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Profile: Peter Jonathan Friedich Alan Emmanuel Smith
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Profile: Peter Smith (Cambridge University)
  1.  137 DLs
    Peter Smith (1998). Approximate Truth for Minimalists. Philosophical Papers 27 (2):119-128.
  2.  130 DLs
    Peter Smith (1998). Approximate Truth and Dynamical Theories. British Journal for the Philosophy of Science 49 (2):253-277.
    Arguably, there is no substantial, general answer to the question of what makes for the approximate truth of theories. But in one class of cases, the issue seems simply resolved. A wide class of applied dynamical theories can be treated as two-component theories—one component specifying a certain kind of abstract geometrical structure, the other giving empirical application to this structure by claiming that it replicates, subject to arbitrary scaling for units etc., the geometric structure to be found in some real-world (...)
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  3.  117 DLs
    Luca Incurvati & Peter Smith (2010). Rejection and Valuations. Analysis 70 (1):3 - 10.
    Timothy Smiley's wonderful paper 'Rejection' (Analysis 1996) is still perhaps not as well known or well understood as it should be. This note first gives a quick presentation of themes from that paper, though done in our own way, and then considers a putative line of objection - recently advanced by Julien Murzi and Ole Hjortland (Analysis 2009) - to one of Smiley's key claims. Along the way, we consider the prospects for an intuitionistic approach to some of the issues (...)
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  4.  107 DLs
    Peter Smith, Formal Logic.
    ... and a reading knowledge of formal logical symbolism is essential too. (Philosophers often use bits of logical symbolism to clarify their arguments.) Because the artificial and simply formal languages of logic give us highly illuminating objects of comparison when we come thinking about how natural languages work. (Relevant to topics in ‘philosophical logic’ and the philosophy of language.) But mainly because it us the point of entry into the study of one of the major intellectual achievements by philosophers of (...)
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  5.  83 DLs
    Peter Smith (1982). Bad News for Anomalous Monism? Analysis 42 (October):220-4.
  6.  78 DLs
    Peter Carruthers & Peter K. Smith (eds.) (1996). Theories of Theories of Mind. Cambridge University Press.
    Theories of Theories of Mind brings together contributions by a distinguished international team of philosophers, psychologists, and primatologists, who between them address such questions as: what is it to understand the thoughts, feelings, and intentions of other people? How does such an understanding develop in the normal child? Why, unusually, does it fail to develop? And is any such mentalistic understanding shared by members of other species? The volume's four parts together offer a state of the art survey of the (...)
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  7.  72 DLs
    Peter Smith (2003). An Introduction to Formal Logic. Cambridge University Press.
    Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, (...)
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  8.  67 DLs
    Peter Smith, Back to Basics: Revisiting the Incompleteness Theorems.
    Preface 1 The First Theorem revisited 1.1 Notational preliminaries 1.2 Definitional preliminaries 1.3 A general version of G¨ odel’s First Theorem 1.4 Giving the First Theorem bite 1.5 Generic G¨ odel sentences and arithmetic truth 1.6 Canonical and standard G¨ odel sentences 2 The Second Theorem revisited 2.1 Definitional preliminaries 2.2 Towards G¨ odel’s Second Theorem 2.3 A general version of G¨ odel’s Second Theorem 2.4 Giving the Second Theorem bite 2.5 Comparisons 2.6 Further results about provability predicates 2.7 Back (...)
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  9.  61 DLs
    Luca Incurvati & Peter Smith (2012). Review of P. Maddy, Defending the Axioms: On the Philosophical Foundations of Set Theory. [REVIEW] Mind 121 (481):195-200.
  10.  59 DLs
    Peter Smith, Godel Without (Too Many) Tears.
    odel’s Theorems (CUP, heavily corrected fourth printing 2009: henceforth IGT ). Surely that’s more than enough to be going on with? Ah, but there’s the snag. It is more than enough. In the writing, as is the way with these things, the book grew far beyond the scope of the lecture notes from which it started. And while I hope the result is still pretty accessible to someone prepared to put in the time and effort, there is – to be (...)
