In Spandrels of Truth, Beall concisely presents and defends a modest, so-called dialetheic theory of transparent truth.

Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.

A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the rich (...) will enroll. There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid, that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments. (shrink)

Semantic and soritical paradoxes challenge entrenched, fundamental principles about language - principles about truth, denotation, quantification, and, among others, 'tolerance'. Study of the paradoxes helps us determine which logical principles are correct. So it is that they serve not only as a topic of philosophical inquiry but also as a constraint on such inquiry: they often dictate the semantic and logical limits of discourse in general. Sixteen specially written essays by leading figures in the field offer new thoughts and arguments (...) about the paradoxes. (shrink)

The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.

Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience, examples that demonstrate the application of concepts, and guides to further reading.

The two purposes of this essay. The general philosophical problem with most versions of social libertarianism and how this essay will proceed. The specific problem with liberty explained by a thought-experiment. The positive and abstract theory of interpersonal liberty-in-itself as ‘the absence of interpersonal initiated constraints on want-satisfaction’, for short ‘no initiated impositions’. The individualistic liberty-maximisation theory solves the problems of clashes, defences, and rectifications without entailing interpersonal utility comparisons or libertarian consequentialism. The practical implications of instantiating liberty: three rules (...) of liberty-in-practice, 1) initial ultimate control of one’s body, 2) initial ultimate control of one’s used resources, 3) consensual interpersonal interactions and resource transfers. These rules are economically efficient and maximise general want-satisfaction. Private property and legal remedies are additional practical institutional aspects, but to which ‘initiated impositions’ then apply prima facie. Libertarian law is often mistaken for complete libertarianism. Moral explanations are a separate issue. The three main moral theories imply libertarianism, but it can be morally posited independently of them. Critical rationalism and its application. No empirical or argumentative support for theories. An important ambiguity with ‘justification’. How the epistemology applies to the theory of liberty and its application but remains separable in principle. Conclusion: there are further published explanations but this should be enough to generate useful criticism. Appendix replying to some typical comments. (shrink)

The Liar paradox raises foundational questions about logic, language, and truth. A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it says that it is false.How, (...) then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another.JC Beall presents fourteen new essays and an extensive introduction, which examine the nature of the Liar paradox and its resistance to any attempt to solve it. Written by some of the world's leading experts in the field, the papers in this volume will be an important resource for those working in truth studies, philosophical logic, and philosophy of language, as well as those with an interest in formal semantics and metaphysics. (shrink)

I have argued that without an adequate solution to the knower paradox Fitch's Proof is- or at least ought to be-ineffective against verificationism. Of course, in order to follow my suggestion verificationists must maintain that there is currently no adequate solution to the knower paradox, and that the paradox continues to provide prima facie evidence of inconsistent knowledge. By my lights, any glimpse at the literature on paradoxes offers strong support for the first thesis, and any honest, non-dogmatic reflection on (...) the knower paradox provides strong support for the second. Whether verificationists want to go the route I've suggested is not for me todecide. As in the previous section my aim has been that of defending the mere viability of verificationism in the face of what many, many philosophers have taken to be its death-knell, namely Fitch's Proof. But, as the final objection makes clear, showing that verificationism can live in the face of Fitch's Proof is one thing; showing that it should live is another project. If nothing else, I hope that this papershows that verificationists still have a project to pursue; Fitch's Proof, contrary to popular opinion, need not bury verificationism.13. (shrink)

J C Walker; The Philosopher’s Touchstone: towards pragmatic unity in educational studies, Journal of Philosophy of Education, Volume 19, Issue 2, 30 May 2006, P.

A series of papers on different aspects of practical knowledge by Roderick Chisholm, Rudolf Haller, J. C. Nyiri, Eva Picardi, Joachim Schulte Roger Scruton, Barry Smith and Johan Wrede.

We are pluralists about logical consequence [1]. We hold that there is more than one sense in which arguments may be deductively valid, that these senses are equally good, and equally deserving of the name deductive validity. Our pluralism starts with our analysis of consequence. This analysis of consequence is not idiosyncratic. We agree with Richard Jeffrey, and with many other philosophers of logic about how logical consequence is to be defined. To quote Jeffrey.

J C Forge; A Role for Philosophy of Science in the Teaching of Science, Journal of Philosophy of Education, Volume 13, Issue 1, 30 May 2006, Pages 109–117, http.

