This paper considers two reasons that might support Russell’s choice of a ramified-type theory over a simple-type theory. The first reason is the existence of purported paradoxes that can be formulated in any simple-type language, including an argument that Russell considered in 1903. These arguments depend on certain converse-compositional principles. When we take account of Russell’s doctrine that a propositional function is not a constituent of its values, these principles turn out to be too implausible to make these arguments troubling. (...) The second reason is conditional on a substitutional interpretation of quantification over types other than that of individuals. This reason stands up to investigation: a simple-type language will not sustain such an interpretation, but a ramified-type language will. And there is evidence that Russell was tacitly inclined towards such an interpretation. A strong construal of that interpretation opens a way to make sense of Russell’s simultaneous repudiation of propositions and his willingness to quantify over them. But that way runs into trouble with Russell’s commitment to the finitude of human understanding. (shrink)

This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...) the model-theoretic concepts, based on those in [7], that guide the rest of this paper. Section 3 presents Natural Deduction systems IK and CK, formalizations of intuitionistic and classical one-step versions of K. In these systems, occurrences of step-markers allow deductions to display deductive structure that is covered over in familiar “no step” proof-theoretic systems for such logics. Box and Diamond are governed by Introduction and Elimination rules; the familiar K rule and Necessitation are derived (i.e. admissible) rules. CK will be the result of adding the 0-version of the Rule of Excluded Middle to the rules which generate IK. Note: IK is the result of merely dropping that rule from those generating CK, without addition of further rules or axioms (as was needed in [7]). These proof-theoretic systems yield intuitionistic and classical consequence relations by the obvious definition. Section 4 provides some examples of what can be deduced in IK. Section 5 defines some proof-theoretic concepts that are used in Section 6 to prove the soundness of the consequence relation for IK (relative to the class of models defined in Section 2.) Section 7 proves its completeness (relative to that class). Section 8 extends these results to the consequence relation for CK. (Looking ahead: Part 2 will investigate one-step proof-theoretic systems formalizing intuitionistic and classical one-step versions of some familiar logics stronger than K.). (shrink)

Part 1 [Hodes, 2021] “looked under the hood” of the familiar versions of the classical propositional modal logic K and its intuitionistic counterpart. This paper continues that project, addressing some familiar classical strengthenings of K and GL), and their intuitionistic counterparts. Section 9 associates two intuitionistic one-step proof-theoretic systems to each of the just mentioned intuitionistic logics, this by adding for each a new rule to those which generated IK in Part 1. For the systems associated with the intuitionistic counterparts (...) of D and T, these rules are “pure one-step”: their schematic formulations does not use □ or ♢. For the systems associated with the intuitionistic counterparts of K4, etc., these rules meet these conditions: neither □ nor ♢ is iterated; none use both □ and ♢. The join of the two systems associated with each of these familiar logics is the full one-step system for that intuitionistic logic. And further “blended” intuitionistic systems arise from joining these systems in various ways. Adding the 0-version of Excluded Middle to their intuitionistic counterparts yields the one-step systems corresponding to the familiar classical logics. Each proof-theoretic system defines a consequence relation in the obvious way. Section 10 examines inclusions between these consequence relations. Section 11 associates each of the above consequence relations with an appropriate class of models, and proves them sound with respect to their appropriate class. This allows proofs of some failures of inclusion between consequence relations. Section 12 proves that the each consequence relation is complete or weakly complete, that relative to its appropriate class of models. The Appendix presents three further results about some of the intuitionistic consequence relations discussed in the body of the paper. For Keywords, see Part 1. (shrink)

Discourse carries thin commitment to objects of a certain sort iff it says or implies that there are such objects. It carries a thick commitment to such objects iff an account of what determines truth-values for its sentences say or implies that there are such objects. This paper presents two model-theoretic semantics for mathematical discourse, one reflecting thick commitment to mathematical objects, the other reflecting only a thin commitment to them. According to the latter view, for example, the semantic role (...) of number-words is not designation but rather the encoding of cardinality-quantifiers. I also present some reasons for preferring this view. (shrink)

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships between various (...) cut-conditions in the absence of finitariness or of monotonicity. (shrink)

A model-theoretic approach to the semantics of set-theoretic discourse.

