A semantics for logical necessity, based on Carnap's criterion of adequacy, is given with respect to the ontology of logical atomism. A calculus for sentential (propositional) modal logic is described and shown to be complete with respect to this semantics. The semantics is then modified in terms of a restricted notion of 'all possible worlds' in the interpretation of necessity and shown to yield a completeness theorem for the modal logic S5. Such a restricted notion introduces (...) material content into the meaning of necessity so that, in addition to atomic facts, there are "modal facts" that distinguish one world from another. (shrink)

Some philosophers, for example Quine, doubt the possibility of jointly using modalities and quantification. Simple model-theoretic considerations, however, lead to a reconciliation of quantifiers with such modal concepts as logical, physical, and ethical necessity, and suggest a general class of modalities of which these are instances. A simple axiom system, analogous to the Lewis systems S1 —S5, is considered in connection with this class of modalities. The system proves to be complete, and its class of theorems decidable.

Book synopsis: The philosophy of modality investigates necessity and possibility, and related notions--are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be explained in other terms? This volume presents new work on modality by established leaders in the field and by up-and-coming philosophers. Between them, the papers address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of (...) modal knowledge, modal logic and its relations to necessary existence and to counterfactual reasoning. The general introduction locates the individual contributions in the wider context of the contemporary discussion of the metaphysics and epistemology of modality. (shrink)

Prior to Kripke’s seminal work on the semantics of modal logic, McKinsey offered an alternative interpretation of the necessity operator, inspired by the Bolzano–Tarski notion of logical truth. According to this interpretation, ‘it is necessary that A’ is true just in case every sentence with the same logical form as A is true. In our paper, we investigate this interpretation of the modal operator, resolving some technical questions, and relating it to the logical interpretation of modality (...) and some views in modal metaphysics. In particular, we present an hitherto unpublished solution to problems 41 and 42 from Friedman’s 102 problems, which uses a different method of proof from the solution presented in the paper of Tadeusz Prucnal. (shrink)

I do not think scholars have thought hard enough about Scotus’s position that there are necessary moral truths over which God has no control. Just about everyone who writes on Scotus’s ethics has noted this position, but none has paid sufficient philosophical attention to it. It turns out that necessary moral truths are logically necessary (in Scotus’s sense of logical modalities), and the fact that they are logically necessary significantly alters how we should understand radical-sounding claims in Scotus to (...) the effect that God can do whatever is logically possible. Demonstrably, what Scotus means is that God can do whatever it is logically possible for God to do, and this class is rather smaller than the class of the logically possible simpliciter. (shrink)

Modal knowledge accounts like sensitivity or safety face a problem when it comes to knowing propositions that are necessarily true because the modal condition is always fulfilled no matter how random the belief forming method is. Pritchard models the anti-luck condition for knowledge in terms of the modal principle safety. Thus, his anti-luck epistemology faces the same problem when it comes to logical necessities. Any belief in a proposition that is necessarily true fulfills the anti-luck condition and, therefore, qualifies (...) as knowledge. Miščević shares Pritchard’s take on epistemic luck and acknowledges the resulting problem. In his intriguing article “Armchair Luck: Apriority, Intellection and Epistemic Luck” Miščević suggests solving the problem by supplementing safety with a virtue theoretic condition-“agent stability”-which he also spells out in modal terms. I will argue that Miščević is on the right track when he suggests adding a virtue-theoretic component to the safety condition. However, it should not be specified modally but rather in terms of performances that manifest competences. (shrink)

An attempt is made to show that Wittgenstein's later philosophy of logic is not the kind of conventionalism which is often ascribed to him. On the contrary, Wittgenstein gives expression to a “mixed” theory which is not only interesting but tends to resolve the perplexities usually associated with the question of the a priori character of logical truth. I try to show that Wittgenstein is better understood not as denying that there are such things as “logical rules” nor (...) as denying that the results of applying such rules are “logically necessary,” but as trying to understand what it is to appeal to a logical rule and what it means to say that the results of applying such a rule are “necessary.” He is not so much overthrowing standard accounts of logical necessity as discovering the limits of the concept. (shrink)

