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123698.354889
In the course of presenting his own solution to the insolubles (logical paradoxes such as the Liar), Marsilius of Inghen criticises four earlier theories, which appear to be those of Albert of Saxony, (the early) Buridan, Roger Swyneshed and a modification of William Heytesbury’s solution which we find in many textbooks and anonymous treatises known as presentations of the Logica Oxoniensis. Marsilius’s solution bears interesting resemblances to all four, but has its own distinctive features. The core idea of his solution is that all propositions have a two-fold signification, a material signification and a formal one. The material signification, also called the primary or direct signification, is what most would call the proposition’s usual signification; e.g., the material signification of ‘This proposition is false’ is that that proposition is false. Its formal, aka indirect or reflexive, signification is, in the case of affirmative propositions, that the subject and predicate supposit for the same thing, and in the case of negative propositions, that they do not. This reflexive signification derives from the meaning of the (affirmative resp. negative) copula. Thus the reflexive signification of ‘This proposition is false’ is that ‘this proposition’ and ‘false’ supposit for the same thing, that is, that it is false that that proposition is false. Presenting Marsilius’s formal signification in such cases as stating of that proposition’s being false, for example (which is the material signification of ‘This proposition is false’), that it is false (that is, falls under the supposition of ‘false’) suggested to Paul Spade that Marsilius’s solution was a development of Gregory of Rimini’s account. I will argue that any resemblance here is, in the absence of any external evidence, superficial and coincidental, and that Marsilius’s view is much closer to the Oxford solutions and Albert’s—Albert and Marsilius being, after all, members of the English Nation at Paris. Marsilius’s arguments in favour of his theory, and his application of the solution to a range of insolubles, are well worth looking at in detail, which I will do, though not at the length which Marsilius devotes to it.
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123720.355001
Paul Vincent Spade contrasts the calm and measured reaction of medieval thinkers to the “insolubles” (logical paradoxes such as the Liar) with the troubled response of philosophers and mathematical logicians more recently to the semantic antinomies in modern logic and set theory. The latter is often described as a crisis in the foundations of mathematics. But there was a comparable crisis in medieval philosophy and theology, namely over the apparent incompatibility of the newly rediscovered Aristotelian logic and Christian theology, specifically in the latter’s doctrine of the Trinity. According to that doctrine, codified at the fourth Lateran Council in 1215, God is undivided in his essence but distinct according to the properties of the three persons. This appears to open the faithful to heresy through the following expository syllogism: Haec essentia est filius Haec essentia est pater Ergo pater est filius, contradicting the distinctness of the Son and the Father. The paralogism can also be formulated as a first-figure syllogism in Darii as follows: Omnis deus est pater Filius in divinis est deus Igitur Filius in divinis est pater.
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297924.355018
This chapter reviews empirical research on the rules governing assertion and retraction, with a focus on the normative role of truth. It examines whether truth is required for an assertion to be considered permissible, and whether there is an expectation that speakers retract statements that turn out to be false. Contrary to factive norms (such as the influential “knowledge norm”), empirical data suggests that there is no expectation that speakers only make true assertions. Additionally, contrary to truth-relativist accounts, there is no requirement for speakers to retract statements that are false at the context of assessment. We conclude by suggesting that truth still plays a crucial role in the evaluation of assertions: as a standard for evaluating their success, rather than permissibility.
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672951.35503
Kennedy (Linguist Philos 30:1–45, 2007) forcefully proposes what is now a widely assumed semantics for absolute gradable adjectives. On this semantics, maximum standard adjectives like “straight” and “dry” ascribe a maximal degree of the underlying quantity. Meanwhile, minimum standard adjectives like “bent” and “wet” merely ascribe a non-zero, non-minimal degree of the underlying quantity. This theory clashes with the ordinary intuition that sentences like “The stick is straight” are frequently true while sentences like “The stick is bent” are frequently informative, and fans of the indicated theory of absolute gradable adjectives appeal to loose talk in response. One goal of this paper is to show that all extant theories of loose talk are inconsistent with this response strategy. Another goal is to offer a revised version of Hoek’s (Philos Rev 127:151–196, 2018, in: Proceedings of the 22nd Amsterdam Colloquium, 2019) recent theory of loose talk that accommodates absolute gradable adjectives after all, while being defensible against a range of important concerns.