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  11.  56 DLs
    Peter Smith (2011). Squeezing Arguments. Analysis 71 (1):22 - 30.
    Many of our concepts are introduced to us via, and seem only to be constrained by, roughand-ready explanations and some sample paradigm positive and negative applications. This happens even in informal logic and mathematics. Yet in some cases, the concepts in question – although only informally and vaguely characterized – in fact have, or appear to have, entirely determinate extensions. Here’s one familiar example. When we start learning computability theory, we are introduced to the idea of an algorithmically computable function (...)
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  12.  56 DLs
    Peter Smith (1975). Solitary Speakers. Mind 84 (336):590-594.
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  13.  56 DLs
    Chris Jarrold, Peter Carruthers, Jill Boucher & Peter K. Smith (1994). Pretend Play. Mind and Language 9 (4):445-468.
    Children’s ability to pretend, and the apparent lack of pretence in children with autism, have become important issues in current research on ‘theory of mind’, on the assumption that pretend play may be an early indicator of metarepresentational abilities.
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  14.  55 DLs
    Peter Smith & O. R. Jones (1986). The Philosophy of Mind: An Introduction. Cambridge University Press.
    This is a straightforward, elementary textbook for beginning students of philosophy. The general aim is to provide a clear introduction to the main issues arising in the philosophy of mind. Part I discusses the Cartesian dualist view which many find initially appealing, and contains a careful examination of arguments for and against. Part II introduces the broadly functionalist type of physicalism which has Aristotelian roots. This approach is developed to yield accounts of perception, action, belief and desire, and the emerging (...)
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  15.  53 DLs
    Peter Smith, Field on Truth: How Complex is Too Complex?
    In a reading group, we’ve been working through the first three parts of Field’s Saving Truth from Paradox, by the end of which he has presented his core proposals. At this point, we’ve now rather lost the will to continue – for this is an astonishingly badly written book, which makes ridiculous demands on the patience of even a sympathetic reader. It so happened that it fell to me to introduce the last two chapters in Part III, Ch. 17 in (...)
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  16.  51 DLs
    Peter Smith, Basic Reading on Computable Functions.
    This is an annotated reading list on the beginning elements of the theory of computable functions. It is now structured so as to complement the first eight lectures of Thomas Forster’s Part III course in Lent 2011 (see the first four chapters of his evolving handouts).
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  17.  50 DLs
    Peter Smith, Tennenbaum's Theorem.
    We are going to prove a key theorem that tells us just a bit more about the structure of the non-standard countable models of first-order Peano Arithmetic; and then we will very briefly consider whether any broadly philosophical morals can be drawn from the technical result.
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  18.  48 DLs
    Peter Smith (1999). Index to Volume 59, 1999. Analysis 59 (264):362–364.
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  19.  45 DLs
    Peter Smith, Laws of Nature.
    Where to begin? I’ll take three books from my shelves. First, now nearly forty years old, a little book of television lectures by the great physicist Richard Feynman, The Character of Physical Law. He talks about the laws of motion, the inverse square law of gravitation, conservation laws, symmetry principles and the various ways these all hang together. Feynman obviously takes it that it is a prime aim of science to discover such laws. But what are laws? He writes – (...)
     
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  20.  44 DLs
    Peter Smith (1984). Anomalous Monism and Epiphenomenalism: A Reply to Honderich. Analysis 44 (2):83-86.
  21.  43 DLs
    Peter Smith, Wittgenstein on Mathematics and Games.
    Unlike his other major typescripts, the Big Typescript is divided into titled chapters, themselves divided into titled sections. But within a section we still get a collection of remarks typically without connecting tissue and lacking any transparently significant ordering or helpful signposting. So we still encounter the usual difficulties in trying to think our way through into what Wittgenstein might be wanting to say. Some enthusiasts like to try to persuade us that the aphoristic style is really of the essence. (...)