An examination of the grounds of logical necessity is offered by taking its lead from Barry Stroud’s challenge to the possibility of articulating satisfactorily any such grounds in full generality. The intelligibility of logical aliens is also considered, and different conceptions of such aliens, some more radical in their treatment of the issue than others, are examined as well. Logical aliens are beings whose thinking goes beyond the limits of thought, presumably with a logic different from (...) our own. I argue that logical aliens are either something straightforward and unproblematic or something we cannot recognize as logical. In either case, there are ways of accommodating such aliens despite the fact that the search for grounds of logical necessity is ultimately misguided. (shrink)

In two early papers, Max Cresswell constructed two formal logics of propositional identity, pcr and fcr, which he observed to be respectively deductively equivalent to modal logics s4 and s5. Cresswell argued informally that these equivalences respectively “give . . . evidence” for the correctness of s4 and s5 as logics of broadly logical necessity. In this paper, I describe weaker propositional identity logics than pcr that accommodate core intuitions about identity and I argue that Cresswell’s informal arguments (...) do not firmly and without epistemic circularity justify accepting s4 or s5. I also describe how to formulate standard modal logics (k, s2, and their extensions) with strict equivalence as the only modal primitive. (shrink)

Myles Brand and Marshall Swain advocate the principle that if A is the set of conditions individually necessary and jointly sufficient for the occurrence of B, then if C is a set of conditions individually necessary for the occurrence of B, every member of C is a member of A. I agree with John Barker and Risto Hilpinen who each argue that this principle is not true for causal necessity and sufficiency, but I disagree with their claim that it (...) is true for logical necessity and sufficiency. The original appeal of the principle may be due to confusing two kinds of totality: to say that when every member of set A obtains, then every condition necessary for E obtains is not to say that every condition necessary for E is a member of A. All the authors mentioned believe that causal necessity precludes logical necessity. I deny this on the basis of an example from kinematics. Hume has not refuted definitions of causation in terms of logically necessary and sufficient conditions, nor have Brand and Swain. (shrink)

For three hundred years two conflicting views of the world (1) have provided the overall frameworks for thought in western culture. The present paper shows neither view is sufficient for human understanding of many important systems and behaviors. A third view which appears sufficient is presented. Illustrations of the third view show increased understanding is obtained in many problems. The sufficiency of the historic views and the route to the third view are provided through discussion of the issue of multi-disciplinarity, (...) the question of whether it is possible to base everything we know on one discipline, or, on the contrary, if there is a logical necessity for using principles and concepts from many disciplines to achieve human understanding of the world. The present article provides three distinct proofs of the logical necessity of multi-disciplinarity. The proofs proceed via study of: (1) the hierarchical structure of proto-typical systems in various areas of human concern; (2) the use of “integrated-control-information” by life forms and human artifacts; and (3) an extension of the theory of dimensions. The three proofs interlock, confirm, and extend each other. (shrink)

It may sometimes be useful in philosophy to state a method of argument in very simple and even over-simplified terms; it may at a certain stage be useful to ignore for the moment the details and difficulties of particular philosophical arguments, and to try to state simply what is commonly assumed in a variety of different and even opposing arguments.

1. The early philosophy--language as picture -- 2. Logic and ontology -- 3. "My world and its value" -- 4. The later philosophy--views and reviews -- 5. Method and essense -- 6. Meaning -- 7. Criteria -- 8. Knowing, naming, certainty, and idealism -- 9. The private language argument -- 10. Logical necessity and rules -- 11. Philosophy of mathematics -- 12. Persons -- 13. Psychology and conceptual relativity -- 14. Aesthetics, ethics, and religion -- 15. Elective affinities.

The famous Cartesian Nicolas Malebranche (1638-1715) espoused the occasionalist doctrine that ‘there is only one true cause because there is only one true God; that the nature or power of each thing is nothing but the will of God; that all natural causes are not true causes but only occasional causes’ (LO, 448, original italics). One of Malebranche’s well-known arguments for occasionalism, known as, the ‘no necessary connection’ argument (or, NNC ) stems from the principle that ‘a true cause… is (...) one such that the mind perceives a necessary connection between it and its effect’ (LO, 450). The outline of this paper is as follows. I explicitly layout NNC and articulate some of its prima facie strengths (§1). I then critically discuss, what I take to be, the two main arguments against NNC of the Lee-Pyle interpretation (§2). The main conclusion from (§2) is that Malebranche did not abandon NNC in his later works given textual evidence from the Dialogues, contrary to the Lee-Pyle interpretation. In (§3) I discuss in what ways Suárez, Leibniz, Régis and Spinoza all accepted the main premise of NNC. Then, I rebut Steven Nadler’s influential and unchallenged criticism that Malebranche conflated causal and logical necessity, and provide a more accurate interpretation of Malebranche that only commits him to a partial reduction of causal to logical necessity (§4). (shrink)

