"If-then" as a version of "Implies"

Russell’s role in the controversy about the paradoxes of material implication is usually presented as a tale of how even the greatest minds can fall prey of basic conceptual confusions. Quine accused him of making a silly mistake in Principia Mathematica. He interpreted “if- then” as a version of “implies” and called it material implication. Quine’s accusation is that this decision involved a use-mention fallacy because the antecedent and consequent of “if- then” are used instead of being mentioned as the premise and the conclusion of an implication relation. It was his opinion that the criticisms and alternatives to the material implication presented by C. I. Lewis and others would never be made in the first place if Russell simply called the Philonian construction “material conditional” instead of “material implication”. Quine’s interpretation on the topic became hugely influential, if not universally accepted. This paper will present the following criticisms against this interpretation: (1) the notion of material implication does not involve a use-mention fallacy, since the components of “if-then” are mentioned and not used; (2) Quine’s belief that the components of “if-then” are used was motivated by a conditional-assertion view of conditionals that is widely controversial and faces numerous difficulties; (3) if anything, it was Quine who could be accused of fallacious reasoning: he ignored that in the assertion of a conditional is the whole proposition that is asserted and not its constituents; (4) the Philonian construction remains counter-intuitive even if it is called “material conditional”; (5) the Philonian construction is more plausible when it is interpreted as a material implication

Defining implication relation for classical logic

Classical logic is unfortunately defective with its problematic definition of implication relation, the "material implication". This work presents a corrected definition of implication relation to replace material implication in classical logic. Common "paradoxes" of material implication are avoided while simplicity and usefulness of the system are reserved with this definition of implication relation.Comment: 12 pages, 1 figure; major revision in formalizatio

Indicative Conditionals are Material - Expanding the Survey

Adam Rieger (2013) has carried out a survey of arguments in favour of the material account of indicative conditionals. These arguments involve simple and direct demonstrations of the material account. I extend the survey with new arguments and clarify the logical connections among them. I also show that the main counter-examples against these arguments are not successful either because their premises are just as counter-intuitive as the conclusions, or because they depend on contextual fallacies. The conclusion is that the unpopularity of the material account is unjustified and that a more systematic approach in the analysis of arguments is long overdue in our attempts to understand the nature of conditionals

Entailment II

We here propose a solution to the problem we have raised. Basically, the mathematical notion of entailment seems to be connected to the inferential rules from Classical Logic, so that if we have P: x belongs to the reals, and Q: x+2=5 =\u3e x=3, P |= Q. Notwithstanding, we would also have that if P: x belongs to the interval (7,10), and Q: x+2=5 =\u3e x=3, P |= Q. The second instance of entailment does not seem to be justifiable if our intuition is consulted: Even though we could say that absurdity implies anything in Classical Logic, entailment should be a concept that belongs to the metalogic, not to the logic of the system, so that we should not be inside of the Classical Logic World by the time we assess things in what regards entailment. As another point, our discussions in Entailment led us to choose the sense has as a consequence for entailment, so that it is not really acceptable that we have, as a consequence, using normal language, of x being inside of the real interval (7,10) that if x+2=5, then x=3. If x is in that interval, x+2 should not be 5, unless we are talking about moduli of vectors. However, when we transfer to Classical Logic, in having the antecedent false, and the consequent false as well, we have that the implication, which some call material, is true. We here discuss this sort of matter in detail, and hope to get to the bottom of the issue, and perhaps to a universal solution

Non-Boolean classical relevant logics I

Under embargo until: 2020-12-13Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as a necessary property for a logic to have in order for it to not validate the so-called paradoxes of implication. The Entailment Theorem on the other hand was regarded as both necessary and sufficient. This paper shows that the latter theorem also holds for classical logic, and so cannot be regarded as a sufficient property for blocking the paradoxes. The concept of suppression is taken up, but shown to be properly weaker than that of variable sharing.acceptedVersio

The Inextricable Link Between Conditionals and Logical Consequence

There is a profound, but frequently ignored relationship between the classical notion of logical consequence (formal implication) and material implication. The first repeats the patterns of the latter, but with a wider modal reach. It is argued that this kinship between formal and material implication simply means that they express the same variety of implication, but differ in scope. Formal implication is unrestricted material implication. This apparently innocuous observation has some significant corollaries: (1) conditionals are not connectives, but arguments; (2) the traditional examples of valid argumentative forms are metalogical principles that express the properties of logical consequence; (3) formal logic is not a useful guide to detect valid arguments in the real world; (4) it is incoherent to propose alternatives to the material implication while accepting the classical properties of formal implication; (5) the counter-examples to classical argumentative forms and conditional puzzles are unsound

A logical analysis of soft systems modelling: implications for information system design and knowledge based system design

The thesis undertakes an analysis of the modelling methods used in the Soft Systems Methodology (SSM) developed by Peter Checkland and Brian Wilson. The analysis is undertaken using formal logic and work drawn from modern Anglo-American analytical philosophy especially work in the area of philosophical logic, the theory of meaning, epistemology and the philosophy of science. The ability of SSM models to represent causation is found to be deficient and improved modelling techniques suitable for cause and effect analysis are developed. The notional status of SSM models is explained in terms of Wittgenstein's language game theory. Modal predicate logic is used to solve the problem of mapping notional models on to the real world. The thesis presents a method for extending SSM modelling in to a system for the design of a knowledge based system. This six stage method comprises: systems analysis, using SSM models; language creation, using logico-linguistic models; knowledge elicitation, using empirical models; knowledge representation, using modal predicate logic; codification, using Prolog; and verification using a type of non-monotonic logic. The resulting system is constructed in such a way that built in inductive hypotheses can be falsified, as in Karl Popper's philosophy of science, by particular facts. As the system can learn what is false it has some artificial intelligence capability. A variant of the method can be used for the design of other types of information system such as a relational database