Papers in Journal by Massimiliano Carrara
Are identity criteria grounding principles? A prima facie answer to this question is positive. Sp... more Are identity criteria grounding principles? A prima facie answer to this question is positive. Specifically, two-level identity criteria can be taken as principles related to issues of identity among objects of a given kind compared with objects of a more basic kind. Moreover, they are grounding metaphysical principles of some objects with regard to others. In the first part of the paper we criticise this prima facie natural reading of identity criteria. This result does not mean that identity criteria could not be taken as grounding principles. In the second part, we propose some basic steps towards a conceptual reading of grounding. Such a way of understanding it goes along with an epistemic reading of identity criteria.
The standard rule of single privative modification replaces privative modifiers by Boolean negati... more The standard rule of single privative modification replaces privative modifiers by Boolean negation. This rule is valid, for sure, but also simplistic. If an individual a instantiates the privatively modified property (MF) then it is true that a instantiates the property of not being an F, but the rule fails to express the fact that the properties (MF) and F have something in common. We replace Boolean negation by property negation, enabling us to operate on contrary rather than contradictory properties. To this end, we apply our theory of intensional essentialism, which operates on properties (intensions) rather than their extensions. We argue that each property F is necessarily associated with an essence, which is the set of the so-called requisites of F that jointly define F. Privation deprives F of some but not all of its requisites, replacing them by their contradictories. We show that properties formed from iterated privatives, such as being an imaginary fake banknote, give rise to a trifurca-tion of cases between returning to the original root property or to a property contrary to it or being semantically undecidable for want of further information. In order to determine which of the three forks the bearers of particular instances of multiply modified properties land upon we must examine the requisites, both of unmodified and modified properties. Requisites underpin our presuppositional theory of positive predication. Whereas privation is about being deprived of certain properties, the assignment of requisites to properties makes positive predication possible, which is the predication of properties the bearers must have because they have a certain property formed by means of privation. KEYWORDS Iterated modification ⋅ privative modification ⋅ property negation ⋅ contraries ⋅ requisite property ⋅ intensional essentialism
The standard rule of single privative modification replaces privative modifiers by Boolean negati... more The standard rule of single privative modification replaces privative modifiers by Boolean negation. This rule is valid, for sure, but also simplistic. If an individual a instantiates the privatively modified property (MF) then it is true that a instantiates the property of not being an F, but the rule fails to express the fact that the properties (MF) and F have something in common. We replace Boolean negation by property negation, enabling us to operate on contrary rather than contradictory properties. To this end, we apply our theory of intensional essentialism, which operates on properties (intensions) rather than their extensions. We argue that each property F is necessarily associated with an essence, which is the set of the so-called requisites of F that jointly define F. Privation deprives F of some but not all of its requisites, replacing them by their contradictories. We show that properties formed from iterated privatives, such as being an imaginary fake banknote, give rise to a trifurcation of cases between returning to the original root property or to a property contrary to it or being semantically undecidable for want of further information. In order to determine which of the three forks the bearers of particular instances of multiply modified properties land upon we must examine the requisites, both of unmodified and modified properties. Requisites underpin our presuppositional theory of positive predication. Whereas privation is about being deprived of certain properties, the assignment of requisites to properties makes positive predication possible, which is the predication of properties the bearers must have because they have a certain property formed by means of privation.
Following the speech act theory, we take hypotheses and assertions as linguistic acts with differ... more Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola (1995, Erkenntnis, 43, 81–109) by outlining a pragmatic logic for assertions and hypotheses. On the basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses.
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0. Per il dialeteista esistono contraddizioni vere, cioè enunciati simultaneamente veri e falsi, ... more 0. Per il dialeteista esistono contraddizioni vere, cioè enunciati simultaneamente veri e falsi, detti dialeteie. 1 Si tratta di una posizione filosofica ampiamente discussa e criticata in letteratura. 2 Considereremo qui alcune critiche e repliche che ci sembrano particolarmente rilevanti.
In To be is to be the object of a possible act of choice (6) the authors defended Boolos' thesis ... more In To be is to be the object of a possible act of choice (6) the authors defended Boolos' thesis that plural quantification is part of logic. To this purpose, plural quantification was explained in terms of plural reference, and a semantics of plural acts of choice, performed by an ideal team of agents, was introduced. In this paper, following that approach, we develop a theory of concepts that – in a sense to be explained – can be labelled as a theory of logical concepts. Within this theory we propose a new logicist approach to natural numbers. Then, we compare our logicism with Frege's traditional logicism.
