideas are relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research. (shrink)
The paper is concerned with the idea that the world is the totality of facts, not of things – with what is involved in thinking of the world in that way, and why one might do so. It approaches this issue through a comparison between Wittgenstein’s Tractatus and the identity theory of truth proposed by Hornsby and McDowell.The paper’s positive conclusion is that there is a genuine afﬁnity between these two. A negative contention is that the modern identity theory is (...) vulnerable to a complaint of idealism that the Tractatus can deﬂect. (shrink)
A way of reading the Tractatus has been proposed which, according to its advocates, is importantly novel and essentially distinct from anything to be found in the work of such previously influential students of the book as Anscombe, Stenius, Hacker or Pears. The point of difference is differently described, but the currently most used description seems to be Goldfarb’s term ‘resolution’ – hence one speaks of ‘the resolute reading’. I’ll shortly ask what resolution is. For now, it is enough that (...) it aims to give full weight to the penultimate section of the Tractatus in which Wittgenstein declares his propositions to be nonsense, where giving full weight to that declaration involves not hearing it as allowing that those ‘nonsensical’ propositions might have another kind of ‘sense’. In that same section Wittgenstein explains that these nonsense propositions, while devoid of meaning, have a use: to make the kind of use of them that their author intends – and so to understand him – requires recognizing that they are nonsense; and through that recognition one ‘surmounts’ these propositions, and is led ‘to see the world aright’. So there is a point to all this nonsense. What point? (shrink)
In 'On the nature of truth and falsehood' Russell offers both a multiple relation theory of judgment and a correspondence theory of truth. It has been a prevailing understanding of the Tractatus that Wittgenstein rejects Russell’s multiple relation idea but endorses the correspondence theory. Ramsey took the opposite view. In his 'Facts and Propositions', Ramsey endorses Russell’s multiple relation idea, rejects the correspondence theory, and then asserts that these moves are both due to Wittgenstein. This chapter will argue that Ramsey’s (...) ascriptions are both correct. The extent of the agreement between Ramsey and Wittgenstein will be argued, moreover, to count definitively against standard understandings of Ramsey as a redundancy theorist of truth. Wittgenstein is no correspondence theorist and Ramsey is no redundancy theorist; rather, both philosophers offer identity theories of truth. (shrink)
Wittgenstein presents in the Tractatus a variable purporting to capture the general form of proposition. One understanding of what Wittgenstein is doing there, an understanding in line with the ‘new’ reading of his work championed by Diamond, Conant and others, sees it as a deflationary or even an implosive move—a move by which a concept sometimes put by philosophers to distinctively metaphysical use is replaced, in a perspicuous notation, by an innocent device of generalization, thereby dispersing the clouds of philosophy (...) that formerly surrounded the concept. By asking how Wittgenstein supposed his variable to work, and what work he imagined it was fit for, the paper questions the adequacy of that understanding. (shrink)
Wittgenstein, in the Tractatus, conceives the world as ‘the totality of facts’. Type-stratiﬁcation threatens that conception : the totality of facts is an obvious example of an illegitimate totality. Wittgenstein’s notion of truthoperation evidently has some role to play in avoiding that threat, allowing propositions, and so facts, to constitute a single type. The paper seeks to explain that role in a way that integrates the ‘philosophical’ and ‘technical’ pressures on the notion of an operation.