Hume's doctrine of natural belief allows that certain beliefs are justifiably held by all men without regard to the quality of the evidence which may be produced in their favour. Examples are belief in an external world and belief in the veracity of our senses. According to R. J. Butler, Hume argues in the Dialogues that belief in God is of this sort. More recently John Hick has argued that for some people it is as natural to believe in God (...) as to believe in an external world. I shall first inquire what Hume understands by reasonable belief and by natural belief. I shall then use the results of this investigation to argue, against Butler, that belief in God is not a natural belief; and against Hick, more briefly, that his thesis is not viable in as far as it depends upon Hume's doctrine of natural belief. These discussions are important to the philosophy of religion since by means of natural beliefs it could be urged that belief in God is something justifiable without reference to reason or evidence: a position which would be of immense value to the theist. (shrink)

In this paper we continue the study of inner models of the type studied inInner models for set theory—Part I.The present paper is concerned exclusively with a particular kind of model, the ‘super-complete models’ defined in section 2.4 of I. The condition of 2.4 and the completeness condition 1.42 imply that such a model is uniquely determined when its universal class Vmis given. Writing condition and the completeness conditions 1.41, 1.42 in terms of Vm, we may state the definition in (...) the form:3.1. Dfn.A classVmis said to determine a super-complete model if the model whose basic notions are defined by,satisfies axiomsA, B, C.N. B. This definition is not necessarily metamathematical in nature. If desired, it could be written out quite formally as the definition of a notion ‘SCM’ thus:whereψ is the propositional function expressing in terms ofUthe fact that the model determined byUaccording to 3.1 satisfies the relativization of axioms A, B, C. E.g. corresponding to axiom A1m, i.e.,,ψ contains the equivalent term. All the relativized axioms can be similarly expressed in this way by first writing out the relativized form and then replacing ‘ϕ bywhich is in turn replaced by, and similarly replacing ‘ϕ’ by ‘ϕ’ by ‘), andThusψ is obtained in primitive notation. (shrink)

The Aristotle-Kant tradition requires that autonomous activity must originate within the self and points toward a new type of causation (different from natural efficient causation) associated with teleology. Notoriously, it has so far proven impossible to uncover a workable model of causation satisfying these requirements without an increasingly unsatisfying appeal to extra-physical elements tailor-made for the purpose. In this paper we first provide the essential reason why the standard linear model of efficient causation cannot support the required model of agency: (...) its causal thread model of efficient causation cannot support the core requirement that an action is determined by, and thus an expression of, the agent’s nature. We then provide a model that corrects these deficiencies, constructed naturalistically from within contemporary biology, and argue that it provides an appropriate foundation for all the features of genuine agency. Further, we provide general characterisations of freedom and reason suitable to this bio-context (but that also capture the core classical conceptions) and show how this model reconciles them. (shrink)

On the face of it, Maurice Merleau-Ponty’s views bear a strong resemblance to contemporary disjunctivist theories of perception, especially John McDowell’s epistemological disjunctivism. Like McDowell (and other disjunctivists), Merleau-Ponty seems to be a direct realist about perception and holds that veridical and illusory perceptions are distinct. This paper furthers this comparison. Furthermore, it is argued that elements of Merleau-Ponty’s thought provide a stronger case for McDowell’s kind of epistemological view than McDowell himself provides. Merleau-Ponty’s early thought can be used to (...) develop a unique version of epistemological disjunctivism that is worth consideration alongside contemporary views on perceptual knowledge. (shrink)

In this third and last paper on inner models we consider some of the inherent limitations of the method of using inner models of the type defined in 1.2 for the proof of consistency results for the particular system of set theory under consideration. Roughly speaking this limitation may be described by saying that practically no further consistency results can be obtained by the construction of models satisfying the conditions of theorem 1.5, i.e., conditions 1.31, 1.32, 1.33, 1.51, viz.:This applies (...) in particular to the ‘complete models’ defined in 1.4. Before going on to a precise statement of these limitations we shall consider now the theorem on which they depend. This is concerned with a particular type of complete model examples of which we call “proper complete models”; they are those complete models which are essentially interior to the universe, those whose classes are sets of the universe constituting a class thereof, i.e., those for which the following proposition is true:The main theorem of this paper is that the statement that there are no models of this kind can be expressed formally in the same way as the axioms A, B, C and furthermore it can be proved that if the axiom system A, B, C is consistent then so is the system consisting of axioms A, B, C, plus this new hypothesis that there exist no proper complete models. When combined with the axiom ‘V = L’ introduced by Gödel in this new hypothesis yields a system in which any normal complete model which exists has for its universal class V, the universal class of the original system. (shrink)