Where $\underline{a}$ is a Turing degree and ξ is an ordinal $ , the result of performing ξ jumps on $\underline{a},\underline{a}^{(\xi)}$ , is defined set-theoretically, using Jensen's fine-structure results. This operation appears to be the natural extension through $(\aleph_1)^{L^\underline{a}}$ of the ordinary jump operations. We describe this operation in more degree-theoretic terms, examine how much of it could be defined in degree-theoretic terms and compare it to the single jump operation.

Proof uses forcing on perfect trees for 2-quantifier sentences in the language of arithmetic. The result extends to exact pairs for the hyperarithmetic degrees.

Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke concerning formulae with two monadic predicates.

Let I be a countable jump ideal in $\mathscr{D} = \langle \text{The Turing degrees}, \leq\rangle$ . The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a (1) computes. We may replace "the join of an I-exact pair" in the above theorem by "a weak uniform upper bound on I". We also answer two minimality questions: the class of uniform upper bounds on I (...) never has a minimal member; if ∪ I = L α [ A] ∩ ω ω for α admissible or a limit of admissibles, the same holds for nice uniform upper bounds. The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces. (shrink)

Where AR is the set of arithmetic Turing degrees, 0 (ω ) is the least member of { $\mathbf{\alpha}^{(2)}|\mathbf{a}$ is an upper bound on AR}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on HYP, whose hyperjump is the degree of Kleene's O. This paper generalizes this example, using an iteration of the jump operation into the transfinite which is based on (...) results of Jensen and is detailed in [3] and [4]. In $\S1$ we review the basic definitions from [3] which are needed to state the general results. (shrink)

This paper presents a model-theoretic semantics for discourse "about" natural numbers, one that captures what I call "the mathematical-object picture", but avoids what I can "the mathematical-object theory".

Two slogans define structuralism: contemporary mathematics studies structures; mathematical objects are places in those structures. Shapiro’s version of structuralism posits abstract objects of three sorts. A system is “a collection of objects with certain relations” between these objects. “An extended family is a system of people with blood and marital relationships.” A baseball defense, e.g., the Yankee’s defense in the first game of the 1999 World Series, is a also a system, “a collection of people with on-field spatial and (...) ‘defensive-role’ relations”. “A structure is the abstract form of a system” ; it consists of “a collection of places [sometimes called positions or offices] and a finite collection of functions and relations on these places”. (shrink)

Two currently much discussed views about truth, truth pluralism and truth relativism, are found in Sellars’s writings. I show that his motivations for adoping these views are interestingly different from those shared by most of their recent advocates. First, I explain how Sellars comes to embrace a version of truth pluralism. I argue that his version overcomes a difficulty confronting pluralists, albeit at a serious cost. Then I argue that Sellars’s truth pluralism isn’t motivated by his interest in domains of (...) discourse beyond the “matter-of-factual.” Rather, the key to his truth pluralism, his analysis of truth as “semantical assertibility,” is motivated by the same consideration that leads him to adopt truth relativism. This is his interest in applying semantic notions to discourse that embodies conceptual structures other than ours. Despite their common motivation, I conclude that Sellars’s relativism is independent of, and indeed stands in tension with, the analysis of truth that underlies his pluralism. (shrink)

Note: This draft was updated on November 10, 2020. Discussing federal statutes, Justice Scalia tells us that “[t]he stark reality is that the only thing that one can say for sure was agreed to by both houses and the president (on signing the bill) is the text of the statute. The rest is legal fiction." How should we take this claim? If we take "text" to mean the printed text, that text without more is just a series of marks. If (...) instead we take "text" (as we must) to refer to something off the page such as the "meaning" of the series of marks at issue, what is that meaning and how do we know that all the legislators "agreed" on that "meaning"? In seeking answers here, we necessarily delve into semiotics (i.e., the “general theory of signs”) by noting that meaningful ink marks ("signifiers) signify a meaning beyond themselves (the "signified.") Thus, understanding how signs function is integral to lawyers' textual and linguistic analysis. Additionally, as this article demonstrates, legal analysis and rhetoric are much impoverished if lawyers ignore nonverbal signs such as icons, indices, and nonverbal symbols. In providing a broad overview of semiotics for lawyers, this article thus (1) begins with a general definition of signs and the related notion of intentionality. It then turns to, among other things, (2) the structure and concomitants of signs in more detail (including the signifier and the signified), (3) the possible correlations of the signifier and the signified that generate signs of interest to lawyers such as the index, the icon, and the symbol; (5) the expansion of legal rhetoric through use of the index, the icon, and the non-verbal as well as the verbal symbol, (6) the nature of various semiotic acts in public and private law (including assertives, commissives, directives, and verdictives); (7) the interpretation and construction of semiotic acts (including contracts as commissives and legislation as directives); (8) the role of speaker or reader meaning in the interpretation and construction of semiotic acts; (9) the semiotics of meaning, time, and the fixation of meaning debate; (10) the impact of signifier drift; (11) the distinction between sense and understanding; and (12) some brief reflections on semiotics and the First Amendment. This article also provides an Appendix of further terms and concepts useful to lawyers in their explorations of semiotics. (shrink)

