This paper corrects a mistake I saw students make but I have yet to see in print. The mistake is thinking that logically equivalent propositions have the same counterexamples—always. Of course, it is often the case that logically equivalent propositions have the same counterexamples: “every number that is prime is odd” has the same counterexamples as “every number that is not odd is not prime”. The set of numbers satisfying “prime but not odd” is the same as the set of (...) numbers satisfying “not odd but not not-prime”. The mistake is thinking that every two logically-equivalent false universal propositions have the same counterexamples. Only false universal propositions have counterexamples. A counterexample for “every two logically-equivalent false universal propositions have the same counterexamples” is two logically-equivalent false universal propositions not having the same counterexamples. The following counterexample arose naturally in my sophomore deductive logic course in a discussion of inner and outer converses. “Every even number precedes every odd number” is counterexemplified only by even numbers, whereas its equivalent “Every odd number is preceded by every even number” is counterexemplified only by odd numbers. Please let me know if you see this mistake in print. Also let me know if you have seen these points discussed before. I learned them in my own course: talk about learning by teaching! (shrink)

SummaryScientists regard their inductive hypotheses as confirmed when consistence exists between two or more results obtained by differing methods. Three hierarchical levels of confirmation are applied. Certainty is obtained by the deductive element of the third level. The question of uniformity o i nature is less decisive than the question whether or not the complexity of the processes observed or the limited scope of our senses and instruments permits to see through the causal connections involved.

It is plausible that the universe exists: a thing such that absolutely everything is a part of it. It is also plausible that singular, structured propositions exist: propositions that literally have individuals as parts. Furthermore, it is plausible that for each thing, there is a singular, structured proposition that has it as a part. Finally, it is plausible that parthood is a partial ordering: reflexive, transitive, and anti-symmetric. These plausible claims cannot all be correct. We canvass some costs of (...) denying each claim and conclude that parthood is not a partial ordering. Provided that the relevant entities exist, parthood is not anti-symmetric and proper parthood is neither asymmetric nor transitive. (shrink)

We examine second order intuitionistic propositional logic, IPC². Let $F_\exists $ be the set of formulas with no universal quantification. We prove Glivenko's theorem for formulas in $F_\exists $ that is, for φ € $F_\exists $ φ is a classical tautology if and only if ¬¬φ is a tautology of IPC². We show that for each sentence φ € $F_\exists $ (without free variables), φ is a classical tautology if and only if φ is an intuitionistic tautology. As a (...) corollary we obtain a semantic argument that the quantifier V is not definable in IPC² from ⊥, V, ^, →. (shrink)

Critical review of Scott Soames's What is Meaning?

// tl;dr A Proposition is a Way of Thinking // -/- This chapter is about type-theoretic approaches to propositional content. Type-theoretic approaches to propositional content originate with Hintikka, Stalnaker, and Lewis, and involve treating attitude environments (e.g. "Nate thinks") as universal quantifiers over domains of "doxastic possibilities" -- ways things could be, given what the subject thinks. -/- This chapter introduces and motivates a line of a type-theoretic theorizing about content that is an outgrowth of the recent literature (...) on epistemic modality, according to which contentful thought is broadly "informational" in its nature and import. The general idea here is that an object of thought is not a way *the world* could be, but rather a way *one's perspective* could be (with respect to a relevant representational question). I will spend the middle part of this chapter motivating and developing a version of this strategy that is, I’ll argue, well-suited to explaining clear phenomena concerning the attribution of perspectival attitudes -- in particular, attitudes towards loosely information-sensitive propositions -- with which extant approaches struggle. My overarching goal here will be to motivate a distinctive version of the "informational" approach -- the "Flexible Types" approach, which is based on the theory proposed in Charlow (2020). According to the Flexible Types approach, propositional attitude verbs are quantifiers over sets of possibilities, but a possibility is a type-flexible notion -- sometimes a possible world, sometimes a perspective, sometimes a set of possible worlds, sometimes a set of perspectives. -/- After introducing the Flexible Types approach, this chapter circles back to more traditional concerns for the analysis of propositions as types of possibilities -- Frege's Puzzle and the problem of Logical Omniscience. Here too the Flexible Types approach bears fruit. Although there are certainly significant differences -- I note some in the concluding section -- the gist of this theory is Hinitkkan or Lewisian in spirit (if not quite in letter). We can make progress on addressing the challenges for the analysis of propositional content in terms of types of possibilities, through empirically driven refinement of our notion of what kind of thing a "doxastic possibility" is. (shrink)

