This paper presents a unified, more-or-less complete, and largely pragmatic theory of indicative conditionals as they occur in natural language, which is entirely truth-functional and does not involve probability. It includes material implication as a special—and the most important—case, but not as the only case. The theory of conditional elements, as we term it, treats if-statements analogously to the more familiar and less controversial other truth-functional compounds, such as conjunction and disjunction.

Extends the theory of conditional elements in three ways. The critical way, primarily due to the senior author, is the solution to the fallacy of the strengthened antecedent within classical logic.

We put forth a theory of conditional elements which can be used to dismiss apparent challenges to the truth-functionality of the conditional without apparent circularity. In the process, we refine the ideas of Yoes, published in an earlier paper in this journal, broadening and deepening them.

This paper deals with Austinian ifs of every stripe within classical logic. It is argued that they are truth-functional and the theory of conditional elements is used. Ellipsis is key. Corrects an error in Fulda (2010) in translation and therefore scope. -/- The PDF is made available gratis by the Publisher.

In "Material Implications" (1992), mathematical discourse was said to be different from ordinary discourse, with the discussion centering around conditionals. This paper shows how.

In this paper, the author addresses the problem of socialisation of children with a history of disabilities and mental retardation by means of visual arts. It is important to look at the very sphere of life of these categories of children. As a rule, these children, for the most part, live in dysfunctional families, which makes it almost impossible to provide them with a form of socialization. This article focuses on the extent to which and how a programme of socialisation (...) of these children can be achieved through the medium of visual arts. At the moment there are works of modern pedagogues who have devoted their scientific researches to this problem, but there are few teachers-artists who deal with this problem. In this article the author devotes his creative attention to this issue and reflects on what means of fine arts and visual literacy can develop and guide in the right direction the socialization of children and young people with disabilities by means of fine arts. A number of scientific works devoted to this problem are seriously reviewed. The author is actively trying to draw the attention of the teaching community to the problem of prevailing social conditions, to reach an educational and cognitive level and, as a consequence, to a better product of the set task of socialization of children with special needs and disabilities in the learning process by means of subject disciplines: drawing, painting, composition, printmaking, etc. (shrink)

The main aim of this paper is to study the notion of conditional right by means of constructive type theory (CTT) which provides the means to develop a system of contentual inferences rather than of syntactic derivations. Moreover, in line with Armgardt, we will first study the general notion of dependence as triggered by hypotheticals and then the logical structure of dependence specific to conditional right. I will develop this idea in a dialogical framework where the distinction between (...) play-object and strategy-object leads to the further distinction between two basic kinds of pieces of evidence and where meanings is constituted by the interaction of obligations and entitlements. The present paper is based on Rahman (2015). However, though the underlying CTT-analysis is the same, the dialogical reconstruction makes use of a new way of linking dialogical logic and CTT. Introduction. (shrink)

We present a necessary and sufficient condition for the embeddability of a finite principally decomposable lattice into the computably enumerable degrees preserving greatest element.

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' (...) uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation"--Publisher. (shrink)

In the middle of myMathematical logicI defined a certain class of formulae as “stratified,” and conjectured that exclusion from this class is a feature “shared, presumably, by all the untenable statements(p. 157). This ushered in a set of axioms of class-membership which Rosser has since shown to be inconsistent. Accordingly, inElement and numberI dropped the principle*200, in which had been assembled axioms to the effect, roughly, that “stratified functions of elements are elements.” In lieu of*200 I set forth (...) alternatives in which no appeal is made to stratification. The system ofMathematical logicexclusive of*200 carries over as an unchanging framework; and this framework admits, we know, of a simple consistency proof. My concern in the present paper is to draw attention to certain relationships between this framework and earlier theories. (shrink)

According to just war theory, a resort to war is justified only if it satisfies the right intention condition. This article offers a critical examination of this condition, defending the thesis that, despite its venerable history as part of the just war tradition, it ought to be jettisoned. When properly understood, it turns out to be an unnecessary element of jus ad bellum, adding nothing essential to our assessments of the justice of armed conflict.

We compare diverse degrees of compactness and finiteness in Boolean algebras with each other and investigate the influence of weak choice principles. Our arguments rely on a discussion of infinitary distributive laws and generalized prime elements in Boolean algebras. In ZF set theory without choice, a Boolean algebra is Dedekind finite if and only if it satisfies the ascending chain condition. The Denumerable Subset Axiom implies finiteness of Boolean algebras with compact top, whereas the converse fails in ZF. Moreover, (...) we derive from DS the atomicity of continuous Boolean algebras. Some of the results extend to more general structures like pseudocomplemented semilattices. (shrink)

Conditional logic is the deductive system , where is the set of propositional connectives {, ,} and is the structural finitary consequence relation on the absolutely free algebra that preserves degrees of truth over the structure of truth values C, . HereC is the non-commutative regular extension of the 2-element Boolean algebra to 3 truth values {t, u, f}, andfut. In this paper we give a Gentzen type axiomatization for conditional logic.

The article deals with the concept of educational mobility and its role in the modern educational process. Due to the insufficient development of this concept in the theory and practice of school education, the author creates a universal structural and functional model for the formation of this skill, which is why special attention was paid to the complex of pedagogical conditions that can ensure the effective functioning of all elements of the system.