This Article explores the interpretation and construction of executive orders using as examples President Trump’s two executive orders captioned “Protecting the Nation From Foreign Terrorist Entry Into the United States” (the “Two Executive Orders”). President Trump issued the Two Executive Orders in the context of (among other things) Candidate Trump’s statements such as: “Islam hates us,” and “[W]e can’t allow people coming into this country who have this hatred.” President Trump subsequently provided further context including his tweet about the second (...) of his Two Executive Orders: “People, the lawyers and the courts can call [the second of the Two Executive Orders] whatever they want, but I am calling it what we need and what it is, a TRAVEL BAN!” Although President Trump replaced the first of the Two Executive Orders with the second one and although the Supreme Court by orders dated October 10, 2017 and October 24, 2017, vacated and remanded litigation involving the second order on grounds of mootness, the Two Executive Orders remain highly instructive for those who would understand the interpretation and construction of executive orders. This article therefore examines in detail the original speaker's (i.e., President Trump's) intended meaning and effect of the Two Executive Orders. It performs such examination using insights from the semiotic subfield of pragmatics, a semiotic subfield which explores how real-world people actually use, interpret, and construe language in various real-world contexts (including contexts where the issuer of the Two Executive Orders himself has claimed that “Islam hates us” and has tweeted “TRAVEL BAN!”). Using such insights of pragmatics, this Article also explores why reasonable judges thoroughly versed in legal theory, legal practice, and pragmatics should conclude that President Trump unlawfully targeted Muslims in the Two Executive Orders. This Article, among other things, also questions the sensibility of such notions as “facial legitimacy” to the extent such notions suggest text has meaning apart from context. Keywords: executive orders, speaker meaning, interpretation, construction, semiotics, pragmatics, originalism, speech acts, context, facial legitimacy, Constitutionality, First Amendment,Trump v. Int’l Refugee Assistance Project, Scalia, immigration, semantics, original meaning, travel ban, Trump, textualism. (shrink)

Neil Gorsuch lauds judges who purport to “apply the law as it is, focusing backward, not forward, and looking to text, structure, and history to decide what a reasonable reader at the time of the events in question would have understood the law to be . . . .” It’s hard to see how such a form of Originalism withstands scrutiny. -/- First, using “reasonable reader” understandings rather than speaker meaning turns language and law on their heads. Audiences effectively become (...) the speakers in ordinary speech (since reader or audience meaning prevails), and audiences (and thus the ruled) effectively become the rulers when interpreting law (since audiences’ meaning prevails). -/- Second, since laws look forward to govern conduct, how can best legal practices keep such a backward focus? -/- Third, words (however understood by others at the time “originally” uttered) may or may not (depending on speaker and not reader meaning) signify concepts whose meanings embrace change over time. For example, the word “planet” used by a speaker before the discovery of Uranus and Neptune may or may not include further planets depending upon what the speaker meant by “planet.” (The same applies to the inclusion or exclusion of Pluto had the speaker used the word “planet” after the discovery of Pluto but before its exclusion by current science.) Unlike the “reasonable” reader of Gorsuch’s Originalism as phrased above, speakers run the gamut from reasonable to unreasonable, from informed to uninformed, and from thoughtful to thoughtless. -/- Fourth, to the extent a judge is principally “constrained” by a text or texts (as he may determine), by dictionaries that he chooses, and by “history” as the judge understands it, isn’t judicial activism encouraged rather than restrained? Talk of a “reasonable” reader masks the fact that there can be multiple “reasonable” conclusions of what a reasonable or unreasonable speaker meant. Is a judge not therefore left to pick definitions and applications of terms that accord with the judge’s understandings of history, understandings that may well be colored by the judge’s politics and judicial philosophy? This applies to principles as well as labels for things. Principles are also subject to multiple frames, and their terms are subject to multiple definitions therefore raising the very same questions just raised above. -/- Finally, such Originalism doesn’t merely fail with legal texts. It also fails when applied to other texts (including sacred texts such as the Ten Commandments) and when used to interpret art (such as “Landscape with the Fall of Icarus” often attributed to Bruegel and which inspired such great ekphrasis as Auden’s “Musée Des Beaux Arts”). These further failures underscore the dysfunction of Originalism in Gorsuch's form noted above. -/- Keywords: Originalism, Neil Gorsuch, Text, Textualism, Scalia, Interpretation, Pragmatics, Speaker Meaning, Art, Painting, Bruegel, Auden, Ekphrasis, Icarus, Bible, Ten Commandments, Herod, Declaration of Independence, Abraham Lincoln. (shrink)