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  22.  43 DLs
    Peter Smith, Introducing Wilfrid Hodges, a Shorter Model Theory.
    In the opening chapter of ‘the Shorter Hodges’, we get a lot of fixing of terminology and notation, and some fairly natural definitions of ideas like that of isomorphism between structures. There are no really tricky ideas which need further exploration, nor any nasty proofs that could do with more elaboration. So I don’t pretend to have anything very thrilling by way of introductory comments. But let me make some more general philosophical comments.
     
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  23.  40 DLs
    Peter Smith, Curry's Paradox, Lukasiewicz, and Field.
    In approaching Ch. 4 of Saving Truth from Paradox, it might be helpful first to revisit Curry’s original paper, and to revisit Lukasiewicz too, to provide more of the scenesetting that Field doesn’t himself fill in. So in §1 I’ll say something about Curry, in §2 we’ll look at what Lukasiewicz was up to in his original three-valued logic, and in §3 we’ll look at the move from a three-valued to a many-valued Lukasiewicz logic. In §4, I move on to (...)
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  24.  38 DLs
    Peter Smith, Church's Thesis After 70 Years.
    In the section ‘Further reading’, I listed a book that arrived on my desk just as I was sending IGT off to the press, namely Church’s Thesis after 70 Years edited by Adam Olszewski et al. On the basis of a quick glance, I warned that the twenty two essays in the book did seem to be of ‘variable quality’. But actually, things turn out to be a bit worse than that: the collection really isn’t very good at all! After (...)
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  25.  37 DLs
    Luca Incurvati & Peter Smith (2012). Is 'No' a Force-Indicator? Sometimes, Possibly. Analysis 72 (2):225-231.
    Some bilateralists have suggested that some of our negative answers to yes-or-no questions are cases of rejection. Mark Textor (2011. Is ‘no’ a force-indicator? No! Analysis 71: 448–56) has recently argued that this suggestion falls prey to a version of the Frege-Geach problem. This note reviews Textor's objection and shows why it fails. We conclude with some brief remarks concerning where we think that future attacks on bilateralism should be directed.
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  26.  34 DLs
    Peter Smith, The Galois Connection Between Syntax and Semantics.
    Preface 1 Partially ordered sets 1.1 Posets introduced 1.2 Partial orders and strict orders 1.3 Maps between posets 1.4 Compounding maps 1.5 Order similarity 1.6 Inclusion posets as typical..
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  27.  33 DLs
    Peter Smith (1984). Could We Be Brains in a Vat. Canadian Journal of Philosophy 14 (1):115--23.
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  28.  32 DLs
    Peter Smith, Squeezing Church's Thesis Again.
    In the very last chapter of my Introduction to Gödel Theorems, I rashly claimed that there is a sense in which we can informally prove Church’s Thesis. This sort of claim isn’t novel to me: but it certainly is still very much the minority line. So maybe it is worth rehearsing some of the arguments again. Even if I don’t substantially add to the arguments in the book, it might help to approach things in a different order, with some different (...)
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  29.  30 DLs
    Peter Smith, The First Incompleteness Theorem.
    • How to construct a ‘canonical’ Gödel sentence • If PA is sound, it is negation imcomplete • Generalizing that result to sound p.r. axiomatized theories whose language extends LA • ω-incompleteness, ω-inconsistency • If PA is ω-consistent, it is negation imcomplete • Generalizing that result to ω-consistent p.r. axiomatized theories which extend Q..
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  30.  30 DLs
    Peter Smith, Induction, More or Less.
    The first main topic of this paper is a weak second-order theory that sits between firstorder Peano Arithmetic PA1 and axiomatized second-order Peano Arithmetic PA2 – namely, that much-investigated theory known in the trade as ACA0. What I’m going to argue is that ACA0, in its standard form, lacks a cogent conceptual motivation. Now, that claim – when the wraps are off – will turn out to be rather less exciting than it sounds. It isn’t that all the work that (...)
