Search results for 'propositional copula' (try it on Scholar)

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  1. Proving in Finite Many-Valued Propositional (forthcoming). An Algorithm for Axiomatizing and Theorem Proving in Finite Many-Valued Propositional Logics* Walter A. Carnielli. Logique Et Analyse.
     
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  2.  18
    Paloma Pérez-Ilzarbe (2009). Jerónimo Pardo on the Unity of Mental Propositions. In J. Biard (ed.), Le langage mental du Moyen Âge à l'Âge Classique. Peeters Publishers
    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 (...)
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  3. J. Adam Carter & Jesper Kallestrup (2015). Extended Cognition and Propositional Memory. Philosophy and Phenomenological Research 92 (2):n/a-n/a.
    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 (...)
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  4.  32
    Chris J. Mitchell, Jan De Houwer & Peter F. Lovibond (2009). The Propositional Nature of Human Associative Learning. Behavioral and Brain Sciences 32 (2):183-198.
    The past 50 years have seen an accumulation of evidence suggesting that associative learning depends on high-level cognitive processes that give rise to propositional knowledge. Yet, many learning theorists maintain a belief in a learning mechanism in which links between mental representations are formed automatically. We characterize and highlight the differences between the propositional and link approaches, and review the relevant empirical evidence. We conclude that learning is the consequence of propositional reasoning processes that cooperate with (...)
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  5. Mark E. Richard (1990). Propositional Attitudes: An Essay on Thoughts and How We Ascribe Them. New York: Cambridge University Press.
    This book makes a stimulating contribution to the philosophy of language and philosophy of mind. It begins with a spirited defense of the view that propositions are structured and that propositional structure is "psychologically real." The author then develops a subtle view of propositions and attitude ascription. The view is worked out in detail with attention to such topics as the semantics of conversations, iterated attitude ascriptions, and the role of propositions as bearers of truth. Along the way (...)
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  6. Richard Gaskin (2008). The Unity of the Proposition. Oxford University Press.
    Truth, falsity, and unity -- Sentences, lists, and collections -- Declarative and other kinds of sentence -- Declarative sentences and propositions -- Sentences, propositions, and truth-values -- Sentences, propositions, and unity -- Unity and complexity -- Reference and supposition -- Reference and signification -- Linguistic idealism and empirical realism -- Russell on truth, falsity, and unity : 1903 -- Russell on truth, falsity, and unity : 1910-13 -- Russell on truth, falsity, and unity : 1918 -- Sense, reference, and propositions (...)
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  7. Daniel Howard-Snyder (2013). Propositional Faith: What It is and What It is Not. American Philosophical Quarterly 50 (4):357-372.
    Reprinted in Philosophy of Religion: An Anthology, Wadsworth 2015, 6th edition, eds Michael Rea and Louis Pojman. What is propositional faith? At a first approximation, we might answer that it is the psychological attitude picked out by standard uses of the English locution “S has faith that p,” where p takes declarative sentences as instances, as in “He has faith that they’ll win”. Although correct, this answer is not nearly as informative as we might like. Many people say (...)
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  8.  63
    Robert J. Matthews (2007/2010). The Measure of Mind: Propositional Attitudes and Their Attribution. Oxford University Press.
    A prospective introduction -- The received view -- Troubles with the received view -- Are propositional attitudes relations? -- Foundations of a measurement-theoretic account of the attitudes -- The basic measurement-theoretic account -- Elaboration and explication of the proposed measurement-theoretic account.
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  9. Thomas Kelly (2002). The Rationality of Belief and Other Propositional Attitudes. Philosophical Studies 110 (2):163-96.
    In this paper, I explore the question of whether the expected consequences of holding a belief can affect the rationality of doing so. Special attention is given to various ways in which one might attempt to exert some measure of control over what one believes and the normative status of the beliefs that result from the successful execution of such projects. I argue that the lessons which emerge from thinking about the case ofbelief have important implications for the way we (...)