As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1,. 2, 2022), Our universe is but one page in a large book [4]. For example, things and Beings can travel between Universes, intentionally or unintentionally. In this short remark, we revisit and offer short remark to Neil’s ideas and trying to connect them with geometrization of musical chords as presented by D. Tymoczko and others, then to Escher staircase and then to Jacob’s (...) ladder which seems to point to possibility to interpret Jacob’s vision as described in the ancient book of Genesis as inter dimensional or heavenly staircase, e.g. an inter dimensional bridge between heaven and earth (see also classic book: Hofstadter, Godel, Escher, Bach). Jacob’s vision of angels going down to earth from that staircase has been depicted for instance in William Blake art etc. In our communication with others via physics literature and discussions etc, we came to several conclusions as follows: Firstly, possibility of quantum wormhole effect to mirror particle universe, which sometimes it is termed non-orientable wormhole. While such mirror particles effect have been more than 50 years predicted with the so-called parity violation (cf. Lee & Yang, 1950s), and that is called symmetry breaking. Secondly, a series of extended experiments on laser irradiated cold water may suggest possible transition from a phase of water to be at least partially fourth phase of water, which may be composed of crystalline water (see e.g. Gerald Pollack, and also Harold Aspden on liquid crystalline). If we can imagine laser cooling effect can be done in protracted time, then we can achieve a physical representation of Aspden’s liquid crystalline. Therefore, in subsequent article (Part II) we outlined simple model of such an effect of tunneling via quantum liquid crystalline Universe, which may likely be modeled with iced-water. It is interesting to remark here that certain experiments by Stockholm University scientists have shown that X-ray triggered water can exhibit properties just like liquid crystal (cf. PRL, 2020). That is why we consider it possible that there can be quantum phase transition where liquid water (comprised of iced cubes and water) can exhibit effects such as tunneling in quantum liquid crystalline Universe. Last but not least, we admit that what we outlined here is just an initial phase; and if you wish, perhaps we can call such experiments as “wormhole-at-lab” experiments (abbreviated: WHALE). (shrink)

The present article was partly inspired by G. Pollack’s book, and also Dadoloff, Saxena & Jensen (2010). As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1, No. 2, 2022), for example, things and Beings can travel between Universes, intentionally or unintentionally [4]. In this short remark, we revisit and offer short remark to Neil Boyd’s ideas and trying to connect them with geometry of musical chords as presented by D. Tymoczko and (...) others, then to Escherian staircase and then to Jacob’s ladder which seems to pointto possibility to interpret Jacob’s vision as described in the ancient book of Genesis as interdimensional staircase, e.g. an interdimensional bridge between heaven and earth (cf. classic book: Hofstadter, Godel, Escher, Bach). Jacob’s vision of angels going down to earth from that staircase has been depicted for instance in William Blake art etc. In our communication with others via physics literature and discussions etc, we came to several conclusions as follows: Firstly, possibility of wormhole effect to mirror particle universe, which sometimes it is termed non-orientable wormhole. While such mirror particles effect have been more than 50 years predicted with the so-called parity violation (cf. Lee & Yang, 1950s), and that is called symmetry breaking. Secondly, a series of extended experiments on laser irradiated cold water may suggest possible transition from a phase of water to be at least partially fourth phase of water, which may be composed of crystalline water (see e.g. Gerald Pollack, and also Harold Aspden on liquid crystalline). If we can imagine laser cooling effect can be done in protracted time, then we can achieve a physical representation of Aspden‘s liquid crystalline. Therefore, in this article we outline a series of simple experiments of laser irradiated iced-water along with beryl and selenite crystals in order to see possibility of such a quantum tunneling via quantum liquid crystalline Universe hypothesis, which may likely be modeled with iced-water. It is interesting to remark here that certain experiments by Stockholm University scientists have shown that X-ray triggered water can exhibit properties just like liquid crystal (cf. PRL, 2020). That is why we consider it possible that there can be quantum phase transition where liquid water (comprised of iced cubes and water) can exhibit effects such as tunneling in quantum liquid crystalline Universe. Last but not least, we admit that what we outlined here is just aninitial phase; and if you wish, perhaps we can call such experiments as “wormhole-at-lab” experiments (abbreviated: WHALE). (shrink)