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  31.  29 DLs
    Peter Smith & Jones O. R. (1986). The Philosophy of Mind. Cambridge University Press.
    This is a straightforward, elementary textbook for beginning students of philosophy. The general aim is to provide a clear introduction to the main issues arising in the philosophy of mind. Part I discusses the Cartesian dualist view which many find initially appealing, and contains a careful examination of arguments for and against. Part II introduces the broadly functionalist type of physicalism which has Aristotelian roots. This approach is developed to yield accounts of perception, action, belief and desire, and the emerging (...)
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  32.  29 DLs
    Peter Smith (2009). Critical Notice of C. Parsons, Mathematical Thought and its Objects. [REVIEW] Analysis 69 (3):549-557.
    Needless to say, Charles Parsons’s long awaited book1 is a must-read for anyone with an interest in the philosophy of mathematics. But as Parsons himself says, this has been a very long time in the writing. Its chapters extensively “draw on”, “incorporate material from”, “overlap considerably with”, or “are expanded versions of” papers published over the last twenty-five or so years. What we are reading is thus a multi-layered text with different passages added at different times. And this makes for (...)
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  33.  26 DLs
    Peter Smith, Kleene's Proof of G¨Odel's Theorem.
    There is a familiar derivation of G¨ odel’s Theorem from the proof by diagonalization of the unsolvability of the Halting Problem. That proof, though, still involves a kind of self-referential trick, as we in effect construct a sentence that says ‘the algorithm searching for a proof of me doesn’t halt’. It is worth showing, then, that some core results in the theory of partial recursive functions directly entail G¨ odel’s First Incompleteness Theorem without any further self-referential trick.
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  34.  25 DLs
    Peter Smith, Getting Published.
    Publish or perish? Well, like it or not (and I for one don't!--for I fear it encourages narrowness and scholasticism), having a track record of pieces accepted for publication is now more or less a sine qua non for getting a foot on the first rung of the profession, as a junior research fellow or temporary lecturer. And when it comes to applying for a permanent lectureship a good track record of publication and clear evidence that you are going to (...)
     
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  35.  24 DLs
    Peter Smith, Induction and Predicativity.
    I am interested in the philosophical prospects of what is called ‘predicativism given the natural numbers’. And today, in particular, I want to critically discuss one argument that has been offered to suggest that this kind of predicativism can’t have a stable philosophical motivation. Actually you don’t really need to know about predicativism to find some stand-alone interest in the theme I will be discussing. But still, it’s worth putting things into context. So I’m going to start by spending a (...)
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  36.  24 DLs
    Peter Smith (2010). Rejection and Valuations. Analysis 70 (1):3 - 10.
    Timothy Smiley’s wonderful paper ‘Rejection’ (1996) is still perhaps not as well known or well understood as it should be. This note first gives a quick presentation of themes from that paper, though done in our own way, and then considers a putative line of objection – recently advanced by Julien Murzi and Ole Hjortland (2009) – to one of Smiley’s key claims. Along the way, we consider the prospects for an intuitionistic approach to some of the issues discussed in (...)
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  37.  23 DLs
    Peter Smith, Developing a Writing Style.
    Like the other major journals, ANALYSIS can accept less than 10% of submissions. So standards are fierce. Many submissions are ruled out of court for being badly argued or for re-inventing the wheel or for being plain boring. But a fair proportion end up on the rejection pile simply because they are badly written. I saw far too much bad prose (to be sure, some of the prose that gets published is not exactly wonderful: I assure you that a lot (...)
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  38.  23 DLs
    Peter Smith, The MRDP Theorem.
    Here is Hilbert is his famous address of 1900: The supply of problems in mathematics is inexhaustible, and as soon as one problem is solved numerous others come forth in its place. Permit me in the following, tentatively as it were, to mention particular definite problems, drawn from various branches of mathematics, from the discussion of which an advancement of science may be expected.
