06/05 - Marco Ruffino

A Puzzle About Frege’s Singular Senses

In this paper I discuss what seems to be a puzzle for Frege’s notion of singular senses (i.e., the senses of singular terms) assuming the interpretation that, for him, every singular term is reducible to (or express the same sense as) some definite description. Singular senses are supposed to be complete (or saturated), but they are composed of the incomplete (unsaturated) senses of the concept-words of the descriptions. I ask how the definite article (or what it expresses) “transforms” an unsaturated sense into a saturated one, and review some attempted explanations in the literature. I argue that none of them is compatible with Frege’s broader views in semantics. Next I discuss one alternative that Frege himself endorses (the definite article indicating an attitude on the speaker’s part). This alternative, I argue, is also incompatible with his semantics. I conclude that Frege has no coherent view on singular senses.

*DF-IFCH and CLE-UNICAMP

Colloquium Logicae: Prof. Dr. Wolfgang Lenzen

"Leibniz Logic" on Wednesday April 15th, 16:30, Gödel Room at CLE- UNICAMP

"A Survey on Epistemic Logic" on Thursday 16th, 14:00, Gödel Room at CLE- UNICAMP

Biography and eulogy: Prof. Wolfgang Lenzen (in German)

http://www.lumer.info/wp-content/uploads/2012/04/C005_LumerMeyer_VorwortFSLenzen.pdf

Department of Philosophy, Universität Osnabrück, Germany

25/03 - Lucas Rosenblatt (Colloquium Logicae)

Capturing Naive Validity in the Strict-Tolerant Approach

Rejecting the structural rule of Cut has been recently proposed as a strategy to avoid both the usual semantic paradoxes and the so-called Validity Paradox. In this paper we consider if a theory that rejects Cut is capable of accurately representing its own notion of validity. We claim that the standard rules governing a naive validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a serious problem: an internalized version of Cut can be proved. We also evaluate a number of possible ways of escaping this difficulty.

11/03 - Emiliano Boccardi

If it ain’t Moving it shall not be Moved: real passage for A-theorists

Imagine two friends sitting on a beach, looking at a ship far away. Because of the distance, they cannot just tell by looking at it whether the ship is moving or not. “I bet it’s moving” says one. “No it’s not!”, says the other. Do they disagree about something? And if yes, what is the disagreement exactly about?

After some time the two friends look again and the ship has obviously moved, although it looks to them just as still as it looked before: its position (relative to them) has changed. “Aha!”, says the first, “I told you it was moving!” “You were right, it was moving. I lost the bet!”, says the other. What was this bet about?

Physics and mathematics  textbooks  follow  Bertrand  Russell  in accounting  for  a  body‘s instantaneous velocity not merely as equal to, but moreover as identical to the time-derivative of its trajectory. On this view, a body’s instantaneous velocity is ontologically parasitic on its trajectory. This deflationist understanding of change was heavily inspired by Weierstrass’ and Cantor’s understanding of limit and infinity. According to Weierstrass’ conception of limits and infinitesimals (now the received view), variables are just denotational schemas: they contribute to the sole purpose of denoting large numbers of (unchanging) facts about their values. The values of the variables do not themselves vary: they do not “approach”, let alone “reach” their limits, or change in any sense, contrary to what they were ambiguously alleged to be doing in prior formulations (since Newton’s and Leibniz’s). Of course, according to this conception, neither do variables themselves vary or change, in spite of their evocative name. It was this reconceptualization of the notion of limit that inspired Russell’s treatment of the antinomies involved in the notion of indefinitely growing series of things (such as those involved in Zeno’s paradoxes): “Weierstrass”, he says, “by strictly banishing all infinitesimals has at last shown that we live in an unchanging world, and that [Zeno’s] arrow, at every moment of its flight, is truly at rest” (POM, p. 347).

Likewise, many philosophers of time argue that the passage of time is identical with the fact that different times subsequently instantiate presentness.

However, I shall argue in the first part of this talk, it is tempting to think that the initial disagreement between the two friends is about a property instantiated by the ship at (and only at) the time of the bet (t1). What they observe at the time of the assessment of the bet (t2), according to this intuitive view, is the comparative fact that the ship’s location at t1 is different from its location at t2. They agree that this provides indirect evidence for the further (non-comparative) fact that the ship was moving at t1. If the ship is found at different positions at times right after t1, this must be because at t1 it possessed an intrinsic kinematic quantity in addition to its position.

If this explanatory pattern is sound, then the comparative fact that (a) the location of the ship at t1 is different from its location at t2, must be ontologically distinct from the (non-comparative) fact that (b) the object has been in motion for enough times between t1 and t2. In short, according to this view, the displacement of the ship is a posthumous consequence of its state of motion (velocity) throughout the time interval considered, hence fact b (the explanans) cannot be identical to fact a (the explanandum). Analogously, I shall defend the thesis that yesterday became past because time passes. The passage of time ought to explain the ensuing comparative fact that Today’s presentness followed Yesterday’s presentness, so it cannot be thought of as identical with it. The ensuing view construes passage as an intrinsic, non-comparative feature of time instants.

In the second, more tentative part of the talk, I shall bring this issue to bear on the formal semantics of axiomatic treatments of aspect. In particular, I shall consider different solutions to the so called Imperfective Paradox, and test them against the desiderata put forward in the first part of the talk.

