The philosophical case for extended cognition is often made with reference to ‘extended-memory cases’ ; though, unfortunately, proponents of the hypothesis of extended cognition as well as their adversaries have failed to appreciate the kinds of epistemological problems extended-memory cases pose for mainstream thinking in the epistemology of memory. It is time to give these problems a closer look. Our plan is as follows: in §1, we argue that an epistemological theory remains compatible with HEC only if its epistemic (...) assessments do not violate what we call ‘the epistemic parity principle’. In §2, we show how the constraint of respecting the epistemic parity principle stands in what appears to be a prima facie intractable tension with mainstream thinking about cases of propositional memory. We then outline and evaluate in §3 several lines of response. (shrink)

Expressivists about normative thought and discourse traditionally deny that there are nondeflationary normative propositions. However, it has recently been suggested that expressivists might avoid a number of problems by providing a theory of normative propositions compatible with expressivism. This paper explores the prospects for developing an expressivist theory of propositions within the framework of cognitive act theories of propositions. First, I argue that the only extant expressivist theory of cognitive propositions—Michael Ridge's ‘ecumenical expressivist’ theory—fails (...) to explain identity conditions for normative propositions. Second, I argue that this failure motivates a general constraint—the ‘unity requirement’—that any expressivist theory of propositions must provide a unified nonrepresentational explanation of that in virtue of which propositional attitudes have the content that they have. Third, I argue that conceptual role accounts of content provide a promising framework in which to develop an expressivist theory of cognitive propositions. (shrink)

On Friday God knew everything, including f, a proposition about what Jones would do on Monday; we can write the time-indexed proposition that on Friday God believed f as Bgf. If Jones does not do the thing that makes f true, then the resulting state of affairs will be ∼f. So on Monday, before a certain time – ‘ t time’ – Jones has it in his power to bring it about that ∼f. It seems to follow that on Monday (...) Jones has it in his power to bring it about that on Friday God believed something false. Yet this is impossible, as Bgp ⊃ p . But if f is false – if Jones makes it so on Monday – then so is Bgf, and God is not infallible. So either Jones cannot not do the thing that makes f true, and he has no freewill, or God is not infallible. The traditional responses to this dilemma are subtle, time-honoured and, as I see it, almost completely unconvincing. According to Linda Zagzebski , there are five of them: the Ockhamist response that God’s Friday belief is a so-called ‘soft’ fact, itself a problematic notion; the confused Molinist claim that on Friday God has something called ‘middle knowledge’ , so that God knows what Jones would do, but does not will it or know what Jones would do if … ); and the more sensible but still perplexing solution of Boethius’s that God’s knowing is not in time, so that the time-indexed proposition Bgf is not true. (How does it help to move the knowing that is said to determine our actions from the past to the timeless? It seems to …. (shrink)

Jonathan Vogel has recently argued that counterfactual reliabilism cannot account for higher‐level knowledge that one's belief is true, or not false. His particular argument for this claim is straightforward and valid. Interestingly, there is a parallel argument, based on an alternative but plausible reinterpretation of the main premise in Vogel's argument, which squares CR with higher‐level knowledge both that one's belief is true and that one's belief is not false. I argue that, while Vogel's argument reveals the incompatibility of CR (...) and knowledge of certain higher‐level propositions, it does not establish the general claim that CR is incompatible with knowledge that any of one's beliefs is true, or not false. (shrink)

It is a widely held view in philosophy that propositions perform a plethora of different theoretical roles. Amongst other things, they are believed to be the semantic values of sentences in contexts, the objects of attitudes, the contents of illocutionary acts, and the referents of that-clauses. This assumption is often combined with the claim that propositions have their truth-values eternally. In this paper I aim to show that these two assumptions are incompatible: propositions cannot both fulfill the (...) mentioned roles and be eternally true or false. Following Kaplan and Lewis’s Operator Argument, I argue that compositional semantic values of sentences in contexts do not correspond to eternal propositions. Thus, either we regard the non-eternal entities that in fact realize the semantic role of propositions as also fulfilling the remaining propositional roles, or we abandon the assumption that there is a unique realizer of all the roles. The Operator Argument has recently come under attack, mainly for its tense-logical assumptions. However, rejecting these assumptions is not a sufficient defense of the compatibility of the two claims, since the extensional alternative to the tense-logical framework does not allow us to universally retain eternal propositions as compositional semantic values of sentences either. (shrink)

