41,100 research outputs found
The price of inscrutability
In our reasoning we depend on the stability of language, the fact that its signs do not arbitrarily change in meaning from moment to moment.(Campbell, 1994, p.82)
Some philosophers offer arguments contending that ordinary names such as âLondonâ are radically indeterminate in reference. The conclusion of such arguments is that there is no fact of the matter whether âLondonâ refers to a city in the south of England, or whether instead it refers to
Sydney, Australia. Some philosophers have even suggested that we accept the conclusion of these arguments.
Such a position seems crazy to many; but what exactly goes wrong if one adopts such a view? This paper evaluates the theoretical costs incurred by one who endorses extreme inscrutability of reference (the âinscrutabilistâ). I show that there is one particular implication of extreme
inscrutability which pushes the price of inscrutabilism too high. An extension of the classic âpermutationâ arguments for extreme inscrutability allow us to establish what I dub âextreme indexical inscrutabilityâ. This result, I argue, unacceptably undermines the epistemology of inference.
The first half of the paper develops the background of permutation arguments for extreme inscrutability
of reference and evaluates some initial attempts to make trouble for the inscrutabilist.
Sections 1 and 2 describe the setting of the original permutation arguments for extreme inscrutability.
Sections 3 and 4 survey four potential objections to extreme inscrutability of reference,
including some recently raised in Vann McGeeâs excellent (2005a). Sections 5 sketches how the permutation arguments can be generalized to establish extreme indexical inscrutability; and shows how this contradicts a âstability principleââthat our words do not arbitrarily
change their reference from one moment to the nextâwhich I claim plays a vital role in the epistemology of inference.
The second half of the paper develops in detail the case for thinking that language is stable
in the relevant sense. In section 6, I use this distinction to call into question the epistemological
relevance of validity of argument types; Kaplanâs treatment of indexical validity partially resolves this worry, but there is a residual problem. In section 7, I argue that stability is exactly what is needed to bridge this final gap, and so secure the relevance of validity to good inferential practice. Section 8 responds to objections to this claim.
An appendix to the paper provides formal backing for the results cited in this paper, including a generalization of permutation arguments to the kind of rich setting required for a realistic semantics of natural language.1 Extreme indexical inscrutability results can be proved within
this setting. The first half of the paper shows that the inscrutabilist is committed to extreme indexical inscrutability, which implies that language not determinately âstableâ. The second half of the paper argues that good inference requires stability. The price of inscrutabilism, therefore, is to sever the connection between the validity of argument-forms and inferential practice: and this is too high a price to pay
Two-dimensional models of type theory
We describe a non-extensional variant of Martin-L\"of type theory which we
call two-dimensional type theory, and equip it with a sound and complete
semantics valued in 2-categories.Comment: 46 pages; v2: final journal versio
Fractional-valued modal logic
This paper is dedicated to extending and adapting to modal logic the approach of fractional semantics to classical logic. This is a multi-valued semantics governed by pure proof-theoretic considerations, whose truth-values are the rational numbers in the closed interval [0,1] . Focusing on the modal logic K, the proposed methodology relies on three key components: bilateral sequent calculus, invertibility of the logical rules, and stability (proof-invariance). We show that our semantic analysis of K affords an informational refinement with respect to the standard Kripkean semantics (a new proof of Dugundjiâs theorem is a case in point) and it raises the prospect of a proof-theoretic semantics for modal logic
Logic of Non-Monotonic Interactive Proofs (Formal Theory of Temporary Knowledge Transfer)
We propose a monotonic logic of internalised non-monotonic or instant
interactive proofs (LiiP) and reconstruct an existing monotonic logic of
internalised monotonic or persistent interactive proofs (LiP) as a minimal
conservative extension of LiiP. Instant interactive proofs effect a fragile
epistemic impact in their intended communities of peer reviewers that consists
in the impermanent induction of the knowledge of their proof goal by means of
the knowledge of the proof with the interpreting reviewer: If my peer reviewer
knew my proof then she would at least then (in that instant) know that its
proof goal is true. Their impact is fragile and their induction of knowledge
impermanent in the sense of being the case possibly only at the instant of
learning the proof. This accounts for the important possibility of
internalising proofs of statements whose truth value can vary, which, as
opposed to invariant statements, cannot have persistent proofs. So instant
interactive proofs effect a temporary transfer of certain propositional
knowledge (knowable ephemeral facts) via the transmission of certain individual
knowledge (knowable non-monotonic proofs) in distributed systems of multiple
interacting agents.Comment: continuation of arXiv:1201.3667 ; published extended abstract:
DOI:10.1007/978-3-642-36039-8_16 ; related to arXiv:1208.591
Programming with process groups: Group and multicast semantics
Process groups are a natural tool for distributed programming and are increasingly important in distributed computing environments. Discussed here is a new architecture that arose from an effort to simplify Isis process group semantics. The findings include a refined notion of how the clients of a group should be treated, what the properties of a multicast primitive should be when systems contain large numbers of overlapping groups, and a new construct called the causality domain. A system based on this architecture is now being implemented in collaboration with the Chorus and Mach projects
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