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In I Taking Frege at his Word i , Joan Weiner proposes a wide-ranging re-thinking of Frege's philosophical and mathematical projects. First, much of the discussion of Frege's semantic arguments (or, according to Weiner, lack thereof) in Chapters 4 and 5 (and elsewhere) focuses on whether or not Frege gave I metatheoretical i arguments in I Begriffsschrift i , I Grundgesetze i , and elsewhere. The book concludes with two chapters which focus on fruitful applications of Frege's ideas (on Weiner's understanding of them). [Extracted from the article]

Carl Posy's I Mathematical Intuitionism i is an installment in the increasingly impressive Cambridge Elements in the Philosophy of Math series, edited by Penelope Rush and Stewart Shapiro. Posy motivates the development of intuitionistic logic (of which Brouwer disapproved) as follows: Brouwer doggedly refused to adopt even the simplest logical notation. Posy begins with the observation that, for Brouwer, mathematics is concerned with the construction of mathematical objects in pure intuition, and, as a result, intuitionistic mathematics is synthetic I a priori i (the influence of Kant is of course clear here). [Extracted from the article]

The Embracing Revenge account of semantic paradox avoids the expressive limitations of previous approaches based on the Kripkean fixed point construction by replacing a single language with an indefinitely extensible sequence of languages, each of which contains the resources to fully characterize the semantics of the previous languages. In this paper we extend the account developed in Cook (2008), Cook (2009), Schlenker (2010), and Tourville and Cook (2016) via the addition of intensional operators such as ''is paradoxical''. In this extended framework we are able to characterize the difference between sentences, such as the Liar and the Truth-teller, that receive the same semantic value in minimal fixed points yet seem to involve distinct semantic phenomena. [ABSTRACT FROM AUTHOR]

Robert 'Bob' Hale died on December 12, 2017, after a long bout with cancer. At the time, he was Emeritus Professor of Philosophy at Sheffield University. Prior to that he was Professor of Metaphysical Philosophy at the University of Glasgow, and earlier Reader at the University of St Andrews and Lecturer at the University of Lancaster. He was a British Academy Research Reader (1997–1999), President of the Aristotelian Society (2002–2003), Leverhulme Senior Research Fellow (2009–2011), and was elected fellow of the Royal Society of Edinburgh in 2000. He served on the editorial board of this journal. Hale's philosophical work focused on the metaphysics and epistemology of modality, the philosophy of logic, Gottlob Frege, and the abstractionist, neo-logicist foundation for mathematics. His interests were as broad as the work was deep, and we will not be able to cover all of his contributions here. Given the venue within which this essay is appearing, we will focus on his contributions to the philosophy of mathematics. It happens, however, that Hale's work on modality is not as far removed from his work on neo-logicism as it might first appear. [ABSTRACT FROM AUTHOR]

Fine and Antonelli introduce two generalizations of permutation invariance -- internal invariance and simple/double invariance respectively. After sketching reasons why a solution to the Bad Company problem might require that abstraction principles be invariant in one or both senses, I identify the most finegrained abstraction principle that is invariant in each sense. Hume's Principle is the most fine-grained abstraction principle invariant in both senses. I conclude by suggesting that this partially explains the success of Hume's Principle, and the comparative lack of success in reconstructing areas of mathematics other than arithmetic based on non-invariant abstraction principles. [ABSTRACT FROM AUTHOR]

Gottlob Frege defined cardinal numbers in terms of value-ranges governed by the inconsistent Basic Law V. Neo-logicists have revived something like Frege's original project by introducing cardinal numbers as primitive objects, governed by Hume's Principle. A neo-logicist foundation for set theory, however, requires a consistent theory of value-ranges of some sort. Thus, it is natural to ask whether we can reconstruct the cardinal numbers by retaining Frege's definition and adopting an alternative consistent principle governing value-ranges. Given some natural assumptions regarding what an acceptable neo-logicistic theory of value-ranges might look like, successfully implementing this alternative approach is impossible. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including concept of mathematics in arithmetic and analysis, the laws of arithmetic and philosophy of mathematics.

ABSTRACT Comics comprise a hybrid art form descended from printmaking and mostly made using print technologies. But comics are an art form in their own right and do not belong to the art form of printmaking. We explore some features art comics and fine art prints do and do not have in common. Although most fine art prints and comics are multiple artworks, it is not obvious whether the multiple instances of comics and prints are (or can be) artworks in their own right. The comparison of comics and fine art prints provides a promising test for assessing how hybrid art forms develop more generally, and for assessing how they differ from closely related nonhybrid cousins. [ABSTRACT FROM AUTHOR]

An essay is presented on the practice of separating serialized fiction into canonical and noncanonical subtexts. It offers an examination of "massive serialized collaborative fiction" such as the film series "Star Wars" and the distinction between the canonical and noncanonical divide The author goes on to determine the practical and pragmatic reasons for drawing distinctions between canonical and noncanonical subtexts as well as the philosophically substantial reasons.