Jonathan Vogel has recently argued that counterfactual reliabilism cannot account for higher‐level knowledge that one's belief is true, or not false. His particular argument for this claim is straightforward and valid. Interestingly, there is a parallel argument, based on an alternative but plausible reinterpretation of the main premise in Vogel's argument, which squares CR with higher‐level knowledge both that one's belief is true and that one's belief is not false. I argue that, while Vogel's argument reveals the incompatibility of CR (...) and knowledge of certain higher‐level propositions, it does not establish the general claim that CR is incompatible with knowledge that any of one's beliefs is true, or not false. (shrink)

On a deflationary view of truth the truth predicate does not ascribe a property of any explanatory significance to statements. The truth predicate is merely a device of semantic ascent, by means of which we talk about a statement rather than assert that statement. Such a device is useful for blind truth ascriptions to statements that we cannot explicitly state. Such a view is compatible with truth as correspondence and so does not imply postmodern antirealism, since statements directly asserted (...) are descriptive of the world as it actually is. Getting rid of propositional truth has the advantage of ridding us of abstract truth-bearers that are uncreated by God. (shrink)

This paper discusses the meaning of expressed preference statements. A holistic explanation of preferences is proposed: preference relations between propositions are explained by preference relations over worlds. Only those world-preferences function as explanans which are maximally similar to the actual world, and which are maximally similar to each other. The concept of similarity as intuitive is rejected, and is interpreted instead with reference to causal structure: 'closest to the actual world' is interpreted as compatible with the causal structure (...) of the actual world, and 'most similar to each other' as sharing the same causal background conditions. (shrink)

This paper discusses the meaning of expressed preference statements. A holistic explanation of preferences is proposed: preference relations between propositions are explained by preference relations over worlds. Only those world-preferences function as explanans which are maximally similar to the actual world, and which are maximally similar to each other. The concept of similarity as intuitive is rejected, and is interpreted instead with reference to causal structure: 'closest to the actual world' is interpreted as compatible with the causal structure (...) of the actual world, and 'most similar to each other' as sharing the same causal background conditions. (shrink)

An account of the distinction between singular and general propositions should reflect the core ideas that have motivated the distinction. Those core ideas can be appreciated independently of many commitments regarding the metaphysics of propositions, but theorists with differing views on the latter have given quite different explanations of what it is for a proposition to be singular or general. Many of those explanations turn out not to reflect the core ideas adequately after all, either by misclassifying certain (...) propositions or by failing to be sufficiently informative. A more satisfactory account can be formulated by more directly elaborating on the background ideas motivating the distinction. The resulting account not only does better than its competitors, but is compatible with various views on the metaphysics of propositions. (shrink)

Since Lewis’s (1969) and Aumann’s (1976) pioneering contributions, the concepts of common knowledge and common belief have been discussed extensively in the literature, both syntactically and semantically1. At the individual level the difference between knowledge and belief is usually identified with the presence or absence of the Truth Axiom ( iA → A), which is interpreted as ”if individual i believes that A, then A is true”. In such a case the individual is often said to know that A (thus (...) it is possible for an individual to believe a false proposition but she cannot know a false proposition). Going to the interpersonal level, the literature then distinguishes between common knowledge and common belief on the basis of whether or not the Truth Axiom is postulated at the individual level. However, while at the individual level the Truth Axiom captures merely a relationship between the individuals’ beliefs and the external world, at the interpersonal level it has very strong implications. For example, the following is a consequence of the Truth Axiom: i jA → iA, that is, if individual i believes that individual j believes that A, then individual i herself believes that A. Thus, in contrast to other axioms, the Truth Axiom does not merely reflect individual agents’ “logic of belief”. (The reason why the Truth Axiom is much stronger in an interpersonal context than appears at first glance is that it amounts to assuming that agreement of any individual’s belief with the truth is common knowledge). Given its logical force, it is not surprising to find that it has strong implications for the logic of common knowledge. In particular, if each individual’s beliefs satisfy the strongest logic of knowledge (namely S5 or KT5), the associated common knowledge operator satisfies this logic too. Such is not the case for belief: bereft of the Truth Axiom, even the strongest logic for individual belief (KD45) is insufficient to ensure the satisfaction of the “Negative Introspection” axiom for common belief: ¬ ∗A → ∗¬ ∗A (where ∗ denotes the common belief operator).. (shrink)