This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Con... more This paper proposes a new dialetheic logic, a Dialetheic Logic with Exclusive Assumptions and Conclusions (DLEAC), including classical logic as a particular case. In DLEAC, exclusivity is expressed via the speech acts of assuming and concluding. In the paper we adopt the semantics of the logic of paradox (LP) extended with a generalized notion of model and we modify its proof theory by refining the notions of assumption and conclusion. The paper starts with an explanation of the adopted philosophical perspective, then we propose our DLEAC logic. Finally, we show how DLEAC supports the dialetheic solution of the liar paradox.
The goal of is to sketch the construction of a syntactic categorical model of the bi-intuitionist... more The goal of is to sketch the construction of a syntactic categorical model of the bi-intuitionistic logic of assertions and hypotheses AH, axiomatized in a sequent calculus AH-G1, and to show that such a model has a chirality-like structure inspired by the notion of dialogue chirality by P-A. Melliès . A chirality consists of a pair of adjoint functors L ⊣ R, with L : A → B, R : B → A, and of a functor ( ) * : A → B op satisfying certain conditions. The definition of the logic AH in [3] needs to be modified so that our categories A and B are actually dual. With this modification, a more complex structure emerges.
According to strong composition as identity (CAI), the logical principles of oneone and plural id... more According to strong composition as identity (CAI), the logical principles of oneone and plural identity can and should be extended to the relation between a whole and its parts. Otherwise, composition would not be legitimately regarded as an identity relation. In particular, several defenders of strong CAI have attempted to extend Leibniz's Law to composition. However, much less attention has been paid to another, not less important feature of standard identity: a standard identity statement is true iff its terms are coreferential. We contend that, if coreferentiality is dropped, indiscernibility is no help in making composition a genuine identity relation.
We reconsider the pragmatic interpretation of intuitionistic logic regarded as a logic of asserti... more We reconsider the pragmatic interpretation of intuitionistic logic regarded as a logic of assertions and their justifications and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication . We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses ] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the S4 modal translation, we give a definition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work . A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction. Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is defined and a probabilistic interpretation of linear co-intuitionism is given as in . Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, defined as a hypothesis that in some situation the truth of p is epistemically necessary.
We give a "dialogic interpretation" of multiplicative linear polarized bi-intuitionistic logic by... more We give a "dialogic interpretation" of multiplicative linear polarized bi-intuitionistic logic by specifying what counts as evidence for and evidence against assertions and hypotheses. Assuming a notion of duality between assertions and hypotheses in common sense reasoning, evidence against an assertion A coincides with a scintilla of evidence for the dual hypothesis A ⊥ , and evidence against a hypothesis C is conclusive evidence for the dual assertion C ⊥ . Mathematically, such an interpretation may be regarded as a translation of multiplicative linear polarized bi-intuitionism into intuitionistic multiplicative linear logic with products. The interplay between evidence for and evidence against assertions and hypotheses is inspired by Chu's construction [4], usually regarded as an abstract form of the "game semantics" for linear logic. Here instead of producing models of classical multiplicative linear logic from models of intuitionistic multiplicative linear logic, the construction yields a dual interpretation of linear intuitionism and co-intuitionism. We leave it as an open problem how to extend our "dialogic interpretation" of the whole system of polarized biintuitionistic logic, rather than of its linear part.
In Mathematics is megethology (Lewis, 1993) David K. Lewis proposes a structuralist reconstructio... more In Mathematics is megethology (Lewis, 1993) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos' plural quantification for treating second order logic without commitment to set-theoretical entities.
This special issue collects together nine new essays on logical consequence: the relation obtaini... more This special issue collects together nine new essays on logical consequence: the relation obtaining between the premises and the conclusion of a logically valid argument. This paper is a partial, and opinionated, introduction to the topic. We focus on two influential accounts of consequence, the model-theoretic and the proof-theoretic, and on the seeming platitude that valid arguments necessarily preserve truth. We briefly discuss the main objections these accounts face, as well as Hartry Field's contention that such objections show consequence to be a primitive, indefinable notion, and that we must reject the claim that valid arguments necessarily preserve truth. We make three main claims: (i) that the accounts in question have the resources to meet the objections standardly thought to herald their demise; (ii) that consequence, as opposed to logical consequence, is the epistemologically significant relation philosophers should be mainly interested in; and (iii) that consequence is a paradoxical notion if truth is. for helpful discussion over the years on some of the topics discussed herein. Special thanks to Gil Sagi for detailed and very helpful comments on an earlier draft. Julien Murzi gratefully acknowledges the Analysis Trust, the Alexander von Humboldt Foundation, the University of Kent, and the British Academy for generous financial support during the time this paper or its ancestors were written. Part of §4 is partly drawn from ?, ? and ?.
