In 2001, Le Bars proved that there exists an existential monadic second-order sentence such that the probability that it is true on [Formula: see text] does not converge and conjectured that, for EMSO sentences with two first-order variables, the zero–one law holds. In this paper, we prove that the conjecture fails for [Formula: see text], and give new examples of sentences with fewer variables without convergence.

The proof-theoretic analysis of logical semantics undermines the received view of proof theory as being concerned with symbols devoid of meaning, and of model theory as the sole branch of logical theory entitled to access the realm of semantics. The basic tenet of proof-theoretic semantics is that meaning is given by some rules of proofs, in terms of which all logical laws can be justified and the notion of logical consequence explained. In this paper an (...) attempt will be made to unravel some aspects of the issue and to show that this justification as it stands is untenable, for it relies on a formalistic conception of meaning and fails to recognise the fundamental distinction between semantic definitions and rules of inference. It is also briefly suggested that the profound connection between meaning and proofs should be approached by first reconsidering our very notion of proof. (shrink)

The Strong Normative Constitutivity reading of logical laws in Frege argues that although he regards logical laws as purely descriptive, he in fact accepts that they are normatively constitutive of the act of judgement. There are passages in which Frege seems to commit himself to such an idea. However, we can understand what Frege argues in those passages based only on his conception of logical laws as the most general descriptive laws and his (...) objectivism about truth. If my suggested interpretation is correct, there is a reason to think that logical laws are merely descriptive for Frege. Further, my interpretation shows that the central issue between Frege and psychological logicians is the nature of truth. (shrink)

This chapter looks at a range of objections to theism that one might class as “logical.” Some of these objections aim to show that theism involves an internal logical contradiction. Others aim to show that theism is at least logically incompatible with other beliefs to which the theist is also typically committed. Also included are objections grounded in the thought that theism is nonsensical or meaningless. The chapter provides both an overview of this broad terrain, including a map (...) of possible responses to different kinds of objection, and then a number of examples. (shrink)

This volume centers on philosophical issues of the life sciences, particularly genetics and psychology, and the relevance of statistical data as the foundation for inductive reasoning in areas such as vaccination testing, population genetics, evolutionary theory, and natural selection. Also discussed is the role of psychology in defining thought processes, experiences, and behaviors and their subsequent relation to scientific discovery, and advancing knowledge of the human condition and human potential.

In this paper, I argue that Goff's view that universal consciousness grounds logical laws such as the law of non-contradiction cannot be true on the grounds that we cannot guarantee the classical logic loving nature of universal consciousness that Goff desires in order to ground logical laws. I will present three arguments to show this.

Law's article begins by restating the classical ANT position that objects do not exist `in themselves' but are the effect of a performative stabilization of relational networks. In addition, these material enactments inevitably have a spatial dimension; they simultaneously establish spatial conditions for objectual identity, continuity, and difference. Space must not be reified as a natural, pre-existing container of the social and the material, but is itself a performance. Moreover, there are multiple forms of spatiality beyond the Euclidean space of (...) regions (e.g. networks and fluids), and objects may exist and achieve homeomorphism within several different spatial systems. Technologies such as the Zimbabwe Bush Pump present a fluid object which is able to exist and cohere without the presence of fixed boundaries or the permanence of a particular functional definition. The network logic, however, which gravitates towards stability and functionality, tends to exclude and silence this spatial Other. An alternative political ontology is needed which goes beyond the reification of network space in order to give voice to the fluid objects which escape its unidimensional functionality. (shrink)

According to received wisdom, Kant takes the laws of logic to be normative laws of thought. This has been challenged by Tolley (2006). In this paper, I defend the received wisdom, but with an important modification: Kant's logical laws are constitutive norms for thought. The laws of logic do tell us what thinking is, not because all thoughts are in conformity with logical laws, but because all thoughts are, by nature, subject to the (...) standard of logic. (shrink)

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as (...) those that appear in every one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: a basically Fregean account of the nature of logic still looks quite promising. (shrink)

This work is devoted to the relations between Lambek’s Syntactic Calculus and noncommutative variants of Girard’s Linear Logic; in particular the paper will consider: the geometrical representation of the laws of LC by means of proof-nets; the discovery - due to such a geometrical representation - of some laws of LC not yet considered; the discussion of possible linguistic uses of these new laws.

This paper has three aims: first, to present in a clear way Newton da Costa’s argument against the necessity of logical laws. In order to do so, we need to clearly advance his views on the idea that logic is context-relative, and not known a priori. Doing so, however, requires that we present his methodology for the development of counter-examples to logical laws: the use of hypothetical models in logic. Given that this method has been overlooked (...) in most discussions on the epistemology of logic, our second goal is to present da Costa’s views on it carefully. The discussion of some tensions resulting from the relation of a system of logic and the context it governs, in da Costa’s approach, is our third goal. Basically, da Costa seems to swing between two incompatible views on such relation, requiring sometimes that a logic is dependent on a context, and in other cases, that the nature of the context is dependent on a logic. Bringing this to light may also benefit current discussions on logical relativism. (shrink)

Medvedev's intermediate logic (MV) can be defined by means of Kripke semantics as the family of Kripke frames given by finite Boolean algebras without units as partially ordered sets. The aim of this paper is to present a proof of the theorem: For every set of connectives such that the-fragment ofMV equals the fragment of intuitionistic logic. The final part of the paper brings the negative solution to the problem set forth by T. Hosoi and H. Ono, namely: is an (...) intermediate logic based on the axiom (abc) (ab)(a c) separable? (shrink)

This chapter contains sections titled: The Logical Problem of Evil The Evidential Problem of Evil The Evil God Hypothesis and the Problem of Good Reverse Theodicies Notes.