The final portion of the thesis surveys proposals for the introduction of hidden variables into quantum mechanics, proofs of the impossibility of such hidden-variable proposals, and criticisms of these impossibility proofs. And arguments in favour of the partial-Boolean algebra, rather than the orthomodular lattice, formalization of the quantum propositional structures are reviewed. ;As for , each quantum state-induced expectation-function on a P truth-functionally assigns 1 and 0 values to the elements in a ultrafilter and dual ultraideal of P, where in (...) general the union of an ultrafilter and its dual ultraideal is smaller than the entire structure. Thus it is argued that each expectation-function is the quantum analog of a classical semantic mapping, even though the domain where each expectation-function is bivalent and truth-functional is usually a non-Boolean substructure of P. ;In classical propositional logic, propositions form a Boolean algebra, and each semantic mapping assigns the value 1 to the members of a certain subset of the algebra, namely, an ultrafilter, and assigns 0 to the members of the dual ultraideal, where the union of these two subsets is the entire algebra. The propositional structures of classical mechanics are likewise Boolean algebras, so one can straightforwardly provide a classical semantics, which also satisfies . However, quantum propositional structures are non-Boolean, so it is an open question whether a semantics satisfying , and can be provided. ;Von Neumann first proposed that the algebraic structures of the subspaces of Hilbert space be regarded as the propositional structures P of quantum mechanics. These structures have been formalized in two ways: as orthomodular lattices which have the binary operations "and", "or", defined among all elements, compatible and incompatible ; and as partial-Boolean algebras which have the binary operations defined among only compatible elements. In the thesis, two basic senses in which these structures are non-Boolean are discriminated. And two notions of truth-functionality are distinguished: truth-functionality ,) applicable to the Plattices; and truth-functionality ) applicable to both the Plattices and partial-Boolean algebras. Then it is shown how the lattice definitions of "and", "or", among incompatibles rule out a bivalent, truth-functional ,) semantics for any PQM lattice containing incompatible elements. In contrast, the Gleason and Kochen-Specker proofs of the impossibility of hidden-variables for quantum mechanics show the impossibility of a bivalent, truth-functional ) semantics for three-or-higher dimensional Hilbert space PQM structures; and the presence of incompatible elements is necessary but is not sufficient to rule out such a semantics. ;The thesis investigates the possibility of a classical semantics for quantum propositional structures. A classical semantics is defined as a set of mappings each of which is bivalent, i.e., the value 1 or 0 is assigned to each proposition, and truth-functional, i.e., the logical operations are preserved. In addition, this set must be "full", i.e., any pair of distinct propositions is assigned different values by some mapping in the set. When the propositions make assertions about the properties of classical or of quantum systems, the mappings should also be "state-induced", i.e., values assigned by the semantics should accord with values assigned by classical or by quantum mechanics. (shrink)

Most arguments against God’s existence aim to show that it is incompatible with various apparent features of the world, such as the existence of evil or of human free will. In response, theists have sought to show that God’s existence is compatible with these features of the world. However, the fact that the proposition that God exists is necessary if possible introduces some underappreciated difficulties for these arguments.

When discussing knowledge, two relations are of interest: justified doxastic accessibility \ , she is in \ ) and justification equivalence \ exactly the same justified beliefs that she has in \ ). Speaking of compatibility with the agent’s justified beliefs is potentially ambiguous: either of the two relations \ or \ can be meant. I discuss the possibility of identifying the relation of epistemic accessibility \ , she is in \ ) with the union of \ and \ . (...) Neither Gettier’s examples nor the ‘fake barn’ cases contradict this identification. However, the proposal leads to justification equivalent scenarios being symmetric with respect to knowledge: we cannot know a true proposition in a scenario if it is false in a justification equivalent scenario. This analysis may appear to render non-trivial knowledge impossible. This conclusion follows if the extra premise is granted that for all relevant true propositions there is a justification equivalent scenario in which the proposition is false. I provide a meaning-theoretic argument against this premise. I conclude by pointing out problems that would ensue from giving up the proposed connection between \ , \ and \ and allowing asymmetry of justification equivalent scenarios relative to knowledge. (shrink)