Early modern automata, understood as efforts to ‘model’ life, to grasp its singular properties and/or to unveil and demystify its seeming inaccessibility and mystery, are not just fascinating liminal, boundary, hybrid, crossover or go-between objects, while they are all of those of course. They also pose a direct challenge to some of our common conceptions about mechanism and embodiment. They challenge the simplicity of the distinction between a purported ‘mechanistic’ worldpicture, its ontology and its goals, and on the other hand (...) an attempt to understand ourselves and animals more broadly as flesh-and-blood, affective entities (that is, not just breathing and perspiring, but also desiring and ‘sanguine’ machines, as La Mettrie might have put it). In what follows I reflect on the complexity of early modern mechanism faced with the (living) body, and its mirror image, contemporary theories of embodiment. At times, embodiment theory seems to be governed by a fascination with what the Artificial Life researcher Ezequiel Di Paolo has called ‘biochauvinism’ (Di Paolo, “Extended Life”): an unquestioned belief that ‘living bodies are special’. Yet how does the theorist define this special status? The question is apparently a simple one, or at least promptly yields an aporia which appears simple: to borrow a provocative phrase from Terry Eagleton, embodiment theory is obsessed by the body but terrified of biology. Yet at the same time, at least since Hubert Dreyfus and Andy Clark’s groundbreaking works, embodiment has been a legit part of cognitive science, yielding the even more recently emerged field of ‘embodied cognition’ (see the work of Larry Shapiro), which seeks to depart from traditional cognitive science, especially the latter’s understanding of cognition as computational, in order to instead underscore “the significance of an organism’s body in how and what the organism thinks,” in Shapiro’s words. (shrink)

Jaegwon Kim’s supervenience/exclusion argument attempts to show that non-reductive physicalism is incompatible with mental causation. This influential argument can be seen as relying on the following principle, which I call “the piggyback principle”: If, with respect to an effect, E, an instance of a supervenient property, A, has no causal powers over and above, or in addition to, those had by its supervenience base, B, then the instance of A does not cause E (unless A is identical with B). In (...) their “Epiphenomenalism: The Dos and the Don’ts,” Larry Shapiro and Elliott Sober employ a novel empirical approach to challenge the piggyback principle. Their empirical approach pulls from the experiments of August Weismann regarding the inheritance of acquired characteristics. Through an examination of Weismann’s experiments, Shapiro and Sober extract lessons in reasoning about the epiphenomenalism of a property. And according to these empirically drawn lessons, the piggyback principle is a don’t. My primary aim in this paper is to defend the piggyback principle against Shapiro and Sober’s empirical approach. (shrink)

Rooted in the heart of Vygotsky’s Sociocultural Theory, mediation has recently received considerable attention in the field of TEFL. The existing literature suggests that mediation can play an essential role in language learners’ performance development. In addition, learners need to know about their thinking process which is interpreted as metacognition. This study aimed to investigate the effect of teacher- and peer-assisted evaluative mediation on learners’ metacognitive awareness development. To this end, 40 homogenized intermediate EFL learners were selected using a test (...) of English language proficiency. The participants were then randomly divided into teacher-assisted (n=20) and peer-assisted (n=20) groups. Before the instructional phase, a metacognitive awareness questionnaire was given to the participants. At the instructional phase, the learners in the teacher-assisted group received teacher-assisted mediation. The learners in the peer-assisted group, however, were exposed to mediation provided by their peers. After the instructional phase, the metacognitive awareness questionnaire was given to the participants as the posttest of the study. SPSS was used to analyze the data. The descriptive statistics, the Shapiro-Wilk test of normality, and the Paired Sample T-test for inferential statistics were used to analyze the data. The findings showed that peer-assisted evaluative mediation had positive effects on developing students’ level of metacognitive awareness, whereas teacher-assisted evaluative mediation did not reveal such effects. It could be concluded that peer-assisted evaluative mediation is an effective tool for improving students’ metacognitive awareness. (shrink)