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730523.355041
Discourse involving predicates of personal taste (PPT) such as ‘delicious,’ ‘disgusting,’ ‘fun,’ and ‘cool’ has been a focal point in a large, interdisciplinary body of research spanning the past 20 years. This research has shown that PPT are connected to numerous topics, including disagreement, meaning, context-sensitivity, subjectivity and objectivity, truth, aesthetic and gustatory taste, evaluation, speech acts, and so on. Researchers involved in the PPT debates have developed many subtle and inventive analyses of PPT, so that anyone interested in their behaviour must traverse a complex theoretical landscape. Despite the massive amount of work on the topic, there is a crucial methodological question about PPT that remains underexplored: what sorts of evidence should be called upon to evaluate an analysis of PPT? So far, most researchers have operated from the armchair, using their own intuitions about various linguistic phenomena to evaluate analyses of PPT. In recent years, however, certain philosophers and linguists have found this method wanting, noting that hypotheses about PPT are empirical, and thus need to be evaluated empirically.
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1207963.355052
There is a strikingly rich array of messages that Alphie could, given the right background conditions, communicate to Betty by means of this utterance. For a few examples among many, consider (1)-(26). 1. Carrie will be in the ballroom of the Palmer House Hilton at 1:05pm. 2. Alphie believes that Carrie will be in the ballroom of the Palmer House Hilton at 1:05pm. 3. Alphie has compelling evidence that Carrie will be in the ballroom of the Palmer House Hilton at 1:05pm. 4. Whether Carrie will be in the ballroom of the Palmer House Hilton at 1:05pm is relevant for the purposes of Alphie and Betty’s conversation. 5. Alphie believes that Betty didn’t already know that Carrie will be in the ballroom of the Palmer House Hilton at 1:05pm. 6. Carrie is not presently in the ballroom of the Palmer House Hilton. 7. Carrie will be able to give her talk. 8. Carrie will be late for her talk. 9. Carrie is not in San Francisco. 10. Betty should stall, rather than canceling the session and asking everybody to leave the ballroom. 11. Alphie believes that whether Carrie will be in the ballroom of the Palmer House Hilton at 1:05pm is relevant for the purposes of Alphie and Betty’s conversation.
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1625824.355069
The aim of this paper is to present a constructive solution to Frege’s puzzle (largely limited to the mathematical context) based on type theory. Two ways in which an equality statement may be said to have cognitive significance are distinguished. One concerns the mode of presentation of the equality, the other its mode of proof. Frege’s distinction between sense and reference, which emphasizes the former aspect, cannot adequately explain the cognitive significance of equality statements unless a clear identity criterion for senses is provided. It is argued that providing a solution based on proofs is more satisfactory from the standpoint of constructive semantics.
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1708615.35508
Let’s start with some uncontroversial facts. In 1817–1818, Beethoven composed the Piano Sonata No. 29 in B flat major, Opus 106, which is known as the Hammerklavier Sonata. In 1970, Glenn Gould performed the Hammerklavier in Toronto. In 1995, András Schiff performed the Hammerklavier in New York. We can conclude that there is something— the Hammerklavier—that Beethoven composed and that Gould and Schiff performed. But what sort of thing is this?
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1798990.35509
We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods of functional decomposition, but reduces relations only to ternary relations. An additional construction then decomposes ternary into binary relations, also effectively, by converting certain disjunctions into existential quantifications. The result gives a uniform proof of Peirce’s reduction thesis on finite domains, and shows that the graph of any Sheffer function composes all relations there.
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1799059.3551
We argue that traditional formulations of the reduction thesis that tie it to privileged relational operations do not suffice for Peirce’s justification of the categories, and invite the charge of gerrymandering to make it come out as true. We then develop a more robust invariant formulation of the thesis by explicating the use of triads in any relational operations, which is immune to that charge. The explication also allows us to track how Thirdness enters the structure of higher order relations, and even propose a numerical measure of it. Our analysis reveals new conceptual phenomena when negation or disjunction are used to compound relations.
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2122992.35511
We study the anchoring effect in a computational model of group deliberation on preference rankings. Anchoring is a form of path-dependence through which the opinions of those who speak early have a stronger influence on the outcome of deliberation than the opinions of those who speak later. We show that anchoring can occur even among fully rational agents. We then compare the respective effects of anchoring and three other determinants of the deliberative outcome: the relative weight or social influence of the speakers, the popularity of a given speaker’s opinion, and the homogeneity of the group. We find that, on average, anchoring has the strongest effect among these. We finally show that anchoring is often correlated with increases in proximity to single-plateauedness. We conclude that anchoring can constitute a structural bias that might hinder some of the otherwise positive effects of group deliberation.