Some have argued, following Stalnaker, that a plausible functionalist account of belief requires coarse-grained propositions. I have explored a class of functionalist accounts, and my argument has been that, in this class, there is no account which meetsall of the following conditions: it is plausible, noncircular, and allows for the validity of the argument to coarse-grained propositions. In producing this argument, I believe that I have shown that it might be open to a functionalist to adopt fine-grained (...) class='Hi'>propositions; thus, one might be a functionalist without holding that all mathematical beliefs are about strings of symbols (and that the belief that all bachelors are unmarried men is a belief about words).My project in this paper has been minimal in the following sense. I havenot argued thatno functionalist account of belief which meets the three conditions can be produced; rather, I have simply explored the inadequacies of certain sorts of accounts. I think that this is useful insofar as it makes clear the challenges to be met by an account of belief which can play the required role in the argument to coarse-grained propositions. It is compatible with my position that such an account is forthcoming, insofar as I have not produced a functionalist theory of belief which is clearly non-circular, plausible, and which yields fine-grained propositions. Of course, it is also compatible with my position that no plausible, non-circular functionalist account of belief of any sort can be produced. My argument has been that,if one construes such mental states as belief as functional states, no convincing argument has yet been produced that they require coarse-grained objects. (shrink)

A central argument for the view that God's necessary omniscience [( Bgf p )] precludes freewill is unsound, because the necessity of the consequence is not the necessity of the consequent, and nor is Bgf true. God's belief in some particular proposition f about what I will do is not necessary, as I might do something that makes ~ f true. Fischer and Tognazzini claim that this counterargument argument assumes that I must freely do the something that makes f true. (...) But plainly it doesn't. All that it assumes is that I will do the something that makes f true. It makes no difference whether I do that thing unfreely, or "deterministicall". The argument does not assume the existence of a case of freewill in the face of divine foreknowledge, but instead considers the necessity of God's belief in some particular designated proposition f. The argument does not depend, as Fischer and Tognazzini suppose, on whether God's knowledge is a function of the facts (omniscience) or vice versa (infallibility). (shrink)

_From Naming to Saying_ explores the classicquestion of the unity of the proposition, combining an historical approach with contemporary causal theories to offer a unique and novel solution. Presents compelling and sophisticated answers to questions about how language represents the world. Defends a novel approach to the classical question about the unity of the proposition. Examines three key historical theories: Frege’s doctrine of concept and object, Russell’s analysis of the sentence, and Wittgenstein’s picture theory of meaning. Combines an historical approach (...) with discussion and defense of a contemporary causal theory of the unity of the proposition. Establishes a view compatible with, though not dependent on, a causal theory of meaning. (shrink)

Theories of verisimilitude have routinely been classified into two rival camps—the content approach and the likeness approach—and these appear to be motivated by very different sets of data and principles. The question thus naturally arises as to whether these approaches can be fruitfully combined. Recently Zwart and Franssen (Synthese 158(1):75–92, 2007) have offered precise analyses of the content and likeness approaches, and shown that given these analyses any attempt to meld content and likeness orderings violates some basic desiderata. Unfortunately their (...) characterizations of the approaches do not embrace the paradigm examples of those approaches. I offer somewhat different characterizations of these two approaches, as well as of the consequence approach (Schurz and Weingartner (Synthese 172(3):415–436, 2010) which happily embrace their respective paradigms. Finally I prove that the three approaches are indeed compatible, but only just, and that the cost of combining them is too high. Any account which combines the strictures of what I call the strong likeness approach with the demands of either the content or the consequence approach suffers from precisely the same defect as Popper’s—namely, it entails the trivialization of truthlikeness. The downside of eschewing the strong likeness constraints and embracing the content constraints alone is the underdetermination of the concept of truthlikeness. (shrink)

This paper argues that understanding speech in terms of action requires dispensing with propositions. Austin's outline of speech act theory did not give any role to propositions, which were introduced into speech act theory later on, in order to cope with criticism leveled by Strawson and Searle at Austin's characterization of the locutionary act and his view of the truth/falsity assessment. The introduction of propositions had weakening effects on the claim that speech is action, foregrounding again the (...) received picture of linguistic communication. I show that, in order to make sense of Austin's characterization of the locutionary act, propositions are not needed and give some suggestions as to how one could give an account of the truth/falsity assessment, compatible with the claim that speech is action, without resorting to propositions. (shrink)

Externalism is the view that the contents of many of a person’s propositional attitudes and perhaps sensory experiences are extrinsic properties of the person’s brain: they involve relations between the person’s brain and properties instantiated in his or her present or past environment. Privileged self-knowledge is the view that every human being is able to know directly or non-inferentially, in a way unavailable to anybody else, what he or she thinks or experiences. Now, if what I think is not in (...) my brain, then it seems indeed as if I cannot have any privileged authoritative first-personal access to the content of what I think. Hence, externalism seems inconsistent with privileged self-knowledge. The purpose of this paper is to provide a road towards a conciliation between self-knowledge and externalism. (shrink)