Philosophers often talk about the things we say, or believe, or think, or mean. The things are often called ‘propositions’. A proposition is what one believes, or thinks, or means when one believes, thinks, or means something. Talk about propositions is ubiquitous when philosophers turn their gaze to language, meaning and thought. But what are propositions? Is there a single class of things that serve as the objects of belief, the bearers of truth, and the meanings of utterances? How (...) do our utterances express propositions? Under what conditions do two speakers say the same thing, and what (if anything) does this tell us about the nature of propositions? There is no consensus on these questions—or even on whether propositions should be treated as things at all. During the second Propositions and Same-Saying workshop, which took place on July 19–21 2010 at the University of Sydney, philosophers debated these (and related) questions. The workshop covered topics in the philosophy of language, perception, and metaphysics. The present volume contains revised and expanded versions of the papers presented at the workshop. (shrink)

This paper opens with a presentation of the philosophical underpinning and rationale of the concept of physical literacy. This is followed by an articulation of the concept of physical literacy. Three subsequent sections then consider aspects of the concept in a little more detail. The first investigates the relationship of the physical literacy to the development of a sense of self and to establishing interaction with others. Here the philosophical approach is informed by writings on cognitive development and recent neurological (...) insights. The second considers the universality of the concept and looks briefly at the views of existentialists and of contemporary sociologists. The third section addresses the place of propositional knowledge in being physically literate. The implications of objectifying the body in descriptive language are weighed against the fact that verbally expressed understanding and knowledge are an integral part of Western culture. The debate presented is one of a series that has, over the last five years, mapped the author's work on developing the concept of physical literacy. The aspects chosen to be discussed here are three that have generated considerable interest and debate. In conclusion, there is a short reflection on the implications of the views discussed for education and physical education. (shrink)

It is almost universally accepted that the Frege–Geach Point is necessary for explaining the inferential relations and compositional structure of truth-functionally complex propositions. I argue that this claim rests on a disputable view of propositional structure, which models truth-functionally complex propositions on atomic propositions. I propose an alternative view of propositional structure, based on a certain notion of simulation, which accounts for the relevant phenomena without accepting the Frege–Geach Point. The main contention is that truth-functionally complex propositions do not include (...) as their parts truth-evaluable propositions, but their simulations, which are neither forceful nor truth-evaluable. The view makes room for the idea that there is no such thing as the forceless expression of propositional contents and is attractive because it provides the resources for avoiding a fundamental problem generated by the Frege–Geach Point concerning the relation between forceless and forceful expressions of propositional contents. I further argue that the acceptance of the Frege–Geach Point mars Peter Hanks’ and François Recanati’s recent attempts to resist the widespread idea that assertoric force is extrinsic to the expression of propositional contents. Rejecting this idea, I maintain, requires a deeper break with the tradition than Hanks and Recanati have allowed for. (shrink)

At least since Russell’s influential discussion in The Principles of Mathematics, many philosophers have held there is a problem that they call the problem of the unity of the proposition. In a recent paper, I argued that there is no single problem that alone deserves the epithet the problem of the unity of the proposition. I there distinguished three problems or questions, each of which had some right to be called a problem regarding the unity of the (...) class='Hi'>proposition; and I showed how the account of propositions formulated in my book The Nature and Structure of Content [2007 Oxford University Press] solves each of these problems. In the present paper, I take up two of these problems/questions yet again. For I want to consider other accounts of propositions and compare their solutions to these problems, or lack thereof, to mine. I argue that my account provides the best solutions to the unity problems. (shrink)

This paper contains two traditions of diagrammatic studies namely one, the Euler–Venn–Peirce diagram and the other, following tradition of Aristotle, the square of oppositions. We put together both the traditions to study representations of singular propositions, their negations and the inter relationship between the two. Along with classical negation we have incorporated negation of another kind viz. absence. We have also considered the changes that take place in the context of open universe.