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  10. Sean Crawford (2014). Propositional or Non-Propositional Attitudes? Philosophical Studies 168 (1):179-210.
    Propositionalism is the view that intentional attitudes, such as belief, are relations to propositions. Propositionalists argue that propositionalism follows from the intuitive validity of certain kinds of inferences involving attitude reports. Jubien (2001) argues powerfully against propositions and sketches some interesting positive proposals, based on Russell’s multiple relation theory of judgment, about how to accommodate “propositional phenomena” without appeal to propositions. This paper argues that none of Jubien’s proposals succeeds in accommodating an important range of propositional phenomena, such (...)
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  11. Jan Krajiček (1994). Lower Bounds to the Size of Constant-Depth Propositional Proofs. Journal of Symbolic Logic 59 (1):73-86.
    LK is a natural modification of Gentzen sequent calculus for propositional logic with connectives ¬ and $\bigwedge, \bigvee$ (both of bounded arity). Then for every d ≥ 0 and n ≥ 2, there is a set Td n of depth d sequents of total size O(n3 + d) which are refutable in LK by depth d + 1 proof of size exp(O(log2 n)) but such that every depth d refutation must have the size at least exp(nΩ(1)). The sets (...)
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  12.  73
    Craig French (2012). Does Propositional Seeing Entail Propositional Knowledge? Theoria 78 (2):115-127.
    In a 2010 article Turri puts forward some powerful considerations which suggest that Williamson's view of knowledge as the most general factive mental state is false. Turri claims that this view is false since it is false that if S sees that p, then S knows that p. Turri argues that there are cases in which (A) S sees that p but (B) S does not know that p. In response I offer linguistic evidence to suppose that in (...) contexts “see” does not have the sort of meaning (a purely perceptual meaning) which would sustain Turri's claims about the cases he offers (specifically, the (A) verdicts). (shrink)
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  13. Alex Grzankowski (2012). Not All Attitudes Are Propositional. European Journal of Philosophy (3):374-391.
    Most contemporary philosophical discussions of intentionality start and end with a treatment of the propositional attitudes. In fact, many theorists hold that all attitudes are propositional attitudes. Our folk-psychological ascriptions suggest, however, that there are non-propositional attitudes: I like Sally, my brother fears snakes, everyone loves my grandmother, and Rush Limbaugh hates Obama. I argue that things are as they appear: there are non-propositional attitudes. More specifically, I argue that there are attitudes (...)
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  14.  84
    Robert M. Gordon (2007). Ascent Routines for Propositional Attitudes. Synthese 159 (2):151 - 165.
    An ascent routine (AR) allows a speaker to self-ascribe a given propositional attitude (PA) by redeploying the process that generates a corresponding lower level utterance. Thus, we may report on our beliefs about the weather by reporting (under certain constraints) on the weather. The chief criticism of my AR account of self-ascription, by Alvin Goldman and others, is that it covers few if any PA’s other than belief and offers no account of how we can attain reliability in (...)
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  15.  8
    Hamid Vahid (forthcoming). A Dispositional Analysis of Propositional and Doxastic Justification. Philosophical Studies:1-20.
    An important question in epistemology concerns how the two species of justification, propositional and doxastic justification, are related to one another. According to the received view, basing one’s belief p on the grounds that provide propositional justification to believe p is sufficient for the belief to be doxastically justified. In a recent paper, however, John Turri has suggested that we should reverse the direction of explanation. In this paper, I propose to see the debate in a (...)
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  16. John N. Williams (2008). Propositional Knowledge and Know-How. Synthese 165 (1):107 - 125.
    This paper is roughly in two parts. The first deals with whether know-how is constituted by propositional knowledge, as discussed primarily by Gilbert Ryle (1949) The concept of mind. London: Hutchinson, Jason Stanley and Timothy Williamson (2001). Knowing how. Journal of Philosophy, 98, pp. 411–444 as well as Stephen Hetherington (2006). How to know that knowledge-that is knowledge-how. In S. Hetherington (Ed.) Epistemology futures. Oxford: Oxford University Press. The conclusion of this first part is that know-how sometimes does and (...)