Logical orthodoxy has it that classical first-order logic, or some extension thereof, provides th... more Logical orthodoxy has it that classical first-order logic, or some extension thereof, provides the right extension of the logical consequence relation. However, together with naïve but intuitive principles about semantic notions such as truth, denotation, satisfaction, and possibly validity and other naïve logical properties, classical logic quickly leads to inconsistency, and indeed triviality. At least since the publication of Kripke's Outline of a theory of truth , an increasingly popular diagnosis has been to restore consistency, or at least non-triviality, by restricting some classical rules. Our modest aim in this note is to briefly introduce the main strands of the current debate on paradox and logical revision, and point to some of the potential challenges revisionary approaches might face, with reference to the nine contributions to the present volume. 1 Our discussion is structured thus. Section 1 reviews the Liar and the Knower paradoxes. Section 2 briefly discusses four revisionary approaches. Section 3 sketches a potential challenge for revisionary approaches to semantic paradox. For reasons of space, we have mostly aimed at presenting the big picture, in broad strokes, thus sacrificing many important details.
We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express... more We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express disagreement with the assertion of A by denying A. We show that, if denial is to serve as a means to express disagreement, it must be exclusive, in the sense of being correct only if what is denied is false only. Hence, it can't be expressed in the glut theorist's language, essentially for the same reasons why Boolean negation can't be expressed in such a language either. We then turn to an alternative proposal, recently defended by Beall (in Analysis 73(3):438-445, 2013; Rev Symb Log, 2014), for expressing truth and falsity only, and hence disagreement. According to this, the exclusive semantic status of A, that A is either true or false only, can be conveyed by adding to one's theory a shrieking rule of the form A^:A ' ?, where ? entails triviality. We argue, however, that the proposal doesn't work either. The upshot is that glut theorists face a dilemma: they can either express denial, or disagreement, but not both. Along the way, we offer a bilateral logic of exclusive denial for glut theorists-an extension of the logic commonly called LP.
Dialetheism holds the thesis that certain sentences are dialetheias, i.e. both true and false, an... more Dialetheism holds the thesis that certain sentences are dialetheias, i.e. both true and false, and devises several strategies for avoiding trivialism, the (classical) consequence that all sentences are provable. Two such strategies are aimed at invalidating one of the most direct arguments for trivialism, viz. Curry's Paradox: a proof that you will win the lottery which only resorts to naïve truth-principles, Conditional Proof (CP), modus ponens (MPP) and the standardly accepted structural rules. The first strategy simply consists in observing that the most well-known dialetheist logic, sometimes referred to as the Logic of Paradox (LP), invalidates MPP. The second strategy consists in rather taking one of the primary senses of 'if' to be captured by an entailment connective which does not validate CP. We argue that both strategies prove problematic.
We consider a "polarized" version of bi-intuitionistic logic ] as a logic of assertions and hypot... more We consider a "polarized" version of bi-intuitionistic logic ] as a logic of assertions and hypotheses and show that it supports a "rich proof theory" and an interesting categorical interpretation, unlike the standard approach of C. Rauszer's Heyting-Brouwer logic , whose categorical models are all partial orders by Crolard's theorem . We show that P. A. Melliès notion of chirality appears as the right mathematical representation of the mirror symmetry between the intuitionistic and co-intuitionistc sides of polarized bi-intuitionism. Philosophically, we extend Dalla Pozza and Garola's pragmatic interpretation of intuitionism as a logic of assertions [10] to bi-intuitionism as a logic of assertions and hypotheses. We focus on the logical role of illocutionary forces and justification conditions in order to provide "intended interpretations" of logical systems that classify inferential uses in natural language and remain acceptable from an intuitionistic point of view. Although Dalla Pozza and Garola originally provide a constructive interpretation of intuitionism in a classical setting, we claim that some conceptual refinements suffice to make their "pragmatic interpretation" a bona fide representation of intuitionism. We sketch a meaning-asuse interpretation of co-intuitionism that seems to fulfil the requirements of Dummett and Prawitz's justificationist approach. We extend the Brouwer-Heyting-Kolmogorov interpretation to bi-intuitionism by regarding co-intuitionistic formulas as types of the evidence for them: if conclusive evidence is needed to justify assertions, only a scintilla of evidence suffices to justify hypotheses.
In Mathematics is megethology (Lewis, Philos Math 1:3-23, 1993) Lewis reconstructs set theory com... more In Mathematics is megethology (Lewis, Philos Math 1:3-23, 1993) Lewis reconstructs set theory combining mereology with plural quantification. He introduces megethology, a powerful framework in which one can formulate strong assumptions about the size of the universe of individuals. Within this framework, Lewis develops a structuralist class theory, in which the role of classes is played by individuals. Thus, if mereology and plural quantification are ontologically innocent, as Lewis maintains, he achieves an ontological reduction of classes to individuals. Lewis'work is very attractive. However, the alleged innocence of mereology and plural quantification is highly controversial and has been criticized by several authors. In the present paper we propose a new approach to megethology based on the theory of plural reference developed in To be is to be the object of a possible act of choice (Carrara, Stud Log 96: 289-313, 2010). Our approach shows how megethology can be grounded on plural reference without the help of mereology.