On relational structures and on polymodal logics, we describe operations which preserve local tabularity. This provides new sufficient semantic and axiomatic conditions for local tabularity of a modal logic. The main results are the following. We show that local tabularity does not depend on reflexivity. Namely, given a class $\mathcal {F}$ of frames, consider the class $\mathcal {F}^{\mathrm {r}}$ of frames, where the reflexive closure operation was applied to each relation in every frame in $\mathcal {F}$. We show that if (...) the logic of $\mathcal {F}^{\mathrm {r}}$ is locally tabular, then the logic of $\mathcal {F}$ is locally tabular as well. Then we consider the operation of sum on Kripke frames, where a family of frames-summands is indexed by elements of another frame. We show that if both the logic of indices and the logic of summands are locally tabular, then the logic of corresponding sums is also locally tabular. Finally, using the previous theorem, we describe an operation on logics that preserves local tabularity: we provide a set of formulas such that the extension of the fusion of two canonical locally tabular logics with these formulas is locally tabular. (shrink)

Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. I find that a sufficient condition for the existence of elements of reality, introduced in these proofs, seems to be used also as a necessary condition. I argue that Lorentz-invariant elements of reality can be defined but, as Vaidman pointed out, they won’t satisfy the so-called product rule. In so doing I obtain algebraic constraints on elements of (...) reality associated with a maximal set of commuting Hermitian operators. (shrink)

We examine the maximal-element rationalizability of choice functions with arbitrary domains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier literature, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element rationalizability because of properties imposed on the rationalizing relation. We develop necessary and sufficient conditions for maximal-element rationalizability by itself, and for maximal-element rationalizability in conjunction with additional properties of (...) a rationalizing relation such as reflexivity, completeness, P-acyclicity, quasi-transitivity, consistency and transitivity. (shrink)

We show that a stable groupG satisfying certain commutator conditions is nilpotent. Furthermore, a soluble stable group with generically splitting automorphism of prime order is nilpotent-by-finite. In particular, a soluble stable group with a generic element of prime order is nilpotent-by-finite.

This essay begins by demonstrating how conversations can end before they have a chance to authentically begin. Conversations are stultified by patterns in the human ecology. The first pattern identified is “self-obliviousness” in conversation. “Self-obliviousness” is then tied to patterns of both radical self-assurance and self-diminishment. The underlying idea and argument is that adequate self-awareness is a necessary condition for conversation and this condition is only met as human beings recognize their own selves as relational. The argument then turns to (...) remedies to the pattern. Metacognition as exercised in relation to literary art can reveal the conditions for identifying and recognizing the damaging patterns. By the end of the essay the conditions for creativity in conversation are conflated with the formation of empathetic dispositions and these are only possible through understanding the self in equal relation to other selves. The arguments and examples are from contemporary United States Culture, but the damaging patterns can easily be recognized as elements of the human condition generally. (shrink)

The material interpretation of conditionals is commonly recognized as involving some paradoxical results. I here argue that the truth functional approach to natural language is the reason for the inadequacy of this material interpretation, since the truth or falsity of some pair of statements ‘p’ and ‘q’ cannot per se be decisive for the truth or falsity of a conditional relation ‘if p then q’. This inadequacy also affects the ability of the overall formal system to establish whether or (...) not arguments involving conditionals are valid. I also demonstrate that the Paradox of Indicative Conditionals does not actually involve a paradox, but instead contains some paralogistic elements that make it appear to be a paradox. The discussion of the paradox in this paper further reveals that the material interpretation of conditionals adversely affects the treatment of disjunctions. -/- Much has been said about these matters in the literature that point in the same direction. However, there seems to be some reluctance against fully complying with the arguments against the truth functional account of conditionals, since many of the alternative accounts rely on the material conditional, or at least on an understanding of the conditional as a function of antecedent and consequent in a similar sense as the material conditional. My argument against truth functionality indicates that it may in general involve similar problems to treat conditionals as such functions, whether one deals with theories of truth, assertability or probability. (shrink)

One aspect of the utility of gambling may evidence itself in failures of idempotence, i.e., when all chance outcomes give rise to the same consequence the `gamble' may not be indifferent to its common consequence. Under the assumption of segregation, such gambles can be expressed as the joint receipt of the common consequence and what we call `an element of chance', namely, the same gamble with the common consequence replaced by the status quo. Generalizing, any gamble is indifferent to the (...) joint receipt of its element of chance and a certain consequence, which is called the `kernel equivalent' of the gamble. Under idempotence, the kernel equivalent equals the certainty equivalent. Conditions are reported (Theorem 4) that are sufficient for the kernel equivalents to have the kind of utility representation first discussed by Luce and Fishburn (1991), including being idempotent. This utility representation of the kernel equivalents together with the derived form of utility over joint receipts yields a utility representation of the original structure. Possible forms for the utility of an element of chance are developed. (shrink)

The ubiquitous pathways of positive feedback in the human brain are generally held to be a necessary condition for the phenomenon of conscious sensation. However, no dynamic mechanism, no causal link has been established between the physical brain and its mental attributes, our sensations, thoughts, our consciousness. I suggest that the missing link between the world of neurons and that of mind is to be found in the transformations the brain performs on the coordinates of physical space and time. In (...) particular, the convolution of past, present and future, that characterizes subjective sensations, blurs the distinction between cause and effect, and allows the emergence of a self-generated phenomenon of consciousness. (shrink)