Wittgenstein's lack of sympathy for Shakespeare's works has been well noted by George Steiner and Harold Bloom among others. Wittgenstein writes in 1950, for instance: "It seems to me as though his pieces are, as it were, enormous sketches, not paintings; as though they were dashed off by someone who could permit himself anything, so to speak. And I understand how someone may admire this & call it supreme art, but I don't like it." Of course, the animosity of (...) one great mind for another has its own interest. But the interest here is increased by two factors: (1) Wittgenstein's brief but specific critique of Shakespeare's similes, of interest particularly since he identifies his own philosophical strength half-deprecatingly but still seriously as one of crafting beautiful similes; and (2) Wittgenstein's and Shakespeare's shared concern, as revealed in Stanley Cavell's writings, with the human impulse to skepticism. The present paper considers the importance of these two factors in weighing Wittgenstein's judgment. It suggests that Wittgenstein's frequent charge that Shakespeare is "completely unrealistic" is not a misunderstanding of the Bard (Wittgenstein distinguishes his "failure to understand" from others' willingness to misunderstand Shakespeare) but rather an expression of Wittgenstein's anxiety over Shakespeare's wholly original use of language to represent the sound of the raw motives to skepticism. (shrink)

Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. -/- ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, scope, Tarski (Alfred), tautology, universe of discourse. -/- The entire work is available online free at more than (...) one website. Paste the whole URL. http://archive.org/stream/RobertiAudi_The.Cambridge.Dictionary.of.Philosophy/Robert.Audi_The.Cambrid ge.Dictionary.of.Philosophy -/- The 2015 third edition will be available soon. Before you think of buying it read some reviews on Amazon and read reviews of its competition: For example, my review of the 2008 Oxford Companion to Philosophy, History and Philosophy of Logic,29:3,291-292. URL: http://dx.doi.org/10.1080/01445340701300429 -/- Some of the entries have already been found to be flawed. For example, Tarski’s expression ‘materially adequate’ was misinterpreted in at least one article and it was misused in another where ‘materially correct’ should have been used. The discussion provides an opportunity to bring more flaws to light. -/- Acknowledgements: Each of these entries was presented at meetings of The Buffalo Logic Dictionary Project sponsored by The Buffalo Logic Colloquium. The members of the colloquium read drafts before the meetings and were generous with corrections, objections, and suggestions. Usually one 90-minute meeting was devoted to one entry although in some cases, for example, “axiomatic method”, took more than one meeting. Moreover, about half of the entries are rewrites of similarly named entries in the 1995 first edition. Besides the help received from people in Buffalo, help from elsewhere was received by email. We gratefully acknowledge the following: José Miguel Sagüillo, John Zeis, Stewart Shapiro, Davis Plache, Joseph Ernst, Richard Hull, Concha Martinez, Laura Arcila, James Gasser, Barry Smith, Randall Dipert, Stanley Ziewacz, Gerald Rising, Leonard Jacuzzo, George Boger, William Demopolous, David Hitchcock, John Dawson, Daniel Halpern, William Lawvere, John Kearns, Ky Herreid, Nicolas Goodman, William Parry, Charles Lambros, Harvey Friedman, George Weaver, Hughes Leblanc, James Munz, Herbert Bohnert, Robert Tragesser, David Levin, Sriram Nambiar, and others. -/- . (shrink)

1 Context The idea for the current issue of _Philosophia Scientiæ_ emerged from discussions which took place in the Manchester Ethnomethodology Reading Group. This reading group has its origins in Wes Sharrock’s weekly discussion groups, which have taken place in Manchester (UK) since the early 1970s. As the global Covid-19 pandemic hit in early 2020, the reading group moved online, facilitated by Phil Hutchinson and Alex Holder. Being an online reading group opened up participation to people beyond Northwest UK and (...) within weeks the group became global, with the membership including participants logging on from Canada, Czech Republic, Finland, France, Germany, Greece, Hong Kong, Japan, Macau, New Zealand, Spain, Sweden, and the USA. While the name of the group might indicate an exclusive focus on ethnomethodology, following the naming conventions for academic discussion groups, the name really fails to indicate both the heterogeneity of the group’s reading materials, the interests of t... (shrink)