In this paper I shall present some of the results I have obtained on modal theories which contain quantifiers for propositions. The paper is in two parts: in the first part I consider theories whose non-quantificational part is S5; in the second part I consider theories whose non-quantificational part is weaker than or not contained in S5. Unless otherwise stated, each theory has the same language L. This consists of a countable set V of propositional variables pl, pa, ... , (...) the operators v (or), ~ (not) and □ (necessarily), the universal quantifier (p), p a propositional variable, and brackets ( and ). The formulas of L are then defined in the usual way. (shrink)

Structured propositions are often invoked to explain why intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. As the semantics is standardly developed—for example, in Salmon, Soames :47–87, 1987) and King :516–535, 1995), the semantic value of a complex expression is an ordered complex consisting of the semantic values of its components. Such views, however, trivialize semantic composition since they do not allow for independent constraints on the meaning of complexes. Trivializing semantic composition risks “trivializing semantics” Semantics versus (...) pragmatics, Oxford University Press, Oxford, 2005). Yet, proponents of structured propositions suggest a route to reimpose substantive compositionality. While the mapping from a sentence to the structured proposition it expresses is trivially compositional, there is a non-trivial mapping from the structured proposition to its truth-value. This non-trivial level of semantic composition allows the meanings assigned to complex expressions to impose substantive constraints on the meanings of the simple ones. I first articulate the basic desiderata: an account of structured propositions capable of explaining attitude attributions and of delivering a non-trivially compositional semantics. I then show that the two-stage semantics proposed by standard proponents of structured propositions does not satisfy these joint goals. (shrink)

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 sometimes (...) does not consist in propositional knowledge. The second part defends an analysis of know-how inspired by Katherine Hawley’ (2003). Success and knowledge-how. American Philosophical Quarterly, 40, pp. 19–31, insightful proposal that know-how requires counterfactual success. I conclude by showing how this analysis helps to explain why know-how sometimes does and sometimes does not consist of propositional knowledge. (shrink)

Unintentional plagiarism abounds at universities. The literature offers several explanations for students’ difficulties with acquiring standards of good academic practice. In this paper, I propose an alternative account: unintentional plagiarism can only be understood in the context of implicit but irreconcilable forms of knowledge. While higher education institutions mainly operate within the framework of propositional epistemology, institutions of primary and secondary education tend to furnish students with encyclopedic epistemology. Accordingly, universities and institutions of pre-college education tend to propagate conflicting assumptions (...) regarding the nature of knowledge. Put simply, propositional epistemology is characterized by dialogue, agency and the exchange of ideas, which are ideally made explicit in academic writing. By contrast, encyclopedic epistemology tends to present knowledge monologically, leaving the scholarly conversation around it out. It is highly likely that the hardwired legacy of encyclopedic epistemology among students impedes the acquisition of the dialogism of academic inquiry at universities, resulting in cases of unintentional plagiarism. (shrink)

Bertrand Russell presented three systems of propositional logic, one first in Principles of Mathematics, University Press, Cambridge, 1903 then in “The Theory of Implication”, Routledge, New York, London, pp. 14–61, 1906) and culminating with Principia Mathematica, Cambridge University Press, Cambridge, 1910. They are each based on different primitive connectives and axioms. This paper follows “Peirce’s Law” through those systems with the aim of understanding some of the notorious peculiarities of the 1910 system and so revealing some of the early history (...) of classical propositional logic. “Peirce’s Law” is a valid formula of elementary propositional logic: [ ⊃ p] ⊃ p This sentence is not even a theorem in the 1910 system although it is one of the axioms in 1903 and is proved as a theorem in 1906. Although it is not proved in 1910, the two lemmas from the proof in 1906 occur as theorems, and Peirce’s Law could have been derived from them in a two step proof. The history of Peirce’s Law in Russell’s systems helps to reconstruct some of the history of axiomatic systems of classical propositional logic. (shrink)