Stewart Shapiro and John Myhill tried to reproduce some features of the intuitionistic mathematics within certain formal intensional theories of classical mathematics. Basically they introduced a knowledge operator and restricted the ways of referring to numbers and to finite hereditary sets. The restrictions are very interesting, both because they allow us to keep substitutivity of identicals notwithstanding the presence of an epistemic operator and, especially, because such restrictions allow us to see, by contrast, which ways of reference are not (...) class='Hi'>compatible with the simultaneous maintenance of substitutivity of identicals and the classical notions of truth and knowledge. In this paper the difference between the restricted and the unrestricted kind of reference is put in relation with Russell's ideas on naming and it is argued that the latter as well is compatible with a certain Russellian conception of the understanding of sentences. Then it is discussed whether and how numbers could be conceived as objects of acquaintance. Finally a general question about the notion of logical form is raised. (shrink)

The notion of coexistence between questions is introduced in the framework of Piron's approach to quantum physics, using Aerts' notion of performable-together questions. Relationships between coexistence of questions and Piron's compatibility of propositions are investigated. In particular, properties generated by coexistent and primitive questions are compatible.

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis (...) (SIA), as propounded by John Bell. Despite many parallels between SIA and Leibniz’s approach —the non-punctiform nature of infinitesimals, their acting as parts of the continuum, the dependence on variables (as opposed to the static quantities of both Standard and Non-standard Analysis), the resolution of curves into infinitesided polygons, and the finessing of a commitment to the existence of infinitesimals— I find some salient differences, especially with regard to higher-order infinitesimals. These differences are illustrated by a consideration of how each approach might be applied to Newton’s Proposition 6 of the Principia, and the derivation from it of the v2/r law for the centripetal force on a body orbiting around a centre of force. It is found that while Leibniz’s syncategorematic approach is adequate to ground a Leibnizian version of the v2/r law for the “solicitation” ddr experienced by the orbiting body, there is no corresponding possibility for a derivation of the law by nilsquare infinitesimals; and while SIA can allow for second order differentials if nilcube infinitesimals are assumed, difficulties remain concerning the compatibility of nilcube infinitesimals with the principles of SIA, and in any case render the type of infinitesimal analysis adopted dependent on its applicability to the problem at hand. (shrink)

It is a commonly held view that Frege's doctrine of senses and references is not compatible with the idea that there are de re beliefs. The present paper is meant to challenge that view. Moreover, it seeks to show that, instead of forcing Frege's semantic framework to answer questions raised by twentieth-century philosophy of language, we could try to find other questions to which it might be an answer. It is argued that the proper treatment of Frege's views requires (...) the acknowledgement of the central role of individualistic epistemology in his thought. Once this is recognized, Frege's doctrine of senses and references can be considered a theory, or at least a sketch of a theory, of cognition, which has interesting connections with Kant's and Husserl's views. (shrink)

Originally motivated by a sophism, Pardo's discussion about the unity of mental propositions allows him to elaborate on his ideas about the nature of propositions. His option for a non-composite character of mental propositions is grounded in an original view about syncategorems: propositions have a syncategorematic signification, which allows them to signify aliquid aliqualiter, just by virtue of the mental copula, without the need of any added categorematic element. Pardo's general claim about the simplicity of mental (...) propositions is developed into several specific thesis about mental propositions: a) it is not judgement which gives its unity to mental propositions, but judicative acts always follow some previous apprehensive act that is simple in its own right; b) this simplicity is compatible with a certain kind of complexity, that can be explained in terms of the "causal history" of the acts of knowing; c) traditional conceptions about subject and predicate must be recast, while keeping their usual explicative power concerning logical properties; d) of course, the traditional conception about the copula has been modified, giving rise to a fully innovative conception of the nature of mental propositions. Nevertheless, this innovative conception of mental language seems still infected by certain "common sense" prejudices, which lead Pardo to propose also a provocative conception of vocal language, which I consider unnecessary. (shrink)

_From Naming to Saying _explores the classicquestion of the unity of the proposition, combining an historical approach with contemporary causal theories to offer a unique and novel solution. Presents compelling and sophisticated answers to questions about how language represents the world. Defends a novel approach to the classical question about the unity of the proposition. Examines three key historical theories: Frege’s doctrine of concept and object, Russell’s analysis of the sentence, and Wittgenstein’s picture theory of meaning. Combines an historical approach (...) with discussion and defense of a contemporary causal theory of the unity of the proposition. Establishes a view compatible with, though not dependent on, a causal theory of meaning. (shrink)