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  17.  64
    Alex Grzankowski (2013). Non‐Propositional Attitudes. Philosophy Compass 8 (12):1123-1137.
    Intentionality, or the power of minds to be about, to represent, or to stand for things, remains central in the philosophy of mind. But the study of intentionality in the analytic tradition has been dominated by discussions of propositional attitudes such as belief, desire, and visual perception. There are, however, intentional states that aren't obviously propositional attitudes. For example, Indiana Jones fears snakes, Antony loves Cleopatra, and Jane hates the monster under her bed. The present paper explores such (...)
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  18.  35
    Balder ten Cate (2006). Expressivity of Second Order Propositional Modal Logic. Journal of Philosophical Logic 35 (2):209-223.
    We consider second-order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem–Rosen theorem and the Goldblatt Thomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of SOPML, and we characterize the bounded fragment of first-order logic as being the intersection of first-order logic and SOPML.
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  19. Michael Morreau & Sarit Kraus (1998). Syntactical Treatments of Propositional Attitudes. Artificial Intelligence 106 (1):161-177.
    Syntactical treatments of propositional attitudes are attractive to artificial intelligence researchers. But results of Montague (1974) and Thomason (1980) seem to show that syntactical treatments are not viable. They show that if representation languages are sufficiently expressive, then axiom schemes characterizing knowledge and belief give rise to paradox. Des Rivières and Levesque (1988) characterize a class of sentences within which these schemes can safely be instantiated. These sentences do not quantify over the propositional objects of knowledge and belief. (...)
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  20.  70
    Mauro Ferrari, Camillo Fiorentini & Guido Fiorino (2004). A Secondary Semantics for Second Order Intuitionistic Propositional Logic. Mathematical Logic Quarterly 50 (2):202-210.
    In this paper we propose a Kripke-style semantics for second order intuitionistic propositional logic and we provide a semantical proof of the disjunction and the explicit definability property. Moreover, we provide a tableau calculus which is sound and complete with respect to such a semantics.
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  21. Timothy Schroeder (2006). Propositional Attitudes. Philosophy Compass 1 (1):65-73.
    The propositional attitudes are attitudes such as believing and desiring, taken toward propositions such as the proposition that snow flurries are expected, or that the Prime Minister likes poutine. Collectively, our views about the propositional attitudes make up much of folk psychology, our everyday theory of how the mind works.
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  22.  70
    Jan Almäng (2014). Perception, Non-Propositional Content and the Justification of Perceptual Judgments. Metaphysica 15 (1):1-23.
    It is often argued that for a perceptual experience to be able to justify perceptual judgments, the perceptual experience must have a propositional content. For, it is claimed, only propositions can bear logical relations such as implication to each other. In this paper, this claim is challenged. It is argued that whereas perceptions and judgments both have intentional content, their contents have different structures. Perceptual content does not have a propositional structure. Perceptions and judgments can nevertheless (...)
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  23.  97
    John Dilworth & Dylan Sabo (2014). A Dual-Component View of Propositional Grasping. Erkenntnis 79 (3):511-522.
    On a traditional or default view of the grasping or understanding of a singular proposition by an individual, it is assumed to be a unitary or holistic activity. However, naturalistic views of cognition plausibly could analyze propositional thinking in terms of more than one distinctive functional stage of cognitive processing, suggesting at least the potential legitimacy of a non-unitary analysis of propositional grasping. We outline a novel dual-component view of this kind, and show that it is well supported (...)
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  24.  76
    Jeffrey C. King (2015). Acquaintance, Singular Thought and Propositional Constituency. Philosophical Studies 172 (2):543-560.
    In a recent paper, Armstrong and Stanley argue that despite being initially compelling, a Russellian account of singular thought has deep difficulties. I defend a certain sort of Russellian account of singular thought against their arguments. In the process, I spell out a notion of propositional constituency that is independently motivated and has many attractive features.