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  39.  22 DLs
    Peter Smith (1975). Kirk on Quine's Reasons for Indeterminacy of Translation. Philosophical Studies 27 (6):427 - 431.
    An argument given by kirk ("analysis" 33.6) against quine's 1970 defense of his indeterminacy thesis is discussed. It is shown that kirk's claim that quine's argument is self-Defeating is unacceptable.
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  40.  22 DLs
    Peter Smith, Godel's Theorem: A Proof From the Book?
    Here’s one version G¨ odel’s 1931 First Incompleteness Theorem: If T is a nice, sound theory of arithmetic, then it is incomplete, i.e. there are arithmetical sentences ϕ such that T proves neither ϕ nor ¬ϕ. There are three things here to explain straight away.
     
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  41.  22 DLs
    Peter Smith (1976). Blackburn on Saying That. Philosophical Studies 30 (6):423 - 426.
  42.  21 DLs
    Peter Smith (2008). Ancestral Arithmetic and Isaacson's Thesis. Analysis 68 (297):1–10.
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  43.  21 DLs
    Peter Smith, First-Order Peano Arithmetic.
    Theorem 1. If T is a sound formalized theory whose language contains the language of basic arithmetic, then there will be a true sentence GT of basic arithmetic such that T ￿ GT and ￿ ¬GT, so T must be negation incomplete.
     
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  44.  21 DLs
    Peter Smith, Cuts, Consistency and Axiomatized Theories.
    In the Wednesday Logic Reading Group, where we are working through Sara Negri and Jan von Plato’s Structural Proof Theory – henceforth ‘NvP’ – I today introduced Chapter 6, ‘Structural Proof Analysis of Axiomatic Theories’. In their commendable efforts to be brief, the authors are sometimes a bit brisk about motivation. So I thought it was worth trying to stand back a bit from the details of this action-packed chapter as far as I understood it in the few hours I (...)
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  45.  20 DLs
    Peter Smith, Incompleteness and Undecidability.
    In Episode 1, we introduced the very idea of a negation-incomplete formalized theory T . We noted that if we aim to construct a theory of basic arithmetic, we’ll ideally like the theory to be able to prove all the truths expressible in the language of basic arithmetic, and hence to be negation complete. But Gödel’s First Incompleteness Theorem says, very roughly, that a nice theory T containing enough arithmetic will always be negation incomplete. Now, the Theorem comes in two (...)
     
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  46.  19 DLs
    Peter Smith, There Are Sea-Serpents, Jim, but Not as We Know Them.
    At the last meeting, Tim Crane gave a talk in which he made play with a distinction between ‘believing in’ and ‘believing that’. And he claimed that this distinction could be put to serious philosophical work of interest to serious metaphysicians. My hunch at the time was that this distinction in fact can’t bear any real weight. But I can’t now reconstruct Tim’s own arguments sufficiently to give a fair evaluation of them. However, Tim did say that the distinction he (...)
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  47.  18 DLs
    Peter Smith (1982). In Defence of Lewy. Analysis 42 (3):119 - 124.
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  48.  18 DLs
    Peter Smith (1981). Realism and the Progress of Science. Cambridge University Press.
    This book examines the philosophical foundations of the realist view of the progress of science as cumulative.
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  49.  18 DLs
    Peter Smith, Entailment, with Nods to Lewy and Smiley.
    Last week, we talked a bit about the Anderson-Belnap logic of entailment, as discussed in Priest’s Introduction to Non-Classical Logic. For a quite different approach to entailment, we’ll look next week at Neil Tennant’s account. Doing things rather out of order, this week I’d like to say something more basic about the problems to which both Anderson and Belnap, on the one hand, and Tennant on the other, are responding. This will give me the chance for a bit of nostalgic (...)
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  50.  17 DLs
    Peter Smith (1987). Subjectivity and Colour Vision. Proceedings of the Aristotelian Society 61:245-81.
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