Hume is often read as proposing an instrumental theory of decision, in which an agent's choices are rational if they maximally satisfy her desires, given her beliefs. In fact, Hume denies that rationality can be attributed to actions. I argue that this is not a gap needing to be filled. Hume's theory provides a coherent and self-contained understanding of action, compatible with current developments in experimental psychology and behavioural economics. On Hume's account, desires are primitive psychological motivations which do (...) not have propositional content, and so are not subject to the criteria of rational consistency which apply to propositions. (shrink)

(i) It is propositions, not sentences, that are true or false. It is true ‘Dogs bark’ does not make sense. It is true that dogs bark does. (ii) and (iii) Davidson wrong about ‘that’. (iv) The difference between ‘implies’ and ‘if ... then ...’. (v), (vi), (vii) and (viii) Russell, not Quine, right about the subject matter of logic. (ix) The objectual and substitutional interpretations of quantifiers compatible. (x), (xi), (xii), (xiii), (xiv), (xv) and (xvi) Implications for well-known (...) theories of truth; truth correspondence. (xvii), (xviii) and (xix) and (xx) Implications for the principle of bivalence, the law of excluded middle, and the principle of non-contradiction. (xxi) Recapitulation. (xxii) ‘That’ and entailment. (xxiii) Propositions not entities, subsistent or otherwise. Footnotes1 This article was stimulated by some remarks by J. J. C. Smart in criticism of a piece of work (God, Freedom and Immortality, Ashgate, 1999) that he was kind enough to read for me. I am greatly indebted to my friend David Rees for correcting the manuscript, and making some valuable suggestions concerning its content. (shrink)

In what follows, I will first try to show that both anti-realist and realist intensionalist truthconditional accounts of internal metafictional sentences (i.e., sentences of the form "in the story S, p") are unsatisfactory. Moreover, I will claim that this does not mean that propositional truthconditional accounts of those sentences are to be dispensed with; simply, one has to provide a non-intensionalist propositional truthconditional account of those sentences. Finally, I will show that this account is fully compatible with a realist (...) interpretation of those sentences' truthconditions according to which at least some of those sentences commit one to fictional entities. (shrink)

Our purpose is to formulate a complete logic of propositions that takes into account the fact that propositions are both senses provided with truth values and contents of conceptual thoughts. In our formalization, propositions are more complex entities than simple functions from possible worlds into truth values. They have a structure of constituents (a content) in addition to truth conditions. The formalization is adequate for the purposes of the logic of speech acts. It imposes a stronger criterion (...) of propositional identity than strict equivalence. Two propositions P and Q are identical if and only if, for any illocutionary force F, it is not possible to perform with success a speech act of the form F(P) without also performing with success a speech act of the form F(Q). Unlike hyperintensional logic, our logic of propositions is compatible with the classical Boolean laws of propositional identity such as the symmetry and the associativity of conjunction and the reduction of double negation. (shrink)

The essay first makes some observations on the general interrelationship between the logical writings of Albert and Buridan. Second, it gives an account of a ‘semantic logical model’ for analyzing complex subject terms in some basic categorical propositions which is defended by Albert of Saxony, and briefly recounts Buridan's criticisms of that model. Finally, the essay maintains that the Albertian model is typically compatible with, and a further development of, what is called by a late-fourteenth century anonymous scholar (...) ‘the English-Rule’ but the ‘determinable/determinate’ grammatical model defended by Buridan is not. (shrink)

In this paper I comment on Inan’s notions of propositional and objectual curiosity. Even though Inan offers an interesting and intuitive distinction between propositional and objectual curiosity, I want to question two aspects of his theory of curiosity. One aspect concerns his thesis that propositional curiosity is interdependent on epistemic attitudes such as belief, certainty and interest. Another aspect of his theory that I discuss is his thesis that objectual curiosity is not reducible to propositional curiosity. In more detail, in (...) the fi rst part, I start off by explaining what propositional curiosity is according to Inan and I bring up two worries that I call: (i) over-complexity as a result of subjectivity and (ii) overcomplexity as a result of dynamics for the above mentioned epistemic attitudes. Both worries stress the problem of over-complexity of Inan’s theory of propositional curiosity. In the second part, I argue that objectual curiosity is, contrary to Inan’s hypothesis, reducible to propositional curiosity. I further argue that the object of wh- questions that, according to Inan, express objectual curiosity can either be about the truth value of general or singular proposition. In addition, I suggest that only the reading where wh- questions express curiosity in a form of de re reading and have a singular proposition as their content is the one that is compatible with Inan’s notion of objectual curiosity. (shrink)

