{"title":"Multiset-Multiset Frames","authors":"Takuro Onishi","doi":"10.1007/s10992-024-09764-5","DOIUrl":"https://doi.org/10.1007/s10992-024-09764-5","url":null,"abstract":"<p>This paper presents the notion of <i>multiset-multiset frame</i> (mm-frame for short), a frame equipped with a relation between (finite) multisets over the set of points which satisfies the condition called <i>compositionality</i>. This notion is an extension of Restall and Standefer’s <i>multiset frame</i>, a frame that relates a multiset to a single point. While multiset frames serve as frames for the positive fragments of relevant logics <b>RW</b> and <b>R</b>, mm-frames are for the full <b>RW</b> and <b>R</b> with negation. We show this by presenting a way of constructing an mm-frame from any <i>GS</i>-frame, a frame with two dual ternary relations in which the Routley star is definable.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"2 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Which ‘Intensional Paradoxes’ are Paradoxes?","authors":"Neil Tennant","doi":"10.1007/s10992-024-09761-8","DOIUrl":"https://doi.org/10.1007/s10992-024-09761-8","url":null,"abstract":"<p>We begin with a brief explanation of our proof-theoretic criterion of paradoxicality—its motivation, its methods, and its results so far. It is a proof-theoretic account of paradoxicality that can be given in addition to, or alongside, the more familiar semantic account of Kripke. It is a question for further research whether the two accounts agree in general on what is to count as a paradox. It is also a question for further research whether and, if so, how the so-called Ekman problem bears on the investigations here of the intensional paradoxes. Possible exceptions to the proof-theoretic criterion are Prior’s Theorem and Russell’s Paradox of Propositions—the two best-known ‘intensional’ paradoxes. We have not yet addressed them. We do so here. The results are encouraging. §1 studies Prior’s Theorem. In the literature on the paradoxes of intensionality, it does not enjoy rigorous formal proof of a <i>Gentzenian</i> kind—the kind that lends itself to proof-theoretic analysis of recondite features that might escape the attention of logicians using non-Gentzenian systems of logic. We make good that lack, both to render the criterion applicable to the formal proof, and to see whether the criterion gets it right. Prior’s Theorem is a theorem in an <i>unfree</i>, classical, quantified propositional logic. But if one were to insist that the logic employed be <i>free</i>, then Prior’s Theorem would not be a <i>theorem</i> at all. Its proof would have an <i>undischarged assumption</i>—the ‘existential presupposition’ that the proposition <span>(forall p(Qp!rightarrow !lnot p))</span> exists. Call this proposition <span>(vartheta )</span>. §2 focuses on <span>(vartheta )</span>. We analyse a Priorean <i>reductio</i> of <span>(vartheta )</span> along with the possibilitate <span>(Diamond forall q(Qq!leftrightarrow !(vartheta !leftrightarrow ! q)))</span>. The attempted <i>reductio</i> of this premise-pair, which is constructive, cannot be brought into normal form. The criterion says we have not straightforward inconsistency, but rather genuine paradoxicality. §3 turns to problems engendered by the proposition <span>(exists p(Qpwedge lnot p))</span> (call it <span>(eta )</span>) for the similar possibilitate <span>(Diamond forall q(Qq!leftrightarrow !(eta !leftrightarrow ! q)))</span>. The attempted disproof of this premise-pair—again, a constructive one—cannot succeed. It cannot be brought into normal form. The criterion says the premise-pair is a genuine paradox. In §4 we show how Russell’s Paradox of Propositions, like the Priorean intensional paradoxes, is to be classified as a genuine paradox by the proof-theoretic criterion of paradoxicality.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"36 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141501328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Arithmetic is Necessary","authors":"Zachary Goodsell","doi":"10.1007/s10992-024-09760-9","DOIUrl":"https://doi.org/10.1007/s10992-024-09760-9","url":null,"abstract":"<p>(Goodsell, <i>Journal of Philosophical Logic</i>, <i>51</i>(1), 127-150 2022) establishes the noncontingency of sentences of first-order arithmetic, in a plausible higher-order modal logic. Here, the same result is derived using significantly weaker assumptions. Most notably, the assumption of rigid comprehension—that every property is coextensive with a modally rigid one—is weakened to the assumption that the Boolean algebra of properties under necessitation is countably complete. The results are generalized to extensions of the language of arithmetic, and are applied to answer a question posed by Bacon and Dorr (2024).</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"23 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Truthmaker-based Epistemic Logic","authors":"Vita Saitta","doi":"10.1007/s10992-024-09758-3","DOIUrl":"https://doi.org/10.1007/s10992-024-09758-3","url":null,"abstract":"<p>The aim of this work is to investigate the problem of Logical Omniscience in epistemic logic by means of truthmaker semantics. We will present a semantic framework based on <span>(varvec{W})</span>-models extended with a partial function, which selects the <i>body of knowledge</i> of the agents, namely the set of verifiers of the agent’s <i>total knowledge</i>. The semantic clause for knowledge follows the intuition that an agent knows some information <span>(varvec{phi })</span>, when the <i>propositional content</i> that <span>(varvec{phi })</span> is <i>contained</i> in her total knowledge. We will argue that this idea mirrors the philosophical conception of <i>immanent closure</i> by Yablo (2014), giving to our proposal a strong philosophical motivation. We will discuss the philosophical implications of the semantics and we will introduce its axiomatization.