Patrick Grim Research Articles

Theory of Categories: Key Instruments of Human Understanding, by Patrick Grim and Nicolas Rescher

Theory of Categories: Key Instruments of Human Understanding, by Patrick Grim and Nicolas Rescher

Grim, Omniscience, and Cantor’s Theorem

Although recent evidence is somewhat ambiguous, if not confusing, Patrick Grim still seems to believe that his Cantorian argument against omniscienceis sound. According to this argument, it follows by Cantor’s power set theorem that there can be no set of all truths. Hence, assuming that omniscience presupposes precisely such a set, there can be no omniscient being. Reconsidering this argument, however, guided in particular by Alvin Plantinga’s critique thereof, I find it far from convincing. Not only does it have an enormously untoward side effect, but it is self-referentially incoherent as well.

Grim, Omniscience, and Cantor’s Theorem

Although recent evidence is somewhat ambiguous, if not confusing, Patrick Grim still seems to believe that his Cantorian argument against omniscience is sound. According to this argument, it follows by Cantor’s power set theorem that there can be no set of all truths. Hence, assuming that omniscience presupposes precisely such a set, there can be no omniscient being. Reconsidering this argument, however, guided in particular by Alvin Plantinga’s critique thereof, I find it far from convincing. Not only does it have an enormously untoward side effect, but it is self-referentially incoherent as well.

A Grim Semantics For Logics of Belief

Patrick Grim has presented arguments supporting the intuition that any notion of a totality of truths is incoherent. We suggest a natural semantics for various logics of belief which reflect Grim’s intuition. The semantics is a topological semantics, and we suggest that the \(T_{1} \) condition can be interpreted to reflect Grim’s intuition. Beyond this, we present a natural canonical topological model for K4 and KD4.

De Se Knowledge and the Possibility of an Omniscient Being

In this paper I examine an argument that has been made by Patrick Grim for the claim that de se knowledge is incompatible with the existence of an omniscient being. I claim that the success of the argument depends upon whether it is possible for someone else to know what I know in knowing (F), where (F) is a claim involving de se knowledge. I discuss one reply to this argument, proposed by Edward Wierenga, that appeals to first-person propositions and argue that this response is unsuccessful. I then consider David Lewis’s theory of de se attitudes involving the self-ascription of properties. I claim that, according to this theory, there are two senses in which someone else can know what I know in knowing (F). I then argue that the second sense allows for the compatibility of de se knowledge with the existence of an omniscient being.

The buried quantifier: an account of vagueness and the sorites

Journal Article The buried quantifier: an account of vagueness and the sorites Get access Patrick Grim Patrick Grim SUNY at Stony BrookStony Brook, NY 11794, USApgrim@notes.cc.sunysb.edu Search for other works by this author on: Oxford Academic Google Scholar Analysis, Volume 65, Issue 2, April 2005, Pages 95–104, https://doi.org/10.1093/analys/65.2.95 Published: 01 April 2005

I. Jané. Reflections on Skolem's relativity of set-theoretical concepts. The Philosopher's Annual, edited by Patrick Grim, Peter Ludlow, and Gary Mar, vol. XXIV. CSLI Publications, Stanford, 2003, pp. 95–121 - C. Wright. On being in a quandary: relativism, vagueness, logical revisionism. The Philosopher's Annual, edited by Patrick Grim, Peter Ludlow, and Gary Mar, vol. XXIV. CSLI Publications, Stanford, 2003, pp.

I. Jané. Reflections on Skolem's relativity of set-theoretical concepts. The Philosopher's Annual, edited by Patrick Grim, Peter Ludlow, and Gary Mar, vol. XXIV. CSLI Publications, Stanford, 2003, pp. 95–121 - C. Wright. On being in a quandary: relativism, vagueness, logical revisionism. The Philosopher's Annual, edited by Patrick Grim, Peter Ludlow, and Gary Mar, vol. XXIV. CSLI Publications, Stanford, 2003, pp. 273–325 - Volume 11 Issue 1

Divine omniscience and knowledge de se

Patrick Grim argues that God cannot beomniscient because no one other than me canacquire knowledge de se of myself. Inparticular, according to Grim, God cannot knowwhat I know in knowing that I am making amess. I argue, however, that given twoplausible principles regarding divineattributes there is no reason to accept Grim'sconclusion that God cannot be omniscient. Inthis paper I focus on the relationship betweendivine omniscience and necessaryimpossibilities, in contrast to the generaltrend of research since Aquinas, which hasconcentrated on the relationship between divineomnipotence and necessary impossibilities.