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  25.  91
    Xinli Wang & Ling Xu (2009). The Propositional Vs. Hermeneutic Models of Cross-Cultural Understanding. South African Journal of Philosophy 28 (3):312-331.
    What the authors attempt to address in this paper is a Kantian question: not whether, but how is cross -cultural understanding possible? And specifically, what is a more effective approach for cross -cultural understanding? The answer lies in an analysis of two different models of cross -cultural understanding, that is, propositional and hermeneutic understanding. To begin with, the author presents a linguistic interpretation of culture, i.e., a culture as a linguistically formulated and transmitted symbolic system with its conceptual (...)
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  26.  7
    Michael Kaminski & Nissim Francez (2014). Relational Semantics of the Lambek Calculus Extended with Classical Propositional Logic. Studia Logica 102 (3):479-497.
    We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic.
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  27.  56
    Adam Morton (2009). From Tracking Relations to Propositional Attitudes. European Journal of Analytic Philosophy 5 (2):7-18.
    I explore the possibility that propositional attitudes are not basic in folk psychology, and that what we really ascribe to people are relations to individuals, those that the apparently propositional contents of beliefs, desires, and other states concern. In particular, the relation between a state and the individuals that it tracks shows how ascription of propositional attitudes could grow out of ascription of relations between people and objects.
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  28.  70
    Tobias Hansson Wahlberg (2010). The Tenseless Copula in Temporal Predication. Erkenntnis 72 (2):267 - 280.
    In this paper I explore how the tenseless copula is to be interpreted in sentences of the form “ a is F at t ”, where “ a ” denotes a persisting, changeable object, “ F ” stands for a prima facie intrinsic property and “ t ” for a B-time. I argue that the interpretation of the copula depends on the logical role assigned to the time clause. Having rejected the idea that the time clause is to (...)
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  29.  47
    Alessandro Capone (2013). The Pragmatics of Pronominal Clitics and Propositional Attitudes. Intercultural Pragmatics 10 (3):459-485.
    pronominal clitics, pragmatics and propositional attitudes.
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  30.  5
    Matteo Pascucci (2016). A Unified Semantics for a Family of Modal Logics with Propositional Constants. Logica Universalis 10 (1):45-66.
    This article concerns the metatheory of a class of modal logics whose language includes propositional constants of various kinds. The main novelties are the use of general frames with specific restrictions and the definition of the strict range of a formula. Many examples from the literature are treated within the framework provided and some traditional model-theoretic issues such as preservation results concerning the validity of formulas and definability results concerning frame properties are addressed.
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  31.  7
    Rohan French (2012). Denumerably Many Post-Complete Normal Modal Logics with Propositional Constants. Notre Dame Journal of Formal Logic 53 (4):549-556.
    We show that there are denumerably many Post-complete normal modal logics in the language which includes an additional propositional constant. This contrasts with the case when there is no such constant present, for which it is well known that there are only two such logics.
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  32.  7
    Franco Montagna (2012). Δ-Core Fuzzy Logics with Propositional Quantifiers, Quantifier Elimination and Uniform Craig Interpolation. Studia Logica 100 (1-2):289-317.
    In this paper we investigate the connections between quantifier elimination, decidability and Uniform Craig Interpolation in Δ-core fuzzy logics added with propositional quantifiers. As a consequence, we are able to prove that several propositional fuzzy logics have a conservative extension which is a Δ-core fuzzy logic and has Uniform Craig Interpolation.
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  33.  2
    Michael Kaminski & Nissim Francez (forthcoming). The Lambek Calculus Extended with Intuitionistic Propositional Logic. Studia Logica:1-32.
    We present sound and complete semantics and a sequent calculus for the Lambek calculus extended with intuitionistic propositional logic.
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  34.  44
    Claes Strannegård, Simon Ulfsbäcker, David Hedqvist & Tommy Gärling (2010). Reasoning Processes in Propositional Logic. Journal of Logic, Language and Information 19 (3):283-314.