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Papers in Journal by Massimiliano Carrara
conditions for B to be a consequence of $\Gamma$ in PWK.
preserve truth. We briefly discuss the main objections these accounts face, as well as Hartry Field’s contention that such objections show consequence to be a primitive, indefinable notion, and that we must reject the claim that valid arguments necessarily preserve truth. We suggest that the accounts in question have the resources to meet the objections standardly thought to herald their demise and make two main claims: (i) that consequence, as opposed to logical consequence, is the epistemologically significant relation philosophers should be mainly interested in; and (ii) that consequence is a paradoxical notion if truth is.
as Identity (CAI), the Principle of Indiscernibility of Identicals
can be extended to composition, by resorting to broadly Fregean
relativizations of cardinality ascriptions. In this paper we analyze various ways in
which this relativization could be achieved. According
to one broad variety of relativization, cardinality ascriptions are
about objects, while concepts occupy an additional argument place.
It should be possible to paraphrase the cardinality ascriptions in
plural logic and, as a consequence, relative counting requires the
relativization either of quantifiers, or of identity, or of the
is one of relation. However, some of these relativizations
do not deliver the expected results, and others rely on problematic
assumptions. In another
broad variety of relativization, cardinality ascriptions are about
concepts or sets. The most promising development of this approach is prima
facie
connected with a violation of the so-called Coreferentiality
Constraint, according to which an identity statement is true only if
its terms have the same referent. Moreover -- even provided that the
problem with coreferentiality can be fixed -- the resulting analysis of
cardinality ascriptions meets several difficulties.
Lectures 2016
Dialetheism and the History of (Western) Philosophy
Graham Priest
Distinguished Professor of Philosophy at the Graduate Center, City University of New York,
and Boyce Gibson Professor Emeritus of Philosophy at the University of Melbourne (Australia)
1. Paraconsistent Logic (14 June 2016, 15.30-18.30, Sala delle Edicole, ingresso arco Valaresso)
In this class we will look at paraconsistent logics (logics which tolerate contradictions). We will look at the history of such logics, and some of the basic ideas involved in them. This will involve a little formal logic, but not much.
2. Dialetehesim (15 June 2016, 15-18, Sala delle Edicole, ingresso arco Valaresso)
In this class we will look at the possibility that some contradictions are true (dialetheism), the arguments against it, and some of the arguments for it.
3. Hegel (16 June 2016, 10-13, aula FILM, primo piano Palazzo del Capitanio)
Interpretations of Hegel vary. However, he is arguably the most notable dialetheist in the history of Western philosophy. In this class, we will look at his thought from the perspective of modern dialetheism.
4. The Limits of Thought (16 June 2016, 15-18, aula FILM, primo piano Palazzo del Capitanio)
In this class we will look at one of the most important places where dialetheism seems to appear in philosophy: where a position holds that there are some things that go beyond language, and explains why—in the process, engendering contradiction.
5. Heidegger (17 June 2016, 10-13, aula DIANO, palazzo Liviano)
In this class we will look in detail at one of the philosophers for whom this situation arises: Heidegger, in his wrestling with the problem of being. We will see that he should have been a dialetheist—and perhaps that towards the end of his life actually became one.
Organizzazione scientifica:
Massimiliano Carrara
Dipartimento FISPPA - Università di Padova
Informazioni: [email protected]
The conference will host the main scholars involved in this debate, with the purpose of encouraging innovative solutions to the following open problems:
a) Is there any inferential or evidential connection between Composition as Identity and mereological principles?
b) Does the debate between monism and dualism in the theory of constitution really concern mereology? Is dualism compatible or incompatible with mereological extensionalism?
c) Is it possible and interesting to combine mereological extensionalism and/or Composition as Identity with non-standard doctrines of identity, such as relative identity or milder forms of pluralism about identity?
d) What does the Yi/Sider Collapse show about the application of plural logic to mereology?
e) How do the appeals to the Indiscernibility of Identicals in the debate about Composition as Identity differ from the appeals to the Indiscernibility of Identicals in the debate about the theory of constitution?
f) Is Composition as Identity compatible with non-standard mereologies, or to pluralist theories of parthood?
g) According to Composition as Identity the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. How is this relativization achieved?
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