References

Arntzenius, F. (2000) Are there really instantaneous velocities? Monist 83:187–208

Bach, E. (1986) The algebra of events, Linguistics and Philosophy, 9(1):5–16

Bigelow, J. (1991) Worlds enough for time. Nouˆs 25:1–19
. Bigelow J, Pargetter R (1990) Science and necessity. Cambridge University Press, Cambridge

Boccardi, E. (2015) If it ain't Moving it shall not be Moved, Topoi, 34(1): 171-185

Dowty, D. (1979) Word Meaning and Montague Grammar, Dordrecht: Reidel

Hall, N. (2004) Two concepts of causation. In: Collins, Hall N, Paul, LA (eds)

Causation and counterfactuals. The MIT Press, Cambridge, pp 225–276

James, W. (1987) Writings 1902–1910. Literary Classics of the United States inc., New York

Lange, M. (2005) How can instantaneous velocity fulfill its causal role? Philos Rev 114(4): 433–468

Le Poidevin, R. (2002) Zeno’s arrow and the significance of the present. In: Callender

Craig, University Cambridge (eds) Time, reality and experience. Press, Cambridge


Parsons, T., 1989, “The progressive in English: Events, states and processes”, Linguistics and Philosophy, 12(2): 213–241

–––, 1990, Events in the Semantics of English, Cambridge MA: MIT Press.

Prior, A., 1967, Past, Present, and Future, Oxford: Oxford University Press.

Russell, B. (1938) Principles of mathematics. W.W. Norton & Company, inc, New York


Tooley, M. (1988) In defense of the existence of states of motion. Philos Top 16:225–254

03/12 - Rodolfo Ertola

Adding connectives to non-classical logics

Already in 1919 Skolem studied, from an algebraic point of view, certain operations that appear afterwards from a logical point of view, for example in 1942 in a work by Moisil. This is done in the context of a logic that, more recently, has been called bi-intuitionistic. Some decades afterwards, there also appear many papers by the polish logician Rauszer on the same logic. More recently, in 2009, Priest gave a paraconsistent version of some kind of bi-intuitionistic logic. We have proved that, in fact, using a notion by Urbas, it is strictly paraconsistent. Approximately in the same tradition appears the connective ∆ of fuzzy logic. We have proved that, added to a Heyting algebra, the result is an equational class.

Another tradition was started in Russia by Novikov in the Fifties and corresponds to the notion of intuitionistic connective. These connectives are supposed to give conservative expansions and enjoy the Disjunction Property. Regarding this, we consider some problems that arise in the case of first-order intuitionistic logic for connectives suggested by Smetanich, Kuznetsov, Gabbay, and Humberstone.

Axioms may not be enough for the axiomatization, i.e. in some cases it is necessary to add a rule. From a semantical point of view, the choice is between a truth-preserving or a truth-degree-preserving consequence.

Unicamp - Brazil

19/11 - Esko Turunen, PhD*

A Paraconsistent Version of Pavelka's Fuzzy Logic

In 1979 Jan Pavelka introduced a very general framework to deal with many valued logics. Pavelka's  idea was to process Zadeh's Fuzzy Sets such that theories, rules of inference, proofs as well as  tautologies may be only partial, i.e. fuzzy. Pavelka defined all his concepts in complete residuated lattices. The main issue was to study the circumstances under which the fuzzy semantic consequence operation and fuzzy syntactic operation coincide; such a property is called Pavelka style completeness.  Pavelka solved the problem in the special case that the set of truth values is the Lukasiewicz sturucure, i.e. the real unit interval equipped with standard MV-structure. The present author has recently proved that Pavelka style completeness holds if, and only if the set of truth values is a complete MV-algebra. Thus, if in particular ,the set M of truth values is a certain collection of 2x2-matrices equipped with suitable operations, then M is a complete MV-algebra. In fact, the set M extends Belnap's four valued para consistent logic. Such an approach results a complete many-valued logic that behaves consistently when looking from outside: the structure in related to Lukasiewicz logic which is a consistent logic. However, looking the logic from inside, i.e. a single 2x2-matrix, para consistency steps in. Truth and falsehood are not opposites of each other, and also contradictions and lack of knowledge is involved.

*Tampere University of Technology (Tampere, Finland)

12/11 - Francesc Esteva* & Lluis Godo*

On paraconsistent fuzzy logics

Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. Aiming at studying logics that can handle inconsistency and graded truth at once, this talk will report about recent investigations on how a notion of paraconsistent fuzzy logic can be cast within the framework of the so-called logics of formal inconsistency (LFIs).

As in classical logic, it is clear that the notion of truth-preserving deduction commonly used in systems of mathematical fuzzy logic is incompatible with any form of paraconsistency. However, in the first part of the seminar we will show that, instead, some degree-preserving fuzzy logics exhibit interesting paraconsistency features. We will also consider expansions of these logics with additional negation connectives and study their paraconsistency properties as LFIs.

In the second part of the seminar, we will address a kind of converse problem, namely how to extend a given fuzzy logic with a new “consistency” operator in the style of the LFIs. We will introduce a set of postulates for this type of operators over the corresponding algebras, leading to the definition and axiomatization of a family of logics, expansions of MTL, whose degree-preserving counterpart are paraconsistent and moreover LFIs.

 

In the third and final part of the seminar, we will talk about some remarks on ongoing work on the study on intermediate paraconsistent fuzzy logics between the truth-preserving and degree-preserving logics.

 

*IIIA - CSIC, Barcelona, Spain