Massimiliano Carrara

Identity criteria are used to confer ontological respectability: Only entities with clearly determined identity criteria are ontologically ac-ceptable. From a logical point of view, identity criteria should mirror the identity relation in being reflexive, symmetrical, and transitive. However, this ...

In our paper, we propose a relativisticand metaphysically neutral identity criterionfor biological entities. We start from thecriterion of genidentity proposed by K. Lewinand H. Reichenbach. Then we enrich it to renderit more philosophical powerful and so capableof dealing with the real transformations thatoccur in the extremely variegated biologicalworld.

Identity criteria are used to confer ontological respectability: Only entities with clearly determined identity criteria are ontologically acceptable. From a logical point of view, identity criteria should mirror the identity relation in being reflexive, symmetrical, and transitive. However, this logical constraint is only rarely met. More precisely, in some cases, the relation representing the identity condition fails to be transitive. We consider the proposals given so far to give logical adequacy to inadequate identity conditions. We focus on the most refined proposal and expand its formal framework by taking into account two further aspects that we consider essential in the application of identity criteria to obtain logical adequacy: contexts and granular levels.

Priest’s dialetheism is the view that some sentences, called dialetheias, are both true and false. A crucial problem of dialetheism is that of avoiding trivialism, i.e. the consequence that all sentences are dialetheias. In the present paper we want to discuss Priest’s strategy for avoiding Curry’s paradox, from which trivialism follows. Besides, we will formulate a new version of Curry’s paradox, using a notion of naïve deducibility, which, in our opinion, should be accepted by Priest himself.

Formalizing the ontological commitment of a logical language means offering a way to specify the intended meaning of its vocabulary by constraining the set of its models, giving explicit information about the intended nature of the modelling primitives and their a priori relationships. We present here a formal definition of ontological commitment which aims to capture the very basic ontological assumptions about the intended domain, related to issues such as identity and internal structure. To tackle such issues, a modal framework endowed with mereo-topological primitives has been adopted. The paper is mostly based on a revisitation of philosophical (and linguistic) literature in the perspective of knowledge representation. 1 Introduction First order logic is notoriously neutral with respect to ontological choices: when a logical language is used with the purpose of modelling a particular aspect of reality, the set M of all its models is usually much larger than the set M i of the i...

The aim of this paper is to refine, integrate and apply the methodology of OntoClean. Three aspects are taken into account; two of them concern main ideas of OntoClean, the third one is a study of a particular important application. The first section deals with the topic of identity: formal constraints on identity criteria, com-patibility and identity among identity criteria. The second section deals with rigidity, dependence and existence. The final section investigates how meta-property criteria can be applied to the notion of artifact.

Formalizing the ontological commitment of a logical lan- guage means offering a way to specify the intended meaning of its vocabulary by constraining the set of its models, giv- ing explicit information about the intended nature of the modelling primitives and their a priori relationships. We present here a formal definition of ontological commitment which aims to capture the very basic ontological assump- tions about the intended domain, related to issues such as identity and internal structure. To tackle such issues, a modal framework endowed with mereo-topological primi- tives has been adopted. The paper is mostly based on a re- visitation of philosophical (and linguistic) literature in the perspective of knowledge representation.

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 true. 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, a proof that only resorts to naive 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 are problematic.

Nicholas Rescher, in The Limits of Science (1984), argued that: «perfected science is a mirage; complete knowledge a chimera» . He reached the above conclusion from a logical argument known as Fitch’s Paradox of Knowability. The argument, starting from the assumption that every truth is knowable, proves that every truth is also actually known and, given that some true propositions are not actually known, it concludes, by modus tollens, that there are unknowable truths. Prima facie, this argument seems to seriously narrow our epistemic possibilities and to constitute a limit for knowledge (included scientific knowledge). Rescher’s above quoted conclusion follows the same sort of reasoning. Recently, Bernard Linsky exploited a possible way to block the argument employing a type-distinction of knowledge. If the Knowability paradox is blocked, then Rescher’s conclusion cannot be drawn. After an introduction to the paradox, we suggest, in our paper, a possible way of justifying a type-so...

The Knowability Paradox is a logical argument that, starting from the plainly innocent assumption that every true proposition is knowable, reaches the strong conclusion that every true proposition is known; i.e. if there are unknown truths, there are unknowable truths. The paradox has been considered a problem for every theory assuming the Knowability Principle, according to which all truths are knowable and, in particular, for semantic anti-realist theories. A well known criticism to the Knowability Paradox is the so called restriction strategy. It bounds the scope of the universal quantification in (KP) to a set of formulas whose logical form avoids the paradoxical conclusion. Specifically, Tennant suggests to restrict the quantifier in (KP) to propositions whose knowledge is provably inconsistent. He calls them Anti-Cartesian propositions and distinguished them in three kinds. In this paper we will not be concerned with the soundness of the restriction proposal and the criticisms...