A Neglected Response to the Grim Result

Is there a set of all truths? According to a familiar argument by Patrick Grim the answer is ‘no’. Grim’s argument is a reductio which runs as follows.1 Suppose, for reductio, that there is a set of all truths; call it ‘T’. Let 3(T) be the powerset of T. To each element si of 3(T) there exists a truth. For example, to each si corresponds the following truth si ∈ 3(T) Alternatively, let t1 be a truth. Then for every element si of 3(T), one of the following is a truth

Worlds as complete novels

1. Patrick Grim has argued that there can be no set of all true propositions; for every set having, say, the number 3 as a member, there is the true proposition that 3 belongs to the set, and for every other set the true proposition that 3 doesn't belong to it, so there are at least as many true propositions as sets, making the class of truths a proper class. (In more detail; assume standard, Zermelo-Frankel, set theory, formulated in a language allowing quantification over propositions as well as sets, with Extensionality adjusted to allow propositions or other urelements to be members of sets, and allowing the vocabulary of our theory of propositions as well as set-theoretic jargon to occur in instances of the axiom schemes. The argument sketched above defines a one-one mapping between all the sets and some of the truths. Specify some arbitrary set as corresponding to any true proposition not in the range of this mapping and we have a function from truths onto the sets, so a set of all truths would, by Replacement, yield a set of all sets, something whose existence is refutable in ZF) He concludes from this that possible worlds cannot be construed as complete sets of propositions ('complete novels' in the jargon of the subject); the actual world, after all, would on this construal have to be the set of all true propositions, and every other possible world would be an equally, inadmissably, large set. Since this and similar conceptions of possible worlds have seemed attractive to many philosophers concerned with the metaphysics of modality (etc.), it is worth examining Grim's argument carefully. The propositions correlated with the sets in my version of the argument above are all necessary truths; a set is defined by its members, and so any set including (excluding) the number 3 does so essentially. Necessary truths, however, are in a certain sense the ones that don't have to be mentioned in specifying a possible world; they are true at every world, and so a world is fully determined by the contingent propositions true at it. Could we, then, define a world as the set of these contingent propositions? Grim notes that this was suggested to him by a correspondent, and quickly refutes the suggestion by defining a one-one mapping from the sets to true contingent propositions; pick some arbitrary contingent truth, and take its conjunctions with the necessary truths correlated with the sets earlier. These conjunctions will all be true (having two true conjuncts), contingent (having one contingent conjunct), and distinct (having different necessary conjuncts).

The Incomplete Universe: Totality, Knowledge, and Truth.

Journal Article Book Reviews Get access The Incomplete Universe: Totality, Knowledge, and Truth. By Patrick Grim. (Cambridge, Mass.: MIT Press, 1991. Pp. ix + 165. Price £22.50.) Elliott Mendelson Elliott Mendelson Queens College, CUNY Search for other works by this author on: Oxford Academic Google Scholar The Philosophical Quarterly, Volume 44, Issue 176, July 1994, Pages 409–410, https://doi.org/10.2307/2219630 Published: 01 July 1994

Book Reviews

Journal Article Book Reviews Get access The Incomplete Universe, by Patrick Grim. Cambridge Massachusetts: MIT Press, 1991. Pp. 165. £11.75. A. J. DALE A. J. DALE Computer Science Department University of Newcastle upon TyneNewcastle upon Tyne UK Search for other works by this author on: Oxford Academic Google Scholar Mind, Volume 102, Issue 406, April 1993, Pages 370–373, https://doi.org/10.1093/mind/102.406.370 Published: 01 April 1993

Time, Actuality and Omniscience

Many traditional theists have said that(i) God is propositionally omniscient,i.e. knows all truths. Many traditional theists also hold that(2) God is timeless.That is, these theists hold that though God exists, there is no time at which He exists, and He does not exist earlier or later than anything. Some recent philosophers, among them Arthor Prior, Robert Coburn, Norman Kretz mann, Nicholas Wolterstorfl Richard Gale and Patrick Grim, have argued that(3) There are truths to whose expression ‘now’ is essential, and that (1)–(3) compose an inconsistent set of propositions. These writers argue that due to the semantics of ‘now’, a timeless God cannot know truths to whose expression ‘now’ is essential. To know a truth, it is claimed, one must be able to mentally token a proposition expressing what one knows. To token a truth to whose expression ‘now’ is essential, one must token ‘now’. ‘Now’ and relevantly similar terms (such as tensed verbs) inter alia locate those who use them in time: if one says truly that it is now 3 p.m., it follows that one exists at 3 p.m. So a timeless being cannot use ‘now’ and relevantly similar terms, and so (it is claimed) cannot know truths for whose expression ‘now’ and its ilk are required.

On Sets and Worlds: A Reply to Menzel

Journal Article On sets and worlds: A reply to menzel Get access Patrick Grim Patrick Grim State University of New YorkStony Brook, NY 11794, U.S.A Search for other works by this author on: Oxford Academic Google Scholar Analysis, Volume 46, Issue 4, October 1986, Pages 186–191, https://doi.org/10.1093/analys/46.4.186 Published: 01 October 1986

What Won't Escape Sorites Arguments

Journal Article What won't escape sorites arguments Get access Patrick Grim Patrick Grim State University of New York at Stony Brook Search for other works by this author on: Oxford Academic Google Scholar Analysis, Volume 42, Issue 1, January 1982, Pages 38–43, https://doi.org/10.1093/analys/42.1.38 Published: 01 January 1982