While considerable ink has been spilt over the rejection of idealism by Bertrand Russell and G.E. Moore at the end of the
19th Century, relatively little attention has been directed at Russell’s A Critical Exposition of the Philosophy of Leibniz, a work written in the early stages of Russell’s philosophical struggles with the metaphysics of Bradley, Bosanquet, and
others. Though a sustained investigation of that work would be one of considerable scope, here I reconstruct and develop a
two-pronged argument from the Philosophy of Leibniz that Russell fancied—as late as 1907—to be the downfall of the traditional category of substance. Here, I suggest, one can
begin to see Russell’s own reasons—arguments largely independent of Moore—for the abandonment of idealism. Leibniz, no less
than Bradley, adhered to an antiquated variety of logic: what Russell refers to as the subject-predicate doctrine of logic.
Uniting this doctrine with a metaphysical principle of independence—that a substance is prior to and distinct from its properties—Russell
is able to demonstrate that neither a substance pluralism nor a substance monism can be consistently maintained. As a result,
Russell alleges that the metaphysics of both Leibniz and Bradley has been undermined as ultimately incoherent. Russell’s remedy
for this incoherence is the postulation of a bundle theory of substance, such that the category of “substance” reduces to
the most basic entities—properties. 相似文献
Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning
from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world
functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with
scant resources of effort and time. We begin with a general discussion and quickly move to Section 3 where we introduce five
resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible
logic. We also give several examples of practical reasoning situations to illustrate our principles.
Edited by Hannes Leitgeb 相似文献
This paper presents Automath encodings (which are also valid in LF/λP) of various kinds of foundations of mathematics. Then it compares these encodings according to their size, to find out which foundation is the simplest.
The systems analyzed in this way are two kinds of set theory (ZFC and NF), two systems based on Church's higher order logic (Isabelle/Pure and HOL), three kinds of type theory (the calculus of constructions, Luo's extended calculus of constructions, and Martin-Löf's predicative type theory) and one foundation based on category theory.
The conclusions of this paper are that the simplest system is type theory (the calculus of constructions), but that type theories that know about serious mathematics are not simple at all. In that case the set theories are the simplest. If one looks at the number of concepts needed to explain such a system, then higher order logic is the simplest, with twenty-five concepts. On the other side of the scale, category theory is relatively complex, as is Martin-Löf's type theory.
(The full Automath sources of the contexts described in this paper are one the web at http://www.cs.ru.nl/~freek/zfc-etc/.) 相似文献
If we agree with Michael Jubien that propositions do not exist, while accepting the existence of abstract sets in a realist
mathematical ontology, then the combined effect of these ontological commitments has surprising implications for the metaphysics
of modal logic, the ontology of logically possible worlds, and the controversy over modal realism versus actualism. Logically
possible worlds as maximally consistent proposition sets exist if sets generally exist, but are equivalently expressed as
maximally consistent conjunctions of the same propositions in corresponding sets. A conjunction of propositions, even if infinite
in extent, is nevertheless itself a proposition. If sets and hence proposition sets exist but propositions do not exist, then
whether or not modal realism is true depends on which of two apparently equivalent methods of identifying, representing, or
characterizing logically possible worlds we choose to adopt. I consider a number of reactions to the problem, concluding that
the best solution may be to reject the conventional model set theoretical concept of logically possible worlds as maximally
consistent proposition sets, and distinguishing between the actual world alone as maximally consistent and interpreting all
nonactual merely logically possible worlds as submaximal.
I am grateful to the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), Royal Netherlands
Academy of Arts and Sciences (KNAW), for supporting this among related research projects in philosophical logic and philosophy
of mathematics during my Resident Research Fellowship in 2005-2006. 相似文献
A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob’s assumption is wrongThis is formalized to show that any belief model of a certain kind must have a ‘hole.’ An interpretation of the result is that if the analyst’s tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen 相似文献
Combinator logics are a broad family of substructual logics that are formed by extending the basic relevant logic B with axioms that correspond closely to the reduction rules of proper combinators in combinatory logic. In the Routley-Meyer relational semantics for relevant logic each such combinator logic is characterized by the class of frames that meet a first-order condition that also directly corresponds to the same combinator's reduction rule. A second family of logics is also introduced that extends B with the addition of propositional constants that correspond to combinators. These are characterized by relational frames that meet first-order conditions that reflect the structures of the combinators themselves. 相似文献
Peter Gärdenfors has developed a semantics for conditional logic, based on the operations of expansion and revision applied to states of information. The account amounts to a formalisation of the Ramsey test for conditionals. A conditional A > B is declared accepted in a state of information K if B is accepted in the state of information which is the result of revising K with respect to A. While Gärdenfors's account takes the truth-functional part of the logic as given, the present paper proposes a semantics entirely based on epistemic states and operations on these states. The semantics is accompanied by a syntactic treatment of conditional logic which is formally similar to Gentzen's sequent formulation of natural deduction rules. Three of David Lewis's systems of conditional logic are represented. The formulations are attractive by virtue of their transparency and simplicity. 相似文献
A new logic, quantized intuitionistic linear logic (QILL), is introduced, and is closely related to the logic which corresponds to Mulvey and Pelletier's (commutative) involutive quantales. Some cut-free sequent calculi with a new property quantization principle and some complete semantics such as an involutive quantale model and a quantale model are obtained for QILL. The relationship between QILL and Wansing's extended intuitionistic linear logic with strong negation is also observed using such syntactical and semantical frameworks. 相似文献
This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following (along with Saul Kripke's ‘scepticalsolution’), Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable (even if imaginary) set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective (recognition-transcendent) truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others. 相似文献