This text/courseware package presents a new approach to teaching first-order logic. Taking advantage of Tarski's World 4.0, the text skilfully balances the semantic conception of logic with methods of proof. The book contains eleven chapters, in four parts. Part I is about propositional logic, Part II about quantifier logic. Part III contains chapters on set theory and inductive definitions. Part IV contains advanced topics in logic, including topics of importance in applications of logic in computer science. The Language of First-order (...) Logic contains hundreds of problems and exercises for the user to work through. (shrink)

This paper uses a non-distributive system of Boolean fractions (a|b), where a and b are 2-valued propositions or events, to express uncertain conditional propositions and conditional events. These Boolean fractions, 'a if b' or 'a given b', ordered pairs of events, which did not exist for the founders of quantum logic, can better represent uncertain conditional information just as integer fractions can better represent partial distances on a number line. Since the indeterminacy of some pairs of quantum events (...) is due to the mutual inconsistency of their experimental conditions, this algebra of conditionals can express indeterminacy. In fact, this system is able to express the crucial quantum concepts of orthogonality, simultaneous verifiability, compatibility, and the superposition of quantum events, all without resorting to Hilbert space. A conditional (a|b) is said to be "inapplicable" (or "undefined") in those instances or models for which b is false. Otherwise the conditional takes the truth-value of proposition a. Thus the system is technically 3-valued, but the 3rd value has nothing to do with a state of ignorance, nor to some half-truth. People already routinely put statements into three categories: true, false, or inapplicable. As such, this system applies to macroscopic as well as microscopic events. Two conditional propositions turn out to be simultaneously verifiable just in case the truth of one implies the applicability of the other. Furthermore, two conditional propositions (a|b) and (c|d) reside in a common Boolean sub-algebra of the non-distributive system of conditional propositions just in case b = d, their conditions are equivalent. Since all aspects of quantum mechanics can be represented with this near classical logic, there is no need to adopt Hilbert space logic as ordinary logic, just a need perhaps to adopt propositional fractions to do logic, just as we long ago adopted integer fractions to do arithmetic. The algebra of Boolean fractions is a natural, near-Boolean extension of Boolean algebra adequate to express quantum logic. While this paper explains one group of quantum anomalies, it nevertheless leaves no less mysterious the 'influence-at-a-distance', quantum entanglement phenomena. A quantum realist must still embrace non-local influences to hold that "hidden variables" are the measured properties of particles. But that seems easier than imaging wave-particle duality and instant collapse, as offered by proponents of the standard interpretation of quantum mechanics. (shrink)

Bell-type inequalities on orthomodular lattices, in which conjunctions of propositions are not modeled by meets but by maps for simultaneous measurements -maps), are studied. It is shown, that the most simple of these inequalities, that involves only two propositions, is always satisfied, contrary to what happens in the case of traditional version of this inequality in which conjunctions of propositions are modeled by meets. Equivalence of various Bell-type inequalities formulated with the aid of bivariate maps on orthomodular (...) lattices is studied. Our investigations shed new light on the interpretation of various multivariate maps defined on orthomodular lattices already studied in the literature. The paper is concluded by showing the possibility of using \-maps and \-maps to represent counterfactual conjunctions and disjunctions of non-compatible propositions about quantum systems. (shrink)

In the following text we would like to present the philosophical discussion on untrusting lies, which introduces a space for innocent lie understood as figurative manipulation of the speech: a poetic trope that we would argue could not only be generously used to help us tolerating our sometime deceiving human condition—which is global and universally ours, that of the finitude of human capacity of knowledge and ethical action—but also to maximise our capacity for knowledge formation and adaptation to values. Concepts (...) formation and communication relates to a collective interplay of different interiorized images, before it comes to the exterior in some well-chosen expressions, in self-mastered way; their origin remain in a mentally latent process of selection of content and ideas, as possible solutions of in a games of compatible propositions. These unconscious materials of our life relies on our capacity to identify and quickly switch between different spans, that enable us to focus on complex sets data, all depending very much on figurative manipulations, that should not be confounded with blameworthy and misleading representations. (shrink)

The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: the levels of language, their belonging to indeterminate compatible propositions or indeterminate propositions, being based on universal antinomy and the theory of (...) dialetheism. (shrink)