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2600791.355121
This paper discusses some remarks Kaplan made in ”Bob and Carol and Ted and Alice” concerning empty names. I show how his objections to a particular view involving descriptions derived from Ramsification can be avoided by a nearby alternative framed in terms of discourse reference. I offer a treatment of empty names as variables carrying presuppositions concerning unique occupants of roles, or sets of properties, determined by the originating discourse.
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2708730.35513
Why is copper red? Why is it so soft compared to, say, nickel—the element right next to it in the periodic table? Why is it such a good conductor of electricity? All of this stems from a violation of Hund’s rules. …
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2722426.35514
The mass-count distinction is a morpho-syntactic distinction among nouns in English and many other languages. Tree, chair, person, group, and portion are count nouns, which come with the plural and accept numerals such as one and first; water, rice, furniture, silverware, and law enforcement are mass nouns, which lack the plural and do not accept numerals. The morpho-syntactic distinction is generally taken to have semantic content or reflect a semantic mass-count distinction. At the center of the semantic mass-count distinction is, in some way or another, a notion of being one or being a single entity, the basis of countability. There is little unanimity, however, of how the notion of being a single entity is to be understood and thus what the semantic mass-count distinction consists in.
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2722509.355151
One of the most influential accounts of high-level causation appeals to a notion of proportionality, which aims to identify the cause (variable) at an appropriate level given an effect (variable) of interest. Here we ask the dual question: Given a cause (variable) of interest, what is an appropriate level to model the effect? We argue that this question is not yet settled by the proportionality account and develop a natural counterpart to the proportionality account for this question. We also discuss several challenges for the effect-of-cause question that do not have an analog in the cause-of-effect question.
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2842560.355161
This paper argues for a distinction between fictional characters, as parts of intentionally created abstract artifacts, and intentional objects, as nonexistent objects generated by referential acts that fail to refer. It argues that intentional objects as the nonexistent objects of imagination and other objectual attitudes are well-reflected in natural language, though in a highly restricted way, reflecting their ontological dependence on referential acts. The paper elaborates how that ontological dependence can be understood.
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3353161.35517
tences—‘Snow is white’ is true if and only if snow is white—Quine writes: “To ascribe truth to the sentence is to ascribe whiteness to snow; such is the correspondence, in this example. Ascription of truth just cancels the quotation marks. Truth is disquotation” (PT: 80).
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3361823.355178
Natural language does not express all connectives definable in classical logic as simple lexical items. Coordination in English is expressed by conjunction and, disjunction or, and negated disjunction nor. Other languages pattern similarly. Non-lexicalized connectives are typically expressed compositionally: in English, negated conjunction is typically expressed by combining negation and conjunction (not both). This is surprising: if ∧ and ∨ are duals, and the negation of the latter can be expressed lexically (nor), why not the negation of the former? I present a two-tiered model of the semantics of the binary connectives. The first tier captures the expressive power of the lexicon: it is a bilateral state-based semantics that, under a restriction, can express all and only the distinctions that can be expressed by the lexicon of natural language (and, or, nor). This first tier is characterized by rejection as non-assertion and a Neglect Zero assumption. The second tier is obtained by dropping the Neglect Zero assumption and enforcing a stronger notion of rejection, thereby recovering classical logic and thus definitions for all Boolean connectives. On the two-tiered model, we distinguish the limited expressive resources of the lexicon and the greater combinatorial expressive power of the language as a whole. This gives us a logic-based account of compositionality for the Boolean fragment of the language.
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3863750.355188
A standard line of iambic pentameter is five “feet,” each of which is an “iamb”—an unstressed, then a stressed syllable. Or so says the classical theory of English meter. Similarly, trochaic hexameter is four trochees (stressed-then-unstressed). …
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3934166.355196
Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments in light of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators.
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4079700.355206
This work investigates absolute adjectives in the not very construction and how their pragmatic interpretation depends on the evaluative polarity and the scale structure of their antonymic pairs. Our experimental study reveals that evaluatively positive adjectives (clean) are more likely to be strengthened than evaluatively negative ones (dirty ), and that maximum standard adjectives (clean or closed) are more likely to be strengthened than minimum standard ones (dirty or open). Our findings suggest that both evaluative polarity and scale structure drive the asymmetric interpretation of gradable adjectives under negation. Overall, our work adds to the growing literature on the interplay between pragmatic inference, valence and semantic meaning.