What is the source of the hardness of the logical must? What does the necessity of mathematical and logical inference consist in? If I am plotting the curve y = x2 and assume that x = 2 I must conclude that y = 4; no other consequence can be drawn. What is the nature of this ‘must'?Understanding Wittgenstein's answer to this question is essential to understanding his later philosophy. The question of the nature of logical or (...) mathematical necessity is as fundamental for the Investigations as it obviously was for the Tractatus. Barry Stroud's article “Wittgenstein and Logical Necessity” certainly is still one of the most illuminating and important of the papers dealing with this question. (shrink)

Philosophers from anselm and scotus to hartshorne and malcolm have argued that the true claim that God is a necessary being implies that theism is a-Priori demonstrable. Philosophers such as hick, Penelhum, And geach have denied this, Contending 1) that god's necessity is factual, Indicating his eternal independence, Rather than logical, Indicating his existence in all possible worlds, And 2) that from the former nothing follows a-Priori about the truth or falsity of theism. I argue that factual and (...) logical necessity are conceptually inseparable, That God can be demonstrated to exist in all possible worlds. I take statements about the modalities of existence of things to be equivalent to statements about the modalities of instantiation of concepts, And argue that the concept God is necessarily instantiated, I.E., That God necessarily exists. The argument is compared and contrasted to a similar argument of hartshorne's. (shrink)

My main aim is to sketch a certain reading (‘genealogical’) of later Wittgenstein’s views on logical necessity. Along the way, I engage with the inferentialism currently debated in the literature on the epistemology of deductive logic.

Hale has argued that logical necessities are absolute in the sense that there is no competing kind of modality under which they may be false. In this paper, I argue that there are competing kinds of modality, which I call “essentialist modalities,” under which logical necessities may be false. Since it is counter-intuitive to say that logical necessities are not absolute, my argument, if correct, shows that Hale’s characterization of absolute necessity does not adequately capture the (...) intuitive notion of absolute necessity. Then, a qualified version of Hale’s characterization of absolute necessity is proposed. On the qualified version, the absoluteness of logical necessities is no longer defeated by essentialist possibilities. (shrink)

This study investigated individual differences in the belief bias effect, which is the tendency to accept conclusions because they are believable rather than because they are logically valid. It was observed that the extent of an individual's belief bias effect was unrelated to a number of measures of reasoning competence. Instead, as predicted by mental models theory, it was related to a person's ability to generate alternative representations of premises: the more alternatives a person generated, the less likely they were (...) to show a belief bias effect. In contrast to belief effects, which were predicted by the number of alternatives generated, scores on logical reasoning tasks were predicted by an individual's understanding of the concept of logical necessity. These two mediating variables, ability to generate alternatives and understanding of logical necessity, were themselves predicted by similar variables, such as cognitive motivation and abstract reasoning ability. Our findings strongly support the mental models interpretation of the belief bias effect, and suggest that individual differences in this effect are associated with a specific ability to generate alternatives, rather than with a general logical competence. (shrink)

Kripke and putnam have argued that metaphysical necessity is truth in all possible worlds, Hence is a kind of logica necessity; it is this claim I argue against. My argument proceeds by way of my considering and elaborating an example to show that although 'gold has atomic number 79' be counted a metaphysically necessary truth, There is a possible world in which it is false; it turns out to be for all I show here at most a physical (...) necessity, True in all those worlds structurally similar to the actual world. (shrink)

The issues of just what laws of nature are and what makes statements law-like have been more discussed than advanced. After exploring the general area and uncovering some difficulties which, I suspect, make the case even knottier than generally imagined, I argue that certain resources available only to the theist---in particular, counterfactuals of God’s freedom---may provide the materials needed for constructing solutions.