In Freedom: An Impossible Reality (FAIR), Raymond Tallis finds room in a law-abiding universe for a uniquely human form of agency, capable of envisioning and pursuing genuinely open possibilities, thereby deflecting rather than merely inflecting the course of events, in accordance with self-owned intentions, reasons and goals. He argues that the genuinely free human pursuit of such propositional attitudes depends on our acting from a “virtual outside”, at an epistemic distance from the physical world that reveals not only what is (...) the case, but that it is the case. The enactive approach in cognitive science and philosophy of mind aims to supersede the cognitivist traditional that has long dominated the field, by reframing cognition as an agentʼs immediate, embodied engagement with its environment. In an appendix of FAIR, Tallis argues that this approach risks both eliminating propositional attitudes, and collapsing the epistemic distance between agent and world. He concludes that if enactive theorists are to distinguish between genuinely pursuing an intention and merely responding to a stimulus, their corrective to cognitivism is in need of a correction of its own. This paper argues that such a correction is already to be found within the enactive literature, and furthermore, that it bears striking similarities to Tallis own account of what makes human agency unique. It is therefore concluded that the case for freedom set out in FAIR is compatible with the enactive approach. (shrink)

Whilst much has been said about the implications of predictive processing for our scientific understanding of cognition, there has been comparatively little discussion of how this new paradigm fits with our everyday understanding of the mind, i.e. folk psychology. This paper aims to assess the relationship between folk psychology and predictive processing, which will first require making a distinction between two ways of understanding folk psychology: as propositional attitude psychology and as a broader folk psychological discourse. It will be argued (...) that folk psychology in this broader sense is compatible with predictive processing, despite the fact that there is an apparent incompatibility between predictive processing and a literalist interpretation of propositional attitude psychology. The distinction between these two kinds of folk psychology allows us to accept that our scientific usage of folk concepts requires revision, whilst rejecting the suggestion that we should eliminate folk psychology entirely. (shrink)

There is a thesis that assure the computability between externalize about mental content and self-knowledge (BURGE, 1988). However, this theses, that explore the auto-verification property of claims of the type “I think that p”, works only for assertive claims that are express in the simple present tense. Among the problematic cases are the claims in the past tense and claims about specific propositional attitude. This fails about the thesis of the compatibility is pointed by Boghossian (1992) as a prove of (...) the incompatibility between externalism and self-knowledge. There is a wide bibliography that try to manage the claims in past tense. In these articles (BURGE, 1995), It's argued that the preservative function of memory assure the veracity of the claims in past tense (at last in normal situations). However, there isn't a lot of work about the problem of the claims about specific propositional attitude. This article propose a expanse the preservative memory theory, with the purpose that It manages the self-knowledge of past propositional attitudes. We propose some criteria that define when a claim of this type is true, mainly in the cases that the content of the attitude of the past thought is not identical with the actual thought. The criterion about the similarity of content is the Bernecker's one (2009). The criterion about similarity of attitudes is new: the attitude that S thinks in t1 as if he have had in t2 is similar with the attitude that he had in t 1 iff the actual attitude is entailed by the former. (shrink)

In this article, the attempts by David Lewis and Brian Loar to make perspicuous the logical form of sentences ascribing propositional attitudes to individuals are set out and criticized. Both work within the assumption of the truth of 'type' physicalism, and require that logically perspicuous attitude ascriptions be compatible with the demands of such a doctrine. It is argued that neither carry out this task successfully - Lewis's perspicuous ascriptions have counter-intuitive implications, while Loar's avoidance of these undermines type (...) physicalism itself. (shrink)

Hope, in its propositional construction "I hope that p," is compatible with a stated chance for the speaker that not-p. On fallibilist construals of knowledge, knowledge is compatible with a chance of being wrong, such that one can know that p even though there is an epistemic chance for one that not-p. But self-ascriptions of propositional hope that p seem to be incompatible, in some sense, with self-ascriptions of knowing whether p. Data from conjoining hope self-ascription with outright (...) assertions, with first- and third-person knowledge ascriptions, and with factive predicates suggest a problem: when combined with a plausible principle on the rationality of hope, they suggest that fallibilism is false. By contrast, the infallibilist about knowledge can straightforwardly explain why knowledge would be incompatible with hope, and can offer a simple and unified explanation of all the linguistic data introduced here. This suggests that fallibilists bear an explanatory burden which has been hitherto overlooked. (shrink)