    We conducted a computer-based psychological experiment in which a random mix of 40 tautologies and 40 non-tautologies were presented to the participants, who were asked to determine which ones of the formulas were tautologies. The participants were eight university students in computer science who had received tuition in propositional logic. The formulas appeared one by one, a time-limit of 45 s applied to each formula and no aids were allowed. For each formula we recorded the proportion of the participants (...)
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  35.  57
    William P. Bechtel & A. Abrahamson (1990). Beyond the Exclusively Propositional Era. Synthese 82 (2):223-53.
    Contemporary epistemology has assumed that knowledge is represented in sentences or propositions. However, a variety of extensions and alternatives to this view have been proposed in other areas of investigation. We review some of these proposals, focusing on (1) Ryle's notion of knowing how and Hanson's and Kuhn's accounts of theory-laden perception in science; (2) extensions of simple propositional representations in cognitive models and artificial intelligence; (3) the debate concerning imagistic versus propositional representations in cognitive psychology; (4) recent (...)
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  36.  25
    Brian Hill & Francesca Poggiolesi (2010). A Contraction-Free and Cut-Free Sequent Calculus for Propositional Dynamic Logic. Studia Logica 94 (1):47 - 72.
    In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.
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  37.  16
    Giulia Felappi (2014). On Product‐Based Accounts of Propositional Attitudes. Thought: A Journal of Philosophy 3 (4):302-313.
    Propositional attitude sentences, such as John believes that snow is white, are traditionally taken to express the holding of a relation between a subject and what ‘that’-clauses like ‘that snow is white’ denote, i.e. propositions. On the traditional account, propositions are abstract, mind- and language-independent entities. Recently, some have raised some serious worries for the traditional account and thought that we were mistaken about the kind of entities propositions are. Over the last ten years there has then been a (...)
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  38.  5
    Paloma Pérez-Ilzarbe (2015). The Signification of the Copula in Fernando de Enzinas’ Syncategoremata. Vivarium 53 (2-4):405-423.
    _ Source: _Volume 53, Issue 2-4, pp 405 - 423 This article deals with a brief _difficultas_ in the _Tractatus de compositione propositionis mentalis_ by Fernando de Enzinas: _qualiter copule significent tempus et an copule de presenti et preterito sint synonime_. A progressive determination of the signification of the copula is analysed: first, Enzinas defines his position about the principal syncategorematic signification of the copula; then, he analyses the sense of the consignification of time traditionally attributed to the (...)
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  39.  35
    Philip Hugly & Charles Sayward (1979). More on Propositional Identity. Analysis 39 (3):129-132.
    We give a semantical account of propositional identity which is stronger than mutual entailment. That is, according to our account: (1) if A = B is true in a model, so are A 'validates' B and B 'validates' A. (2) There exist models m such that A 'validates' B and B 'validates' A are true in m but A = B is not true in m. According to our account the following rule is sound: (3) from (.. A..) = (...)
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  40.  47
    Charles Sayward & Philip Hugly (1979). More on Propositional Identity. Analysis 39 (3):129-132.
    We give a semantical account of propositional identity which is stronger than mutual entailment. That is, according to our account: (1) if A = B is true in a model, so are A 'validates' B and B 'validates' A. (2) There exist models m such that A 'validates' B and B 'validates' A are true in m but A = B is not true in m. According to our account the following rule is sound: (3) from (.. A..) = (...)
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  41.  1
    Mohammad Ardeshir & Wim Ruitenburg (1998). Basic Propositional Calculus I. Mathematical Logic Quarterly 44 (3):317-343.
    We present an axiomatization for Basic Propositional Calculus BPC and give a completeness theorem for the class of transitive Kripke structures. We present several refinements, including a completeness theorem for irreflexive trees. The class of intermediate logics includes two maximal nodes, one being Classical Propositional Calculus CPC, the other being E1, a theory axiomatized by T → ⊥. The intersection CPC ∩ E1 is axiomatizable by the Principle of the Excluded Middle A V ∨ ⌝A. If B is (...)