If there is a second dimension of time – a so-called ‘hypertime’ – is it logically possible for the past to change? Some have said yes; others have said no. I say yes provided that one has the appropriate ontological view of hypertime. So far, the ontology of hypertime has seldom been discussed. As such, this paper not only defends the logical possibility of a changing past, but aims to start a discussion on what ontological commitments are required to (...) make sense of a changing past. (shrink)

Playing the mystery card -- "But it fits!" -- Going nuclear -- Moving the semantic goalposts -- "But I just know!" -- Pseudo-profundity -- Piling up the anecdotes -- Pressing your buttons -- Conclusion -- The Tapescrew letters.

Language & Logic -- Glossary -- Aristotle's syllogisms -- Russell's paradox & Frege's logicism -- profile: Aristotle -- Russell's theory of description -- Frege's puzzle -- Gödel's theorem -- Epimenides' liar paradox -- Eubulides' heap -- Science & Epistemology -- Glossary -- I think therefore I am -- Gettier's counter example -- profile: Karl Popper -- The brain in a vat -- Hume's problem of induction -- Goodman's gruesome riddle -- Popper's conjectures & refutations -- Kuhn's scientific revolutions -- Mind (...) & Metaphysics -- Glossary -- Descartes mind-body problem -- Brentano's intentionality -- Fodor's language of thought -- Parfit's persons -- profile: René Descartes -- Chalmer's zombies -- Zeno's paradoxes -- Kant's left hand -- Theseus' ship -- Laplace's demon, determinism, & free will -- Ryle's ghost in the machine -- Ethics & Political Philosophy -- Glossary -- Aristotle's ethics -- States of nature and the social contract -- Kant's categorical imperative -- profile: Immanuel Kant -- Mill's utilitarianism -- Marx's historical materialism -- The trolley problem -- Religion -- Glossary -- Aquinas' five ways -- Anselm's ontological argument -- profile: Thomas Aquinas -- Epicurus' riddle -- Paley's watchmaker -- Pascal's wager -- Hume against miracles -- Grand Moments -- Glossary -- Socrates' method -- Plato's cave -- Aristotle's four causes -- Lucretius' atomism -- profile: Ludwig Wittgenstein -- Berkeley's idealism -- Kant's synthetic a priori -- Hegel's dialectic -- James' pragmatism -- Moore's common sense -- Wittgenstein's picture theory of language -- Continental Philosophy -- Glossary -- Nietzsche's Superman -- profile: Friedrich Nietzsche -- Derrida's deconstruction -- Heidegger's nothing -- Sartre's bad faith. (shrink)

In the Logical Investigations Husserl announced a critique of Lotze’s epistemology, but it was never included in the printed text. The aim of my paper is to investigate the remnant of Husserl’s planned text with special emphasis on the question of whether it goes beyond the obvious aspects of Husserl’s indebtedness to Lotze. Using Husserl’s student notes, excerpts, and book annotations, I refine the dating of Husserl’s encounter with Lotze and separate the various layers of influence. I argue that (...) Husserl’s acquaintance with Lotze’s epistemology forms a separate layer of influence, and that this layer cannot antedate the middle of the decade before the Logical Investigation. Husserl’s investigation of Lotze’s epistemology constitutes the most interesting aspect of the unpublished text that underlies the missing chapter from the Logical Investigations. I show that the most relevant influence of Lotze’s epistemology on Husserl lies in Lotze’s idea of the formal and real significance of logical laws. Although Husserl negatively evaluated Lotze’s epistemological problem both in the planned chapter and in other printed parts of the Logical Investigations, the problem repeatedly surfaced during Husserl’s Göttingen period. Finally, I use an unpublished student transcript to reconstruct Husserl’s SS 1912 seminar on Lotze’s epistemology. I argue that the deeper dimension of Lotze’s epistemological problem (and Husserl’s rejection of it) lies in the way that it highlights the epistemological function of phenomenology. (shrink)

In a recent article (Inquiry, Vol. 19 [1976]), J. W. Meiland addresses the issue of psychologism in logic, which holds that logic is a branch of psychology and that logical laws (such as the Principle of Non?Contradiction) are contingent upon the nature of the mind. Meiland examines Husserl's critique of psychologism, argues that Husserl is not convincing, and offers two new objections to the psychologistic thesis. In this paper I attempt to rebut those objections. In question are the (...) acceptable criteria for determining the possibility or impossibility of systems of logic significantly different from our own. I argue that a criteriological application of our accepted laws of logic to this question commits a circular fallacy. I then argue that, even if we accept logical consistency as a criterion for possibility, a plausible argument for the possibility of valid alternative logics can be constructed by using the functionalist analogy between minds and automata. Finally, I attempt to rebut the claim that in logic the only changes possible are conceptual changes that would not permit a proposition to be both true and false. (shrink)

The most important laws of the propositional calculus are clearly and succinctly stated.