Engineering logical concepts

In what ways can logical concepts be deficient? (inconsistency, conflation of concepts, disharmony, not jointcarving, 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?
Program
8 March
 9:15  10:30: Ole Hjortland "Engineering logical concepts"
 10:45  12: Øystein Linnebo "The paradox of the largest number"
 Lunch
 12:45  2pm: Eric Snyder & Steward Shapiro "Plurality and Paradox"
 2:15  3:30pm: Peter Fritz "In Defense of HigherOrder Logic"
 3:45  5pm: Marcus Rossberg "Engineering Logical Concepts?”
9 March
 9:30  10:45: Craige Roberts & Steward Shapiro "Opentexture, analyticity, model theory, and natural language semantics"
 11  12:15: Gil Sagi "Logic and Natural Language"
 Lunch
 1:15  2:30pm: Hannes Leitgeb "Models with NonRepresenting Concepts: Logicality, Analyticity, Metaphysics"
 2:45  4pm: Kevin Scharp
Peter Fritz
Title: In Defense of HigherOrder Logic
Abstract:
According to a common argument, higherorder logic is incoherent,
since using higherorder logic commits one to claims about
higherorder logic which cannot be expressed in higherorder logic. I
defend higherorder logic against this argument, by clarifying and
distinguishing different versions of it, and showing how its premises
may plausibly be rejected.
Ole Hjortland
TITLE: Engineering logical concepts
ABSTRACT: Antiexceptionalism about logic is the Quinean view that
logical theories have no special epistemological status, in
particular, they are not selfevident or justified a priori. Instead,
logical theories are continuous with scientific theories, and
knowledge of logic is as hardearned as knowledge of physics,
economics, and chemistry. In this paper, I explore how an
antiexceptionalist 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 socalled
meaningvariance argument, and it supports an antiexceptionalist
story about theory choice in logic.
Hannes Leitgeb
TITLE: "Models with NonRepresenting Concepts: Logicality, Analyticity, Metaphysics"
Øystein Linnebo
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 orfar more
plausiblya “successor concept” that is compatible with Cantor’s
theory of the transfinite.
Craige Roberts and Stewart Shapiro
TITLE: "Opentexture, analyticity, model theory, and natural language semantics"
The purpose of this paper is to articulate and evaluate Waismann's
notion of opentexture, from the "Verifiability" paper, and some of
the themes in his "Analyticity" series. One underlying theme is how
far opentexture 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 modeltheoretic notion of logical
consequence. Does the fact that contemporary model theory, and many of
the models for lexical semantics, allow no room for opentexture tell
against those enterprises, as they are currently practiced?
Marcus Rossberg
TITLE: "Engineering Logical Concepts?”
Abstract:
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
language.
Gil Sagi
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 setlike entities as the referents of plural terms,
pluralism does not. Moreover, the primary argument against singularism
is that because such setlike 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 setlike entities as the
referents of certain plural terms. Secondly, these setlike 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 setlike
entities: setformation, pluralityformation, and groupformation are
best understood as potential, rather than completed or actual,
processes.