Three-dimensional seismic data in southwestern Pennsylvania in the Appalachian Plateau demonstrate that the structural style in the Devonian section is dominated by east-vergent folds and reverse faults, which contrasts with that in the Valley and Ridge Province where west-vergent folds and thrusts dominate. Vertical variations in fold curvature and fault throw indicate that the intensity of shortening increases from the Salina to the Onondaga and then decreases from the Onondaga to the Elk. Lateral variations in fold curvature and fault throw (...) indicate that the folds and faults tend to propagate in the cross-strike and along-strike directions. Isochron thickness below the Onondaga increases on the anticlinal, up-thrown side of the faults, whereas isochron thickness above the Onondaga increases to the synclinal, down-thrown side of the faults. In concert with seismic structure and isochron thickness, seismic facies see vertical and lateral variations that are spatially and temporally related to folds and faults. Four years of gas production data from the Middle Devonian Marcellus Shale show that the gas productivity drops near the regional reverse faults, whereas regional drilling patterns from a broader perspective of the Plateau reveal operational gaps near major cross-regional wrench faults. These observations are indicative of the dynamic interplay among hinterland-vergent detachment deformation, syntectonic sedimentation, and shale gas preservation during the Acadian. (shrink)
Kant's introduction of a distinctive form of philosophical investigation and proof, known as transcendental, inaugurated a new philosophical tradition. Transcendental Philosophy and Naturalism assesses the present state and contemporary relevance of this tradition. The contributors aim to understand the theoretical structures involved in transcendental explanation, and to assess the contemporary relevance of the transcendental orientation, in particular with respect to contemporary philosophical naturalism. These issues are approached from both naturalistic and transcendental perspectives.
Crispin Wright and Bob Hale have defended the strategy of defining the natural numbers contextually against the objection which led Frege himself to reject it, namely the so-called ‘Julius Caesar problem’. To do this they have formulated principles (called sortal inclusion principles) designed to ensure that numbers are distinct from any objects, such as persons, a proper grasp of which could not be afforded by the contextual definition. We discuss whether either Hale or Wright has provided independent motivation for a (...) defensible version of the sortal inclusion principle and whether they have succeeded in showing that numbers are just what the contextual definition says they are. (shrink)
0. My aims in this paper are largely expository: I am more interested in presenting the picture theory than deciding its truth. Even so, I hope that the arguments by which I develop the theory will do something to support it, since I believe that what I will present as Wittgenstein's view is indeed the truth. This is not an admission of insanity, though some things that have been thought intrinsic to the picture theory are things it would be insane (...) to believe. So clearly the view I will present, when compared to the most embracing interpretations, is a partial and selective one. It would be another kind of madness, one I am just as eagre to disown, to suppose that my own favoured selection is the only possible one. That is pretty well the last remark in this paper about other commentators. I trust my reticence entitles me to be presumed catholic until proven nonconformist. (shrink)
[A. W. Moore] There are criteria of ineffability whereby, even if the concept of ineffability can never serve to modify truth, it can sometimes serve to modify other things, specifically understanding. This allows for a reappraisal of the dispute between those who adopt a traditional reading of Wittgenstein's Tractatus and those who adopt the new reading recently championed by Diamond, Conant, and others. By maintaining that what the nonsense in the Tractatus is supposed to convey is ineffable understanding, rather than (...) ineffable truth, we can do considerable justice to each of these readings. We can also do considerable justice to the Tractatus. /// [Peter Sullivan] Moore proposes to cut between 'traditional' and 'new' approaches to the Tractatus, suggesting that Wittgenstein's intention is to convey, through the knowing use of nonsense, ineffable understanding. I argue, first, that there is indeed room for a proposal of Moore's general kind. Secondly, though, I question whether Moore's actual proposal is not more in tune with Wittgenstein's later thought than with the attitude of the Tractatus. (shrink)
Nine of the papers collected here derive directly from a conference organized by Schirn in Munich in 1991. Seven others, three of them reprinted, have been intelligently chosen to complement the original nine. The collection has no overarching theme, nor is it dominated by any particular approach to Frege’s thought. It is “a mixed selection”, and aims to reflect “the prevailing tendency in current Frege scholarship”. The influence of Dreben is less in evidence than one might expect, but otherwise the (...) collection meets that broad brief pretty well. Some of the collection’s best papers—for example, those by Burge, Boolos, Dummett, Heck, and Terence Parsons—are essential reading. Inevitably, not all the others have that standing. But, excepting only an over-long essay by the editor, each deserves its place. (shrink)
But logic as it stands, e.g. in Principia Mathematica, can quite well be applied to our ordinary propositions; e.g. from ‘All men are mortal’ and ‘Socrates is a man’ there follows according to this logic ‘Socrates is mortal’, which is obviously correct, even though I equally obviously do not know what structure is possessed by the thing Socrates or the property of mortality. Here they just function as simple objects.