In these few pages I shall try to demonstrate the emptiness of the most cumbersome piece of unexamined intellectual baggage at present being hauled about by English philosophers. I here cite one example to be going on with, at the end of the paper I shall give a handful more, and it would be easy to multiply the number by ten from the writings of reputable philosophers. The outstanding philosophical achievement of the ha1f-century which has just drawn to a close (...) [i.e. the period 1900-1950] has been an appreciation of the peculiar status of a priori judgments and of logically necessary or formally true propositions. . . . Though many problems remain unsolved, the main outline is now clear: formally true statements assert nothing about the world; instead, their function is to state principles according to which empirical propositions are deduced from other empirical propositions . . . (R. B. Braithwaite, ‘Moral Principles and Inductive Policies’, Proceedings of the British Academy 1950). What is wrong with this passage and with the myth of which it is an expression is its assumption that we have clear notions of what it is for a proposition to be logically necessary and of what it is for a proposition to assert something about the world, these notions being such that it is plausible to say that it has recently been discovered that every proposition having the first of these properties lacks the second. This assumption is wrong: there is no body of published theory giving a clear account of such notions, and despite fairly diligent searching I have so far failed to find, among the many philosophers who accept the myth, one who is able when challenged to supplement the literature on this vital point. Let me make it clear at once that I am not going to defend synthetic a priori truths - I am going to attack a popular mishandling of the truth that all necessary truths are analytic, and through this attack to draw right-wing conclusions from left-wing premisses.. (shrink)

According to EJ Lowe, diachronic necessity and synchronic necessity are logically independent. Diachronic possibility concerns what could happen to an object over time and therefore concerns future possibilities for that object given its past history. Synchronic possibility concerns what is possible for an object in the present or at a past present moment. These are logically independent, given certain assumptions. While it may true that because I am 38, it is impossible diachronically for me to be 30 (at (...) least once we restrict the degree of relevant possibility), it is possible, given that at some point in the past, I may have been conceived slightly earlier than I was, that I am now 37. Likewise, it is possible diachronically for me to be somewhere other than where I am, but given that one object cannot be in different places at the same time, it is impossible for me now to be somewhere other than where I am, and this is true at each past point in my history too. There are, then, two axis upon which to distinguish what is and is not possible: tensed possibilities and possibilities of degree, which include nomic, metaphysical, and logical necessities, among others. I examine the interactions between these possibilities and I come to the conclusion that logical necessity is not in fact logical necessity simpliciter. Whether something is logically necessary depends upon tensed possibilities. I argue that while synchronic logical necessity entails diachronic logical necessity, the reverse entailment does not hold. I explore the consequences of this for certain philosophical debates in semantics including the concept of rigid designation, and descriptive names. (shrink)

Some philosophers dispute the claim that there is a notion of logical necessity involved in the concept of logical consequence. They are sceptical about logical necessity. They argue that a proper characterisation of logical consequence - of what follows from what - need not and should not appeal to the notion of necessity at all. Quine is the most prominent philosopher holding such a view. In this doctoral dissertation, I argue that scepticism about (...) logical necessity is not successful. Quine's scepticism takes three forms. Firstly, he is often interpreted as undermining, in his classic paper 'Two Dogmas of Empiricism', the very intelligibility of notions such as meaning, necessity, and analyticity. If the notion of necessity is meaningless, it is clear that ascriptions of logical necessity are also meaningless. In the thesis, I defend Quine's criticism of these notions by situating it in its historical context and emphasising that the real target in those writings is not the intelligibility of these notions as such, but only their Platonistic interpretation. I agree with Quine that a good theory about meaning, necessity, or analyticity must avoid such an ontological commitment. Secondly, Quine advocates, in the same paper, a holistic picture of knowledge and claims that in this picture, ascriptions of logical necessity are superfluous. I then show that holism a la Quine is committed to admit the necessity of statements of logical consequence. Thirdly, there is Quine's substitutional account of logical consequence ). He contends that this theory makes no use of logical necessity, thus showing its superfluousness. I show that any plausible account of logical consequence needs to appeal to logical necessity, thus undercutting Quine's claim - and, more generally, undercutting scepticism about logical necessity. (shrink)

THE position I am going to consider here is that the proposition ‘There is a God’ is tautologous and yet not vacuous. This position was held by Bowman Clarke in his article, ‘Linguistic Analysis and the Philosophy of Religion’. Clarke was trying to refute Findlay’s ontological disproof of the existence of God. So let me first go briefly over Findlay’s ontological disproof.