The field of textbooks in philosophy of mind is a crowded one. I shall consider six recent texts for their pedagogical usefulness. All have been published within the last five years, though two are new editions of previously published books. The first three are authored monographs: by K. T. Maslin, Barbara Montero, and André Kukla and Joel Walmsley. I then review three anthologies, each with two editors: William Lycan and Jesse Prinz, Brie Gertler and Lawrence Shapiro, and Brian McLaughlin (...) and Jonathan Cohen. These six texts constitute a diverse bunch. Within each of the two groups (monographs and anthologies), each individual text differs significantly from the other two in its approach, scope, and thus suitability for various levels of teaching. (shrink)

Hofweber (Ontology and the ambitions of metaphysics, Oxford University Press, 2016) argues for a thesis he calls “internalism” with respect to natural number discourse: no expressions purporting to refer to natural numbers in fact refer, and no apparent quantification over natural numbers actually involves quantification over natural numbers as objects. He argues that while internalism leaves open the question of whether other kinds of abstracta exist, it precludes the existence of natural numbers, thus establishing what he calls “restricted nominalism” about (...) natural numbers. We argue that Hofweber’s internalism fails to establish restricted nominalism. Not only is his primary argument for restricted nominalism invalid, the analysis of quantification proposed threatens to collapse internalism into either a traditional form of error theory or realism. (shrink)

What responsibilities do audiences have in engaging with artworks? Certain audience responses seem quite clear: for example, audiences should not vandalize or destroy artworks; they should not disrupt performances. This paper examines other kinds of resisting responses that audiences sometimes engage in, including petitioning the artist to change their works, altering copies of artworks, and creating new artworks in another artist’s fictional world. I argue for five claims: (1) while these actions can sometimes infringe on the rights of artists, the (...) rights of artists are not absolute; (2) the fact that such actions are based on mistaken interpretations of the artworks has no normative weight; (3) there can be reason to object to additions and alterations whose conception of the artwork is morally worse than the original (and so, there can be reason to support additions and alterations whose conception is morally better); (4) petitioning raises special moral problems; and, most important, (5) some of these actions are valuable because they involve creative and aesthetic activity. Those acts of audience resistance that are creative, morally improve on the original work, and that minimize the infringement of the artists’ rights are good, and should be encouraged. (shrink)

According to traditional logical expressivism, logical operators allow speakers to explicitly endorse claims that are already implicitly endorsed in their discursive practice — endorsed in virtue of that practice’s having instituted certain logical relations. Here, I propose a different version of logical expressivism, according to which the expressive role of logical operators is explained without invoking logical relations at all, but instead in terms of the expression of discursive-practical attitudes. In defense of this alternative, I present a deflationary account of (...) the expressive role of vocabulary by which we ascribe logical relations. (shrink)

In this volume, leading philosophers of psychiatry examine psychiatric classification systems, including the Diagnostic and Statistical Manual of Mental Disorders, asking whether current systems are sufficient for effective diagnosis, treatment, and research. Doing so, they take up the question of whether mental disorders are natural kinds, grounded in something in the outside world. Psychiatric categories based on natural kinds should group phenomena in such a way that they are subject to the same type of causal explanations and respond similarly to (...) the same type of causal interventions. When these categories do not evince such groupings, there is reason to revise existing classifications. The contributors all question current psychiatric classifications systems and the assumptions on which they are based. They differ, however, as to why and to what extent the categories are inadequate and how to address the problem. Topics discussed include taxometric methods for identifying natural kinds, the error and bias inherent in DSM categories, and the complexities involved in classifying such specific mental disorders as "oppositional defiance disorder" and pathological gambling. -/- Contributors George Graham, Nick Haslam, Allan Horwitz, Harold Kincaid, Dominic Murphy, Jeffrey Poland, Nancy Nyquist Potter, Don Ross, Dan Stein, Jacqueline Sullivan, Serife Tekin, Peter Zachar. (shrink)