At the age of 20, and fresh from his undergraduate studies in mathematics, Ramsey set about writing what would be his first substantial publication, his 1923 Critical Notice of Wittgenstein’s Tractatus. It is hard for modern students of that book, who negotiate its obscurities with generations of previous commentary to serve as guides, to appreciate the task Ramsey confronted; and, to the extent that one can appreciate it, it is hard not to feel intimidated by the brilliance of his success. (...) His Critical Notice made Ramsey the first of Wittgenstein’s interpreters.1 In my view it makes him, still, the best. I want to illustrate that here by considering what light his remarks cast on a single passage of the book, in which Wittgenstein advances what might be called his theory of judgement. (shrink)
Quine made it conventional to portray the contradiction that destroyed Frege’s logicism as some kind of act of God, a thunderbolt that descended from a clear blue sky. This portrayal suited the moral Quine was antecedently inclined to draw, that intuition is bankrupt, and that reliance on it must therefore be replaced by a pragmatic methodology. But the portrayal is grossly misleading, and Quine’s moral simply false. In the person of others – Cantor, Dedekind, and Zermelo – intuition was working (...) pretty well. It was in Frege that it suffered a local and temporary blindness. The question to ask, then, is not how Frege was overtaken by the contradiction, but how it is that he didn’t see it coming. The paper offers one kind of answer to that question. Starting from the very close similarity between Frege’s proof of infinity and the reasoning that leads to the contradiction, it asks: given his understanding of the first, why did Frege did not notice the second? The reason is traced, first, to a faulty generalization Frege made from the case of directions and parallel lines; and, through that, to Frege’s having retained, and attempted incoherently to combine with his own, aspects of a pre-Fregean understanding of the generality of logical principles. (shrink)
Ever since the publication of 'Truth' in 1959 Sir Michael Dummett has been acknowledged as one of the most profoundly creative and influential of contemporary philosophers. His contributions to the philosophy of thought and language, logic, the philosophy of mathematics, and metaphysics have set the terms of some of most fruitful discussions in philosophy. His work on Frege stands unparalleled, both as landmark in the history of philosophy and as a deep reflection on the defining commitments of the analytic school.This (...) volume of specially composed essays on Dummett's philosophy presents a new perspective on his achievements, and provides a focus for further research fully informed by the Dummett's most recent publications. Collectively the essays in philosophy of mathematics provide the most sustained discussion to date of the role of Dummett's diagnosis of the root of the logico-mathematical paradoxes in his case for an intuitionist revision of classical mathematics. The themes of other essays include a fundamental challenge to Dummett's Fregean understanding of predication, and a criticism of his case for logical revision outside of mathematics. (shrink)
High-quality 3D seismic data in Clearfield County, central Pennsylvania, reveal subsurface structural details of regional flat-top, box-shaped folds, convergent reverse faults and cross-regional lineaments in the hinge of the Pennsylvanian Salient. Cross-stratal variations in structural relief, bed curvature and seismic facies indicate that the intensity of deformation increases from below the Salina to the Onondaga, and then decreases from above the Onondaga to the Elk. Pre-Onondaga isochron thickness increases on the anticlinal axes, whereas post-Onondaga isochron thickness decreases on the anticlinal (...) axes. The seismically imaged subsurface structures are consistent with outcrop and topographic observations, wireline and FMI image logs and gravity and magnetic intensity measurements. Marcellus Shale gas exploration and production data show that the operational activity and gas productivity drop significantly in Clearfield County and other counties in the hinge of the Salient. We interpret that the regional and cross-regional lineaments folds and faults are a salt-based detachment and wrench faults that were most likely caused by gravitational sliding above the Salina salt during the Acadian. We infer that the co-occurrence of large-scale faults, particularly the cross-regional wrench faults, might have had a significant impact on the Marcellus Shale reservoir integrity and gas productivity in the hinge of the Pennsylvania Salient. These observations and interpretations demonstrate the dynamic interplay among tectonic deformation, syntectonic deposition and shale gas production, thus entailing significant geologic, economic and environmental implications in the Appalachian Basin. (shrink)
