On Formalizing Logical Modalities

This paper is in the scope of the philosophy of modal logic; more precisely, it concerns the semantics of modal logic, when the modal elements are interpreted as logical modalities. Most authors have thought that the logic for logical modality—that is, the one to be used to formalize the notion of logical truth (and other related notions)—is to be found among logical systems in which modalities are allowed to be iterated. This has raised the problem of the adequacy, to that formalization purpose, of some modal schemes, such as S4 and S5 . It has been argued that the acceptance of S5 leads to non-normal modal systems, in which the uniform substitution rule fails. The thesis supported in this paper is that such a failure is rather to be attributed to what will be called “Condition of internalization.” If this is correct, there seems to be no normal modal logic system capable of formalizing logical modality, even when S5 is rejected in favor of a weaker system such as S4, as recently proposed by McKeon.

Boulez – Xenakis: Two Converging Musical Heuristics

What is heuristics? The methods of imagination that prepares for invention and discovery, by accepting that all arguments are good if they can succeed in achieving the proposed goals. A principle is deemed to be heuristic, therefore, when it is considered not on the basis of the truth it supports but by the fact that it contributes wholly or partly to the realisation of some project. In order to compose a work, the creator has a certain number of dominant ideas, which function as pivots or fixed points around which the piece develops. The value of these ideas, which sometimes take the form of theories borrowed from the physical or mathematical sciences, is justified a posteriori, by the realisation of the works that emerge from them, and not a priori: the experimental or logical truth of what they assert, even if confirmed by experimental reality, is put here in brackets. These principles count as opinions for the composer; they are the heuristic principles of creation. The aim of this paper is to analyse the principles that operate as the driving force behind the creation of Boulez and Xenakis.

Identifying Fake News on Social Networks Based on Natural Language Processing: Trends and Challenges

The epidemic spread of fake news is a side effect of the expansion of social networks to circulate news, in contrast to traditional mass media such as newspapers, magazines, radio, and television. Human inefficiency to distinguish between true and false facts exposes fake news as a threat to logical truth, democracy, journalism, and credibility in government institutions. In this paper, we survey methods for preprocessing data in natural language, vectorization, dimensionality reduction, machine learning, and quality assessment of information retrieval. We also contextualize the identification of fake news, and we discuss research initiatives and opportunities.

Logical Form through Abstraction

In a recent book, Logical Form: between Logic and Natural Language, Andrea Iacona argues that semantic form and logical form are distinct. The semantic form of a sentence is something that (together with the meanings of its parts) determines what it means; the logical from of a sentence is something that (all by itself) determines whether it is a logical truth. Semantic form does not depend on context but logical form does: for example, whether ‘This is this’ is a logical truth depends on whether the two occurrences of ‘this’ are used to demonstrate the same individual. I respond by claiming that logical form is indifferent to reference and is sensitive only to obligatory co-reference. When the speaker intends both occurrences of ‘this’ to be interpreted the same way the logical from of ‘This is this’ is a=a, while in a context where the speaker has no such intention it is a=b. This proposal allows a much more conservative revision of the traditional picture than the one suggested by Iacona. Instead of identifying the logical form of a natural language sentence by seeking a formalization in an artificial language, we obtain it through abstraction from its syntactic analysis: replacing the non-logical expressions by schematic letters, making sure that we use identical ones if and only if the speaker intended co-reference.

Logical Conventionalism

This chapter argues that logical truth, validity, and necessity in any language can be fully explained in terms of the language’s linguistic conventions. More particularly, it is demonstrated that unrestricted logical inferentialism is a version of logical conventionalism by arguing for conventionalism in detail and answering various objections involving the role of metasemantic principles and semantic completeness in the conventionalist argument. The chapter then discusses how this account relates to the deflationist accounts offered by Field and others, before turning to the metaphysics and normativity of logic, which it discusses on conventionalist grounds. Overall, this chapter shows that conventionalism leads to a naturalistically acceptable and philosophically plausible theory of logic.

From Logic to Mathematics

Part II (chapters 3-7) of the book developed and defended an inferentialist/conventionalist theory of logic. In this, the opening chapter of part III, it is explained why the extension of part II’s approach from logic to mathematics faces significant philosophical challenges. The first major challenge concerns the ontological commitments of mathematics. It is received wisdom in philosophy that existence claims cannot be analytic or trivially true, making it difficult to see how a conventionalist account of mathematics could possibly be viable. The second major challenge concerns mathematical truth. Unlike (first-order) logical truth, mathematical truth, even in basic arithmetic, is computationally rich. There are serious challenges for conventionalists in trying to capture our intuition that mathematical truth is fully determinate, in light of this feature.

The Very Idea of Truth by Convention

This chapter answers various influential arguments against truth by convention, in general, and logical conventionalism, in particular. The first argument discussed claims that the contingency of our linguistic conventions is incompatible with the necessity of logical truth. The second claims that while conventions can be used to determine the content of a sentence, they cannot possibly make that content be the case (I call this “the master argument” against conventionalism, because of its influence). The third argument discussed is Quine’s famous argument against logical conventionalism. The fourth is a variation on Quinean themes, related to the later Wittgenstein’s radical conventionalism and Dummett’s discussions of Wittgenstein’s views. The fifth and final objection is Williamson’s argument against understanding-assent links. The chapter’s discussion shows that each of these arguments against conventionalism has decisive failings.

Logical Combinatorialism

In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentences. The resulting theory, formulated in higher-order logic, also vindicates the Humean idea that fundamental properties and relations are freely recombinable and a variant of the structural idea that propositions can be decomposed into their fundamental constituents via logical operations. Indeed, it is seen that, although these ideas are seemingly distinct, they are not independent, and fall out of a natural and general theory about the granularity of reality.

New semantics for urn logics: taming the enduring scandal of deduction

The traditional theory of semantic information, originally proposed by [Bar-Hillel, Carnap, 1953], provides a versatile and pretty plausible conception of what kind of thing semantic information is. It embodies, however, the so-called “scandal of deduction”, a thesis according to which logical truths are informationally empty. The scandal of deduction is prob- lematic because it contradicts the fact that ordinary reasoners often do not know whether or not a given sentence is a logical truth. Hence, it is plausible to say, at least from the epistemological standpoint of those reasoners, that such logical sentences are really inform- ative. In order to improve over traditional theory, we can replace its classical metatheory by the so-called urn logics, non-standard systems of logic (described in detail below) that better describe the epistemological standpoint of ordinary reasoners. Notwithstanding, the applic- ation of such systems to the problem of semantic information faces some challenges: first, we must define truth-conditional semantics for these systems. Secondly, we need to precisely distinguish two systems of urn logic, namely, perfect and imperfect urn logics. Finally, we need to prove characterization theorems for both systems of urn logic. In this paper we offer original (and hopefully, elegant) solutions for all such problems.