Engineering logical concepts
In what ways can logical concepts be deficient? (inconsistency, conflation of concepts, disharmony, not joint-carving, unintuitive, etc)
In what ways can logical concepts be improved?
Are logical concepts like other scientific concepts with regard to the previous questions? (yes, because logical expressions are theoretical terms; no, because logic is exceptional)
What is the philosophical status of such improvements (replacement or revision)?
Are logical concepts different from most other scientific concepts by being formal in some sense?
The role of stipulation and definition in fixing logical concepts
Do logical concepts play some special role in our cognitive architecture?
- 9:15 - 10:30: Ole Hjortland "Engineering logical concepts"
- 10:45 - 12: Øystein Linnebo "The paradox of the largest number"
- 12:45 - 2pm: Eric Snyder & Steward Shapiro "Plurality and Paradox"
- 2:15 - 3:30pm: Peter Fritz "In Defense of Higher-Order Logic"
- 3:45 - 5pm: Marcus Rossberg "Engineering Logical Concepts?”
- 9:30 - 10:45: Craige Roberts & Steward Shapiro "Open-texture, analyticity, model theory, and natural language semantics"
- 11 - 12:15: Gil Sagi "Logic and Natural Language"
- 1:15 - 2:30pm: Hannes Leitgeb "Models with Non-Representing Concepts: Logicality, Analyticity, Metaphysics"
- 2:45 - 4pm: Kevin Scharp
Title: In Defense of Higher-Order Logic
According to a common argument, higher-order logic is incoherent,
since using higher-order logic commits one to claims about
higher-order logic which cannot be expressed in higher-order logic. I
defend higher-order logic against this argument, by clarifying and
distinguishing different versions of it, and showing how its premises
may plausibly be rejected.
TITLE: Engineering logical concepts
ABSTRACT: Anti-exceptionalism about logic is the Quinean view that
logical theories have no special epistemological status, in
particular, they are not self-evident or justified a priori. Instead,
logical theories are continuous with scientific theories, and
knowledge of logic is as hard-earned as knowledge of physics,
economics, and chemistry. In this paper, I explore how an
anti-exceptionalist should think about logical concepts, and I argue
for a view according to which logical concepts are the result of
conceptual engineering. The view in turn helps block the so-called
meaning-variance argument, and it supports an anti-exceptionalist
story about theory choice in logic.
TITLE: "Models with Non-Representing Concepts: Logicality, Analyticity, Metaphysics"
TITLE: "The paradox of the largest number"
Is there a largest number? Attempts to answer the question easily lead
to paradox: we are attracted to both a positive and a negative answer.
I show how the paradox can be avoided by adopting either an
Aristotelian conception of potential infinity or--far more
plausibly--a “successor concept” that is compatible with Cantor’s
theory of the transfinite.
Craige Roberts and Stewart Shapiro
TITLE: "Open-texture, analyticity, model theory, and natural language semantics"
The purpose of this paper is to articulate and evaluate Waismann's
notion of open-texture, from the "Verifiability" paper, and some of
the themes in his "Analyticity" series. One underlying theme is how
far open-texture reaches. Do we follow Waismann and restrict it to
empirical predicates, or is the phenomenon more general, applying even
in science and mathematics? Our goal is to explore the extent to
which the Waismannian insights bear on the enterprise of natural
language semantics and of the model-theoretic notion of logical
consequence. Does the fact that contemporary model theory, and many of
the models for lexical semantics, allow no room for open-texture tell
against those enterprises, as they are currently practiced?
TITLE: "Engineering Logical Concepts?”
I will start from the question why the engineering of logical concepts
should deserve any special attention. Is it any different from
engineering other concepts? The investigation detours via a dispute
between Quine and Carnap and comes to considering the relation between
conceptual engineering and ideal language philosophy. I argue that
the conceptual engineering project would benefit from moving closer to
the older, and more radical, conception of explication in an ideal
TITLE: "Logic and Natural Language"
Searle has famously stated that ``Neither Aristotelian nor Russellian
rules give the exact logic of any expression of ordinary language; for
ordinary language has no exact logic.’’ On the other hand, we have
Montague, who claimed: ``There is in my opinion no important
theoretical difference between natural languages and the artificial
languages of logicians’’, and went on to characterize the logic of
natural language. This talk will address the question of whether there
is logic in natural language. However, to understand this question we
need to say what we mean by ``logic’’, ``natural language’’, and logic
being ``in’’ natural language. There are various things we may mean by
these terms that will make us reach different conclusions. I will
offer two routes of explicating the terms involved, which seem to me
most interesting, and by which we obtain different results for the
question at hand.
Stewart Shapiro and Eric Snyder
TITLE: "Plurality and Paradox"
Abstract: There are two general approaches to analyzing plurality in
natural language. The first, which is standard within linguistic
semantics, is singularism. It posits a single reference relation and
analyzes singular and plural nouns via it: singular nouns denote
singular individuals (or "atoms"), while plural nouns denote plural
individuals (or "pluralities"), usually modeled as sums of singular
individuals. The second approach, prominent within philosophy, is
pluralism. It posits two reference relations -- singular reference and
plural reference -- and analyzes plural nouns via the latter. The
important difference between these approaches is that whereas
singularism posits set-like entities as the referents of plural terms,
pluralism does not. Moreover, the primary argument against singularism
is that because such set-like entities iterate, singularism inevitably
leads to Russell's Paradox, and so is ultimately incoherent. We defend
singularism against this charge by establishing three claims. First,
there are natural language examples involving plurals which cannot be
adequately captured by the pluralist semantics. Rather, adequately
capturing their meanings requires positing set-like entities as the
referents of certain plural terms. Secondly, these set-like entities
-- pluralities and groups -- iterate, and it is indeed possible to
formulate a version of Russell's Paradox for each. These take the same
form as Linnebo (2010)'s derivation of Russell's Paradox for sets
within pluralism. Third, and most significantly, Linnebo's strategy
for harnessing Rusell's Paradox for sets extends naturally and
elegantly to the versions involving pluralities and groups. In all
three cases, by modalizing the characterizing principles, we get an
intuitive and general resolution to Russell's Paradox for set-like
entities: set-formation, plurality-formation, and group-formation are
best understood as potential, rather than completed or actual,