A logical argument known as Fitch’s Paradox of Knowability, starting from the assumption that every truth is knowable, leads to the consequence that every truth is also actually known. Then, given the ordinary fact that some true propositions are not actually known, it concludes, by modus tollens, that there are unknowable truths. The main literature on the topic has been focusing on the threat the argument poses to the so called semantic anti-realist theories, which aim to epistemically characterize the notion of truth; according to those theories, every true proposition must be knowable. But the paradox seems to be a problem also for epistemology and philosophy of science: the conclusion of the paradox – the claim that there are unknowable truths – seems to seriously narrow our epistemic possibilities and to constitute a limit for knowledge. This fact contrasts with certain views in philosophy of science according to which every scientific truth is in principle knowable and, at le...

In "The Limits of Science" N. Rescher introduces a logical argument known as the Knowability Paradox, according to which, if every true proposition is knowable, then every true proposition is known, i.e. if there are unknown truths, there are unknowable truths. Rescher argues that the Knowability Paradox, giving evidence to a limit of our knowledge (the existence of unknowable truths) could be used for arguing against perfected science. In this article we present two criticisms against Rescher's argument.

ABSTRACT In Mathematics is megethology (Lewis (1993). Philosophia Mathematica, 1(1), 3-23) 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. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality without plural quantification.

ABSTRACT According to strong composition as identity (CAI), the logical principles of one-one 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. To this aim, we analyse as a case study Cotnoir’s theory of general identity, in which indiscernibility is obtained thanks to a revisionary semantics and true identity statements are allowed to connect non-coreferential terms. We extend Cotnoir’s strategy for indiscernibility to the relation of comaternity, and we show that, neither in the case of composition nor in that of comaternity, indiscernibility contibutes to show that they are genuine identity relations. Finally, we compare Cotnoir’s approach with other versions of strong CAI endorsed by Wallace, Bøhn, and Hovda, and canvass the extent to which they violate coreferentiality. The comparative analysis shows that, in order to preserve coreferentiality, strong CAI is forced to adopt a non-standard semantic treatment of the singular/plural distinction.

ABSTRACT The goal of the paper "Pragmatic and dialogic interpretation of bi-intuitionism. Part I" [3] 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 [8]. A chirality consists of a pair of adjoint functors L ⊣ R, with L: A → B, R: B → A, and of a functor (.)* : A → Bop(0,1) 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.

ABSTRACT According to classical logic, the acceptance of a dialetheia, a proposition that is both true and false, entails trivialism the output that every sentence is true. One way to accept dialetheias but avoid trivialism is to reject the general validity of classical logic, which is the view held by dialetheists, supporters of the existence of dialetheias. In The Logic of Paradox (LP), Priest adopts the material conditional, identifying \(A \rightarrow B\) with \(\lnot A \vee B\). He argues that this is not a genuine conditional because it invalidates modus ponens (MP), an essential rule governing the use of the conditional. In subsequent works he introduces a genuine conditional and tries to avoid Curry’s paradox by invoking a highly problematic modal semantics. The aim of our paper is to argue that a dialetheist can stick to the material conditional and recover the whole of classical logic without falling into trivialism. Our strategy sets forth a way of understanding the notion of assumption suitable for the dialetheic perspective. We show the inadequacy of formal classical logic to capture the intended exclusivity of negation. Finally, we argue that the material conditional is adequate to provide a dialetheic solution to semantic paradoxes.

Abstract - In this paper we focus on a specific aspect of the notion of conceptualisation, ie on the issue of the specification of a certain kind of concept: sortal concept. Our starting point is the intuitive idea that a sortal concept cannot be specified in isolation from a general notion of ...

Abstract Relativists maintain that identity is always relative to a general term (RI). According to them, the notion of absolute identity has to be abandoned and replaced by a multiplicity of relative identity relations for which Leibniz's Law does not hold. For relativists RI is at least ...

Abstract. In “Mathematics is megethology,” Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. ...

The book begins with a prologue (coauthored with Maurizio Ferraris), a fictional dialogue between the characters of Berkeley's Three Dialogues, Hylas and Philonous, and ends with an epilogue, The plane of a Square, a short sequel to EA Abbott's Flatland. In between there ...

From a logical point of view, identity criteria should mirror the identity relation in being reflexive, symmetrical, and transitive. However, the relation representing the identity condition fails to be transitive in many cases. We consider the proposals given so far to give logical ...

In Parts of Classes [Lewis 1991] David Lewis attempts to draw a sharp contrast between mereology and set theory and to assimilate mereology to logic. He argues that, like logic but unlike set theory, mereology is “ontologically innocent”. In mereology, given certain ...