Critical (necessary or sufficient) features in categorisation have a long history, but the empirical evidence makes their existence questionable. Nevertheless, there are some cases that suggest critical feature effects. The purpose of the present work is to offer some insight into why classification decisions might misleadingly appear as if they involve critical features. Utilising Tversky's (1977) contrast model of similarity, we suggest that when an object has a sparser representation, changing any of its features is more likely to lead to (...) a change in identity than it would in objects that have richer representations. Experiment 1 provides a basic test of this suggestion with artificial stimuli, whereby objects with a rich or a sparse representation were transformed by changing one of their features. As expected, we observed more identity judgements in the former case. Experiment 2 further confirms our hypothesis, with realistic stimuli, by assuming that superordinate categories have sparser representations than subordinate ones. These results offer some insight into the way feature changes may or may not lead to identity changes in classification decisions. (shrink)

This paper explains Wittegnstein’s understanding of the ‘grammar’ of our language, tracing its origins in the Tractatus’s concept of logical syntax, and then examining the senses in which Wittegnstein, in his later work, viewed grammar as being ‘arbitrary’. Then, armed with this understanding, it moves on to the task of examining how, within the framework of a Wittegnsteinian view of language, we should understand the inescapable ‘compellingness’ of logical necessity – what Wittegnstein calls the “hardness of the (...) logical must”. Whereas it is often thought that Wittegnstein’s views on the nature of the ‘grammar’ of our concpets leads him towards a vitiatingly conventionalist or anti‐realist understanding of necessity, in which its logical ‘superhardness’ becomes problematic, this paper will argue that there is actually no such tension in Wittegnstein’s thought. In fact, it will be argued, an understanding of the ways in which our conceptual grammar is arbitrary casts a great deal of light on how it is that our concepts can nevertheless support a logically superhard, and normatively commanding, notion of necessity. In support of this view, I distinguish Wittegnstein’s views on necessity from the ‘classical’ conventionalism of the Vienna Circle, and from the radical conventionalism of Michael Dummett, and defend Wittegnstein’s view from a powerful recent attack from Quassim Cassam. (shrink)

Analytical jurisprudence and the legal mainstream perceive legal rights in an interactionist fashion, pursuant to a right-obligation duality. The Paper suggests that this is principally because legal positivism and the analytical Anglo-Saxon legal tradition ground their theories on logical positivism and the Wittgensteinian premise that meaning is produced and asserted in social use, i.e. both consensually and contextually. The paper suggests that there is a surplus of meaning which exists beyond social use and which cannot be conceptualized within the (...) sociolinguistic confines of Wittgenstein’s logic of language. This surplus of meaning corresponds to the essential core of legal rights, which, following Aristotle’s induction and philosophy of the essences, constitutes a necessary property and τὸ τί ἦν εἶναι of legal rights, namely a state of affairs or a state of being that cannot be altered without their necessary breach or, indeed, the negation of their very meaning. The Paper discusses the shortcomings of the Wittgensteinian approach and revisits the philosophical foundations of legal rights by employing Aristotle’s induction and theory of the essences, which the Paper connects to the phenomenological method and particularly Ricoeur’s hermeneutics and Husserl’s transcedental phenomenology. This is a process of abstraction and insight, which aspires to induce a rational revisiting of the general theory of legal rights and address the surplus of meaning that Wittgensteinian logic leaves semantically uncovered. (shrink)

Prior research shows that reasoners' confidence is poorly calibrated (Shynkaruk & Thompson, 2006). The goal of the current experiment was to increase calibration in syllogistic reasoning by training reasoners on (a) the concept of logical necessity and (b) the idea that more than one representation of the premises may be possible. Training improved accuracy and was also effective in remedying some systematic misunderstandings about the task: those in the training condition were better at estimating their overall performance than (...) those who were untrained. However, training was less successful in helping reasoners to discriminate which items are most likely to cause them difficulties. In addition we explored other variables that may affect confidence and accuracy, such as the number of models required to represent the problem and whether or not the presented conclusion was necessitated by the premises, possible given the premises, or impossible given the premises. These variables had systematically different relationships to confidence and accuracy. Thus, we propose that confidence in reasoning judgements is analogous to confidence in memory retrievals, in that they are inferentially derived from cues that are not diagnostic in terms of accuracy. (shrink)

In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces (...) one to reject many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators. (shrink)