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  42.  38
    Graham Oppy (1992). Semantics for Propositional Attitude Ascriptions. Philosophical Studies 67 (1):1 - 18.
    This paper provides a semantics for propositional attitude ascriptions. (In this respect, the title of the paper is quite well chosen.).
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  43.  55
    Robert Trueman (2011). Propositional Functions in Extension. Theoria 77 (4):292-311.
    In his “The Foundations of Mathematics”, Ramsey attempted to marry the Tractarian idea that all logical truths are tautologies and vice versa, and the logicism of the Principia. In order to complete his project, Ramsey was forced to introduce propositional functions in extension (PFEs): given Ramsey's definitions of 1 and 2, without PFEs even the quantifier-free arithmetical truth that 1 ≠ 2 is not a tautology. However, a number of commentators have argued that the notion of PFEs is incoherent. (...)
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  44.  72
    James W. Garson (2010). Expressive Power and Incompleteness of Propositional Logics. Journal of Philosophical Logic 39 (2):159-171.
    Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to restore the standard (...)
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  45.  65
    David Landy (2005). Inside Doubt: On the Non-Identity of the Theory of Mind and Propositional Attitude Psychology. [REVIEW] Minds and Machines 15 (3-4):399-414.
    Eliminative materialism is a popular view of the mind which holds that propositional attitudes, the typical units of our traditional understanding, are unsupported by modern connectionist psychology and neuroscience, and consequently that propositional attitudes are a poor scientific postulate, and do not exist. Since our traditional folk psychology employs propositional attitudes, the usual argument runs, it too represents a poor theory, and may in the future be replaced by a more successful neurologically grounded theory, resulting in a (...)
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  46.  42
    Richard H. Feldman (1986). Davidson's Theory of Propositional Attitudes. Canadian Journal of Philosophy 16 (December):693-712.
    Donald davidson has proposed an account of indirect discourse that has been the subject of a great deal of discussion. Critics have contended that the theory saddles sentences in indirect discourse with implications they do not have, That the theory rests on an unsuitably obscure primitive notion that it cannot be extended to "de re" constructions and that it cannot be extended to sentences about other propositional attitudes such as belief. In this paper, I formulate davidson's theory more precisely (...)
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  47.  4
    M. Alizadeh & M. Ardeshir (2004). On the Linear Lindenbaum Algebra of Basic Propositional Logic. Mathematical Logic Quarterly 50 (1):65.
    We study the linear Lindenbaum algebra of Basic Propositional Calculus, called linear basic algebra.
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  48.  2
    Jordi Rebagliato & Ventura Verdú (1994). A Finite Hilbert‐Style Axiomatization of the Implication‐Less Fragment of the Intuitionistic Propositional Calculus. Mathematical Logic Quarterly 40 (1):61-68.
    In this paper we obtain a finite Hilbert-style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}-formulas containing this fragment.
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  49.  35
    Philip Hugly & Charles Sayward (1976). Prior on Propositional Identity. Analysis 36 (4):182-184.
    Let A, B, C stand for sentences expressing propositions; let A be a component of C; let C A/B be just like C except for replacing some occurrence of A in C by an occurrence of B; let = be a binary connective for propositional identity read as ‘the proposition that __ is the very same proposition as …’. Then authors defend adding ‘from C = C A/B infer A = B’ to Prior’s rules for propositional identity, appearing (...)
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  50.  10
    Uwe Peters (2014). Conscious Propositional Attitudes and Moral Responsibility. Journal of Moral Philosophy 11 (5):585-597.
    By drawing on empirical evidence, Matt King and Peter Carruthers have recently argued that there are no conscious propositional attitudes, such as decisions, and that this undermines moral responsibility. Neil Levy responds to King and Carruthers, and claims that their considerations needn’t worry theorists of moral responsibility. I argue that Levy’s response to King and Carruthers’ challenge to moral responsibility is unsatisfactory. After that, I propose what I take to be a preferable way of dealing with their challenge. I (...)
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