1,444 research outputs found
Computer Science and Metaphysics: A Cross-Fertilization
Computational philosophy is the use of mechanized computational techniques to
unearth philosophical insights that are either difficult or impossible to find
using traditional philosophical methods. Computational metaphysics is
computational philosophy with a focus on metaphysics. In this paper, we (a)
develop results in modal metaphysics whose discovery was computer assisted, and
(b) conclude that these results work not only to the obvious benefit of
philosophy but also, less obviously, to the benefit of computer science, since
the new computational techniques that led to these results may be more broadly
applicable within computer science. The paper includes a description of our
background methodology and how it evolved, and a discussion of our new results.Comment: 39 pages, 3 figure
Normality operators and Classical Recapture in Extensions of Kleene Logics
In this paper, we approach the problem of classical recapture for LP and K3 by using normality
operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical recapture result based on the two logics. In the second part of the paper, we compare the approach in terms of normality operators with an established approach to classical recapture, namely minimal inconsistency. Finally, we discuss technical issues connecting LPe and Ke3 to the tradition of Logics of Formal Inconsistency and Underterminedness
Negation in context
The present essay includes six thematically connected papers on negation in the areas of the philosophy of logic, philosophical logic and metaphysics. Each of the chapters besides the first, which puts each the chapters to follow into context, highlights a central problem negation poses to a certain area of philosophy. Chapter 2 discusses the problem of logical revisionism and whether there is any room for genuine disagreement, and hence shared meaning, between the classicist and deviant's respective uses of 'not'. If there is not, revision is impossible. I argue that revision is indeed possible and provide an account of negation as contradictoriness according to which a number of alleged negations are declared genuine. Among them are the negations of FDE (First-Degree Entailment) and a wide family of other relevant logics, LP (Priest's dialetheic "Logic of Paradox"), Kleene weak and strong 3-valued logics with either "exclusion" or "choice" negation, and intuitionistic logic. Chapter 3 discusses the problem of furnishing intuitionistic logic with an empirical negation for adequately expressing claims of the form 'A is undecided at present' or 'A may never be decided' the latter of which has been argued to be intuitionistically inconsistent. Chapter 4 highlights the importance of various notions of consequence-as-s-preservation where s may be falsity (versus untruth), indeterminacy or some other semantic (or "algebraic") value, in formulating rationality constraints on speech acts and propositional attitudes such as rejection, denial and dubitability. Chapter 5 provides an account of the nature of truth values regarded as objects. It is argued that only truth exists as the maximal truthmaker. The consequences this has for semantics representationally construed are considered and it is argued that every logic, from classical to non-classical, is gappy. Moreover, a truthmaker theory is developed whereby only positive truths, an account of which is also developed therein, have truthmakers. Chapter 6 investigates the definability of negation as "absolute" impossibility, i.e. where the notion of necessity or possibility in question corresponds to the global modality. The modality is not readily definable in the usual Kripkean languages and so neither is impossibility taken in the broadest sense. The languages considered here include one with counterfactual operators and propositional quantification and another bimodal language with a modality and its complementary. Among the definability results we give some preservation and translation results as well
From one to many: recent work on truth
In this paper, we offer a brief, critical survey of contemporary work on truth. We begin by reflecting on the distinction between substantivist and deflationary truth theories. We then turn to three new kinds of truth theory—Kevin Scharp's replacement theory, John MacFarlane's relativism, and the alethic pluralism pioneered by Michael Lynch and Crispin Wright. We argue that despite their considerable differences, these theories exhibit a common "pluralizing tendency" with respect to truth. In the final section, we look at the underinvestigated interface between metaphysical and formal truth theories, pointing to several promising questions that arise here
Lewis meets Brouwer: constructive strict implication
C. I. Lewis invented modern modal logic as a theory of "strict implication".
Over the classical propositional calculus one can as well work with the unary
box connective. Intuitionistically, however, the strict implication has greater
expressive power than the box and allows to make distinctions invisible in the
ordinary syntax. In particular, the logic determined by the most popular
semantics of intuitionistic K becomes a proper extension of the minimal normal
logic of the binary connective. Even an extension of this minimal logic with
the "strength" axiom, classically near-trivial, preserves the distinction
between the binary and the unary setting. In fact, this distinction and the
strong constructive strict implication itself has been also discovered by the
functional programming community in their study of "arrows" as contrasted with
"idioms". Our particular focus is on arithmetical interpretations of the
intuitionistic strict implication in terms of preservativity in extensions of
Heyting's Arithmetic.Comment: Our invited contribution to the collection "L.E.J. Brouwer, 50 years
later
Advances in Proof-Theoretic Semantics
Logic; Mathematical Logic and Foundations; Mathematical Logic and Formal Language
A logic of hypothetical conjunction
This work was supported by the UK Engineering and Physical Sciences Research Council under the research grants EP/K033042/1 and EP/P011829/1.Peer reviewedPostprin
Fitch's knowability axioms are incompatible with quantum theory
How can we consistently model the knowledge of the natural world provided by
physical theories? Philosophers frequently use epistemic logic to model
reasoning and knowledge abstractly, and to formally study the ramifications of
epistemic assumptions. One famous example is Fitch's paradox, which begins with
minimal knowledge axioms and derives the counter-intuitive result that "every
agent knows every true statement." Accounting for knowledge that arises from
physical theories complicates matters further. For example, quantum mechanics
allows observers to model other agents as quantum systems themselves, and to
make predictions about measurements performed on each others' memories.
Moreover, complex thought experiments in which agents' memories are modelled as
quantum systems show that multi-agent reasoning chains can yield paradoxical
results.
Here, we bridge the gap between quantum paradoxes and foundational problems
in epistemic logic, by relating the assumptions behind the recent
Frauchiger-Renner quantum thought experiment and the axioms for knowledge used
in Fitch's knowability paradox. Our results indicate that agents' knowledge of
quantum systems must violate at least one of the following assumptions: it
cannot be distributive over conjunction, have a kind of internal continuity,
and yield a constructive interpretation all at once. Indeed, knowledge provided
by quantum mechanics apparently contradicts traditional notions of how
knowledge behaves; for instance, it may not be possible to universally assign
objective truth values to claims about agent knowledge. We discuss the
relations of this work to results in quantum contextuality and explore possible
modifications to standard epistemic logic that could make it consistent with
quantum theory.Comment: 22 + 7 page
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