It is shown that the logical truth of instances of the T-schema is incompatible with the formal nature of logical truth. In particular, since the formality of logical truth entails that the set of logical truths is closed under substitution, the logical truth of T-schema instances entails that all sentences are logical truths. [ABSTRACT FROM PUBLISHER]

The article discusses the depiction of photographs in comics, suggesting that they are often depicted in a more realistic manner than the other parts of the comic. The author focuses on the idea that photographs are more objective in their representation than other visual art forms and examines possible explanations for the phenomenon of the depiction of photographs in comics. Specific topics include theories of the objective purport of photographs, the objective purport of fictional photographs in comics, and the panel transparency principle in the depiction of characters in comics. Specific comics discussed include "When Is a Door?" by Neil Gaiman and "Fun Home" by Allison Bechdel.

The article examines the philosophical and aesthetic problems related to the issue of defining comics, focusing on the question on an analysis of the assumption that comics must contain pictures to be defined as such. The author's discussion is grounded in the books "The Comics," by Coulton Waugh and "Understanding Comics," by Scott McCloud which argue for the necessity of pictures in comics, a view named the pictorial thesis by the author. Topics include an analysis of Gary Larson's comics with a view of the proposition that pictures contain nothing, a thought experiment based on "Batman #663," written by Grant Morrison and drawn by John van Fleet, and the mereology of comics.

A difficulty for alethic pluralism has been the idea that semantic evaluation of conjunctions whose conjuncts come from discourses with distinct truth properties requires a third notion of truth which applies to both of the original discourses. But this line of reasoning does not entail that there exists a single generic truth property that applies to all statements and all discourses, unless it is supplemented with additional, controversial, premises. So the problem of mixed conjunctions, while highlighting other aspects of alethic pluralism worth investigating further, does not constitute an effective objection to it. [ABSTRACT FROM AUTHOR]

The article discusses the liar paradox and its several variations that were established in the literature on semantic paradox, particularly the Curry paradox and the Yablo paradox. It also explores the Dual Yablurry paradox, as well as the Yablurry paradox simpliciter as types of the Curry-style Yabloesque paradox. It cites that the Liar paradox is a direct self-referential Liar statement.

The article discusses the implications of the truth-theoretic paradox of Stephen Yablo, a professor of the Department of Linguistics and Philosophy. The infinite series of sentences of Yablo's Paradox is also presented. It is stated that the paradox being discussed by Yablo provides a blueprint for constructing a paradox which is non-circular in strong and weak senses. The predicate is a weak predicate fixed point of the relation where it involves a certain sort of circularity.

The article analyzes whether truth can be known in a less constructive way in connection to the puzzle occurring on Raymond Smullyan's island of knights and knaves, the home to two tribes who lend their names to the island. The first tribe, the knights, always tell the truth, while the knaves, always lie. Then, there is a stranger who came across three natives of the island and the three natives make utterances. In conclusion, it it is possible that three beings, each of whom is either an unfailing truth-teller or an unfailing liar, could make utterances, then there are unknowable truths.

Replies to comments on an article examining the revision theory of truth which has counterintuitive consequences. Validity of the proof; Exhibition of a form of circular dependence such that the assignment of truth values cannot be justified in a non-question-begging manner.

Stewart Shapiro and Alan Weir have argued that a crucial part of the demonstration of Frege's Theorem (specifically, that Hume's Principle implies that there are infinitely many objects) fails if the Neo-logicist cannot assume the existence of the empty property, i.e., is restricted to so-called Aristotelian Logic. Nevertheless, even in the context of Aristotelian Logic, Hume's Principle implies much of the content of Peano Arithmetic. In addition, their results do not constitute an objection to Neo-logicism so much as a clarification regarding the view of logic that the Neo-logicist must take. [ABSTRACT FROM PUBLISHER]

Focuses on the adoption of mathematical precision in providing formal semantics for languages. Formalization of relevant natural languages; Greatest advantages of formal semantics; Distinction between representor and artifacts.

Points out the counterintuitive consequences of the Revision Theory of Truth. Details of the Revision Theory of Truth; Advantage of the theory in the treatment of self-referential sentences with a truth predicate; Formal correctness and material adequacy in the judgment of philosophical analyses.

Examines the use of the differing treatments of negation in tracing the differences between intuitionistic logic and its classical counterpart. Intuitionistic failures in double negation elimination and classical reductio ad absurdum; Definition and rules formulated in negation; Ways of handling intuitionistic negation.

The article looks at the paradox of adverb, which is being defined as a linguistic item that expresses a second-level concept that applies to first-level concepts. It presents an argument of the application of adverb and its correlation with adjective. It is noted that the adverb used in the article is equivalent to second-level predicate within higher-order logic.

The article discusses how Finch's paradox regarding the knowability of truth relates to anti-realism and Cartesian statements. The author suggests the knowability principle should be applied only to Cartesian concepts. The author presents proofs that introduce negation but notes statements by philosopher Neil Tennant regarding the difficulty in determining Cartesian truths.