High-quality 3D seismic data in Clearfield County, central Pennsylvania, reveal subsurface structural details of regional flat-top, box-shaped folds, convergent reverse faults, and cross-regional lineaments in the hinge of the Pennsylvanian salient. Cross-stratal variations in structural relief, bed curvature, and seismic facies indicate that the deformational intensity increases from below the Salina to the Onondaga and then decreases from the Onondaga to the Elk. The pre-Onondaga isochron thickness sees an increasing trend but the post-Onondaga isochron thickness sees a decreasing trend on (...) the anticlinal axes. The seismically imaged subsurface structures are consistent with outcrop and topographic observations, wireline and formation microimager logs, and gravity and magnetic intensity measurements. The Marcellus Shale gas exploration and production data indicate that the operational activity and gas productivity drop significantly in Clearfield County and other counties in the hinge of the Pennsylvanian salient. We interpret that the regional folds and faults and cross-regional lineaments are detachment and wrench faults that were most likely caused by gravitational sliding above the Salina during the Acadian. We infer that the co-occurrence of the regional and the cross-regional faults, particularly the cross-regional wrench faults, might have had a significant impact on the Marcellus Shale reservoir integrity and gas productivity in the hinge of the Pennsylvania salient. These observations and interpretations demonstrate the dynamic interplay among tectonic deformation, syntectonic deposition, and shale gas retention, thus entailing significant geologic, economic, and environmental implications in the Appalachian Basin. (shrink)
Self‐evidently the standard work on the topic its whole title defines, Sir Michael Dummett’s Frege: Philosophy of Mathematics (FPM) is also the most profound and creative discussion in recent decades of the problems confronting the branch of philosophy mentioned after the colon. Chapters 14‐18 and 23‐24 of this book constitute a continuous and challenging diagnosis of these problems.1 They culminate in the proposal that these problems present an impasse that can be escaped only by adopting a constructivist understanding of mathematical (...) generality. Dummett’s case for that conclusion is no less complexly over‐layered than the problems themselves. By contrast my aims in this discussion of his case are limited in various ways, and three of these should be mentioned straightaway. In the first place, I will aim to consider a case that, if sound, would warrant a constructivist understanding of generality in mathematics generally (and so I will not be considering lines of argument specific to set theory, or to those parts of mathematics plausibly dependent on notions intrinsic to set theory). Secondly, I aim to consider a case which, while general in its application within mathematics, is not more general than that (and so would not warrant a broader anti‐realism). Reasons for these first two limitations are discussed in section 1. A third limitation is that I will aim only to understand Dummett’s case, and not to assess it. Perhaps some will think this third limitation calls for explanation or excuse. I think it needs no excuse and that the explanation is obvious. When we are dealing with fundamentally important work by a great philosopher, understanding is often ambition enough. In Michael Dummett’s work, that is what we are dealing with. (shrink)
Define ‘het’ as a predicate that truly applies to itself if and only if it does not truly apply to itself and which also truly applies to any predicate that does not truly apply to its own name. We know that the attempted definition of ‘hes’ is a failure, and so a fortiori is that of ‘het’. Similarly, there is no Qussell class which contains itself as a member if and only if it does not contain itself as a member, (...) so a fortiori there is no Russell Class which contains itself as a member if and only if it does not contain itself as a member and which also contains all and only non-self-membered classes (such as the class of dogs). The second conjunct in both the definition of ‘het’ and of the Russell class cannot revive a definition doomed to failure. Likewise, the ‘definition’ of n as ‘n > 1 iff n < 1’ fails, and the attempted definition of m as ‘m > 1 iff m < 1 and m is prime’ is hopeless too; its final clause buys it no respectability. (shrink)
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