Any value statement belongs to a certain value code shared, to a certain degree, by a number of people. Is the value code itself relative or not? To solve this problem, one must assume that universal value statements and principles always have a prima‐facie character. Prima‐facie value propositions not only claim universality but can also be understood as universally valid in the following sense. First, their validity does not depend on an individual's free preferences. Second, although they are culture‐bound, (...) there is something all cultures must have in common. But such prima‐facie propositions do not logically imply a moral judgement in any particular case. They are merely a starting point of an evaluation procedure, i.e., of weighing and balancing, nothing more. On the other hand, the final (contextual, all things considered) evaluations are necessarily relative to a certain culture and, indeed, to individual preferences. When claiming universality of values, people see the first side of the problem. When endorsing relativism, they see only the second side. (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)

In this paper we characterize, classify and axiomatize all universal classes of MV-chains. Moreover, we accomplish analogous characterization, classification and axiomatization for congruence distributive quasivarieties of MV-algebras. Finally, we apply those results to study some finitary extensions of the Łukasiewicz infinite valued propositional calculus.

Peter H. Hare (1935-2008) developed informed, original views about the proposition: some published (Hare 1969 and Hare-Madden 1975); some expressed in conversations at scores of meetings of the Buffalo Logic Colloquium and at dinners following. The published views were expository and critical responses to publications by Curt J. Ducasse (1881-1969), a well-known presence in American logic, a founder of the Association for Symbolic Logic and its President for one term.1Hare was already prominent in the University of Buffalo's Philosophy Department (...) in 1969 when I was appointed. Soon after, he became Chair. As his Associate Chair from 1971to 1975, I spent many hours with him in Buffalo and on professional trips .. (shrink)

In articles such as “Speech Acts without Propositions?” (2006), Marina Sbisà advocates a “strong” conception of speech acts as means by which speakers modify their own and others’ deontic statuses, including their rights, obligations, and commitments. On this basis Sbisà challenges an influential approach to speech acts as typically if not universally possessing propositional contents. Sbisà argues that such an approach leads to viewing speech acts as primarily aimed at communicating propositional attitudes rather than carrying out socially and normatively significant (...) action. For this reason she advocates eschewing propositions from speech act theory’s conceptual toolkit; she also proposes a liberalization of the distinction between illocutionary force and semantic content, which are widely thought to be mutually exclusive. In this chapter we examine Sbisà’s reasoning and argue that while it does justify denying propositional attitudes a central role in communication, it does not justify dispensing with propositions or other contents in our theorizing about speech acts. In addition, we endorse Sbisà’s proposal for liberalizing the force/content distinction, and show a variety of ways in which force indicators may also possess semantic content. (shrink)

When you gaze out at the night sky with its awe-inspiring display of stars and galaxies, do you ever ask yourself if it could be possible that you are actually looking into a mirror? What if we inhabit a universe that perfectly fits our needs here on Earth -- a truly human universe? That's the bold thesis author Deepak Chopra and physicist Menas Kafatos set out to prove: quite literally, "You are the universe." The startling truth is that the everyday (...) world of physical objects "out there" disguises a hidden dimension. By turning our investigation "in here" to the world of consciousness, the real reality emerges. You Are the Universe guides the reader into a realm in which each of us has the power to transform our personal existence, while at the same time fashioning a new story about how time, space, matter, and energy came into existence. Looking to overturn the traditional model of scientific reality, Chopra and Kafatos hold that each of us is a cocreator of reality and we can uncover the hidden dimensions where consciousness is a field of infinite possibilities. This seemingly impossible proposition follows from the cutting-edge modern thinking of the quantum universe and the great mysteries that must be unriddled before human beings actually know who they are. These include but are not limited to questions such as What came before the big bang? Why does the universe fit together so perfectly? Where did time come from? And do we live in a conscious universe? These mysteries are part and parcel of everyone's life. "All of us live in a participatory universe," the authors write. "Once you decide that you want to participate fully with mind, body, and soul, the paradigm shift becomes personal. The reality you inhabit will be yours to either embrace or change. (shrink)

This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode. Moreover, procedures are not (...) mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality. (shrink)