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4169508.355217
In this paper we re-assess the philosophical foundation of Exactly True Logic (ETL), a competing variant of First Degree Entailment (FDE). In order to do this, we first rebut an argument against it. As the argument appears in an interview with Nuel Belnap himself, one of the fathers of FDE , we believe its provenance to be such that it needs to be taken seriously. We submit, however, that the argument ultimately fails, and that ETL cannot easily be dismissed. We then proceed to give an overview of the research that was inspired by this logic over the last decade, thus providing further motivation for the study of ETL and, more generally, of FDE-related logics that result from semantical analyses alternative to Belnap’s canonical one. We focus, in particular, on philosophical questions that these developments raise.
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4265561.355226
On a standard understanding of externalist metasemantic theories, such theories require a speaker to defer to other speakers in order to share content with them. We argue that this standard understanding is mistaken, and that, on a proper understanding of externalism, sharing content does not depend in any way on deference, either to experts, or one’s linguistic community. We defend a version of externalism that we call ‘pure externalism’, and we argue that the idea that shared content requires deference is a residue of internalism/descriptivisism to which externalists ought to be opposed. We also argue that, despite common belief to the contrary, several of the originators of externalism, including Tyler Burge, do not think that deference is in any way relevant, let alone required, for shared externalist content.
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4335243.355235
Since May 1st, Kris Brown, Nathaniel Osgood, Xiaoyan Li, William Waites and I have been meeting daily in James Clerk Maxwell’s childhood home in Edinburgh. We’re hard at work on our project called New Mathematics and Software for Agent-Based models. …
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4342823.355244
The Scene: Socrates is watching a massive protest of students at the School of Athens. Elektra, a protest leader, and Leonidas, a merchant, notice Socrates furrowing his brow in puzzlement. Leonidas: [approaches Socrates] Aha, Socrates. …
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4604751.355254
In this paper, we investigate, by means of a computational model, how individuals map quantifiers onto numbers and how they order quantifiers on a mental line. We selected five English quantifiers (few, fewer than half, many, more than half, and most) which differ in truth conditions and vagueness. We collected binary truth value judgment data in an online quantifier verification experiment. Using a Bayesian three-parameter logistic regression model, we separated three sources of individual differences: truth condition, vagueness, and response error. Clustering on one of the model’s parameter that corresponds to truth conditions revealed four subgroups of participants with different quantifier-to-number mappings and different ranges of the mental line of quantifiers. Our findings suggest multiple sources of individual differences in semantic representations of quantifiers and support a conceptual distinction between different types of imprecision in quantifier meanings. We discuss the consequence of our findings for the main theoretical approaches to quantifiers: the bivalent truth-conditional approach and the fuzzy logic approach. We argue that the former approach neither can explain inter-individual differences nor intra-individual differences in truth conditions of vague quantifiers. The latter approach requires further specification to fully account for individual differences demonstrated in this study.
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4679109.355263
Our aim in this paper is to extend the semantics for the kind of logic of ground developed in [deRosset and Fine, 2023]. In that paper, the authors very briefly suggested a way of treating universal and existential quantification over a fixed domain of objects. Here we explore some options for extending the treatment to allow for a variable domain of objects.
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4891943.355269
Consumption decisions are partly influenced by values and ideologies. Consumers care about global warming, child labor, fair trade, etc. We develop an axiomatic model of intrinsic values – those that are carriers of meaning in and of themselves – and argue that they often introduce discontinuities near zero. For example, a vegetarian’s preferences would be discontinuous near zero amount of animal meat. We distinguish intrinsic values from instrumental ones, which are means rather than ends and serve as proxies for intrinsic values. We illustrate the relevance of our value-based model in different contexts, including equity concerns and prosocial behavior.
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5123551.355276
This picture by Roice Nelson shows a remarkable structure: the hexagonal tiling honeycomb. What is it? Roughly speaking, a honeycomb is a way of filling 3d space with polyhedra. The most symmetrical honeycombs are the ‘regular’ ones. …
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5140798.355282
This axiomatization parallels the structure of first order logic exactly. It can be read as a reduction of the axiom scheme of comprehension of TST(U) to finitely many axiom templates (up to type assignment) or as a reduction of the axiom scheme of stratified comprehension to finitely many axioms. Probably one should assume weak extensionality: nonempty sets with the same elements are equal.