Contrary to economics or history, for example, there does not exist an organized field dedicated to the philosophy of political science. Given that the philosophical issues raised by political science research are just as pressing and vibrant as those raised in these more organized fields, fostering a field that labels itself Philosophy of Political Science (PoPS) is important. PoPS is advanced here as a fruitful meeting place where both philosophers and practicing political scientists contribute and discuss—with philosophical discussions that are (...) close to and informed by actual developments in political science, making philosophy of science continuous with the sciences in line with contemporary naturalist philosophy of science. The topics scrutinized in the different chapters of the Handbook will figure prominently in PoPS, as we lay out in this chapter. (shrink)

Successful athletic performance requires precision in many respects. A batter stands behind home plate awaiting the arrival of a ball that is less than three inches in diameter and moving close to 100 mph. His goal is to hit it with a ba­­t that is also less than three inches in diameter. This impressive feat requires extraordinary temporal and spatial coordination. The sweet spot of the bat must be at the same place, at the same time, as the ball. A (...) basketball player must keep a ball bouncing as she speeds from one end of the court to another, evading defensive players. She may never break pace as she lifts from the ground, throwing the ball fifteen feet toward a hoop that is eighteen inches in diameter. One task facing a psychologist involves explaining how the body does such things within the sometimes very demanding spatial and temporal constraints that a given task imposes. Part of the goal of this chapter is to sketch the commitments of an embodied approach to such an explanation. We shall see that an embodied account of motor skills draws concepts that depart radically from more traditional cognitivist theories of motor activity. Similarly, because an embodied approach to cognition introduces new ways to understand the human capacity for social interaction, it also promises to shed new light on how athletes coordinate their actions with each other. (shrink)

Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.

This article tackles the sole surviving ancient commentary on what was perhaps the second most important Platonic work, with special interest for the manner in which the ancients tackled the setting of Plato's dialogues, Socratic ignorance, Socratic eros, the central myth-like Palinode, and the question of oral as against written teaching.

SNePS, the Semantic Network Processing System 45, 54], has been designed to be a system for representing the beliefs of a natural-language-using intelligent system (a \cognitive agent"). It has always been the intention that a SNePS-based \knowledge base" would ultimatelybe built, not by a programmeror knowledge engineer entering representations of knowledge in some formallanguage or data entry system, but by a human informing it using a natural language (NL) (generally supposed to be English), or by the system reading books or (...) articles that had been prepared for human readers. Because of this motivation, the criteria for the development of SNePS have included: it should be able to represent anything and everything expressible in NL; it should be able to represent generic, as well as speci c information; it should be able to use the generic and the speci c information to reason and infer information implied by what it has been told; it cannot count on any particular order among the pieces of information it is given; it must continue to act reasonably even if the information it is given includes circular de nitions, recursive rules, and inconsistent information. (shrink)

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between (...) the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects. (shrink)

This chapter first seeks to identify Huw Price's reasons for holding that "object naturalism" can be undermined by "subject-naturalistic" inquiry. It then addresses five questions about how his project bears on the prospects for a liberal naturalism. (1) Does Price’s strategy depend on his requirement that the relevant inquiry into human discourse and thought be conducted in natural-scientific terms? (2) Is Price’s strategy even compatible with that requirement? (3) Does the worldview Price arrives at amount to a liberal naturalism, i.e. (...) a naturalism that could be obtained by relaxing a more restrictive version? (4) Is Price’s strategy consistent with a liberal naturalism? (5) Should a proponent of Price’s strategy accept a liberal naturalism? (shrink)

Cognitive agents, whether human or computer, that engage in natural-language discourse and that have beliefs about the beliefs of other cognitive agents must be able to represent objects the way they believe them to be and the way they believe others believe them to be. They must be able to represent other cognitive agents both as objects of beliefs and as agents of beliefs. They must be able to represent their own beliefs, and they must be able to represent beliefs (...) as objects of beliefs. These requirements raise questions about the number of tokens of the belief representation language needed to represent believers and propositions in their normal roles and in their roles as objects of beliefs. In this paper, we explicate the relations among nodes, mental tokens, concepts, actual objects, concepts in the belief spaces of an agent and the agent's model of other agents, concepts of other cognitive agents, and propositions. We extend, deepen, and clarify our theory of intensional knowledge representation for natural-language processing, as presented in previous papers and in light of objections raised by others. The essential claim is that tokens in a knowledge-representation system represent only intensions and not extensions. We are pursuing this investigation by building CASSIE, a computer model of a cognitive agent and, to the extent she works, a cognitive agent herself. CASSIE's mind is implemented in the SNePS knowledge-representation and reasoning system. (shrink)