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"36 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Orthologic of Epistemic Modals","authors":"Wesley H. Holliday, Matthew Mandelkern","doi":"10.1007/s10992-024-09746-7","DOIUrl":"https://doi.org/10.1007/s10992-024-09746-7","url":null,"abstract":"<p>Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form <span>(pwedge Diamond lnot p)</span> (‘<i>p</i>, but it might be that not <i>p</i>’) appears to be a contradiction, <span>(Diamond lnot p)</span> does not entail <span>(lnot p)</span>, which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. Some theories predict that <span>( pwedge Diamond lnot p)</span>, a so-called <i>epistemic contradiction</i>, is a contradiction only in an etiolated sense, under a notion of entailment that does not always allow us to replace <span>(pwedge Diamond lnot p)</span> with a contradiction; these theories underpredict the infelicity of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that intuitively fail, like distributivity and disjunctive syllogism, but also rules like non-contradiction, excluded middle, De Morgan’s laws, and disjunction introduction, which intuitively remain valid for epistemic modals. In this paper, we aim for a middle ground, developing a semantics and logic for epistemic modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We start with an <i>algebraic semantics</i>, based on ortholattices instead of Boolean algebras, and then propose a <i>possibility semantics</i>, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. We then show how to lift an arbitrary possible worlds model for a non-modal language to a possibility model for a language with epistemic modals. The goal throughout is to retain what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"40 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modelling Afthairetic Modality","authors":"Giorgio Venturi, Pedro Yago","doi":"10.1007/s10992-024-09757-4","DOIUrl":"https://doi.org/10.1007/s10992-024-09757-4","url":null,"abstract":"<p>Despite their controversial ontological status, the discussion on arbitrary objects has been reignited in recent years. According to the supporting views, they present interesting and unique qualities. Among those, two define their nature: their assuming of values, and the way in which they present properties. Leon Horsten has advanced a particular view on arbitrary objects which thoroughly describes the earlier, arguing they assume values according to a <i>sui generis</i> modality, which he calls <i>afthairetic</i>. In this paper, we offer a general method for defining the minimal system of this modality for any given first-order theory, and possible extensions of it that incorporate further aspects of Horsten’s account. The minimal system presents an unconventional inference rule, which deals with two different notions of derivability. For this reason and the failure of the <i>Necessitation</i> rule, in its full generality, the resulting system is non-normal. Then, we provide conditional soundness and completeness results for the minimal system and its extensions.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"36 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Some Weakened Forms of Transitivity in the Logic of Conditional Obligation","authors":"Xavier Parent","doi":"10.1007/s10992-024-09748-5","DOIUrl":"https://doi.org/10.1007/s10992-024-09748-5","url":null,"abstract":"<p>This paper examines the logic of conditional obligation, which originates from the works of Hansson, Lewis, and others. Some weakened forms of transitivity of the betterness relation are studied. These are quasi-transitivity, Suzumura consistency, acyclicity and the interval order condition. The first three do not change the logic. The axiomatic system is the same whether or not they are introduced. This holds true under a rule of interpretation in terms of maximality and strong maximality. The interval order condition gives rise to a new axiom. Depending on the rule of interpretation, this one changes. With the rule of maximality, one obtains the principle known as disjunctive rationality. With the rule of strong maximality, one obtains the Spohn axiom (also known as the principle of rational monotony, or Lewis’ axiom CV). A completeness theorem further substantiates these observations. For interval order, this yields the finite model property and decidability of the calculus.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"24 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exact Truthmaker Semantics for Modal Logics","authors":"Dongwoo Kim","doi":"10.1007/s10992-024-09752-9","DOIUrl":"https://doi.org/10.1007/s10992-024-09752-9","url":null,"abstract":"<p>The present paper attempts to provide an exact truthmaker semantical analysis of modalized propositions. According to the present proposal, an exact truthmaker for “Necessarily <i>P</i>” is a state that bans every exact truthmaker for “Not <i>P</i>”, and an exact truthmaker for “Possibly <i>P</i>” is a state that allows an exact truthmaker for <i>P</i>. Based on this proposal, a formal semantics will be developed; and the soundness and completeness results for a well-known family of the systems of normal modal propositional logic will be established. It shall be seen that the present analysis offers an exactification of the standard Kripke semantics in the sense that it analyzes the accessibility relation between possible worlds in terms of the banning and allowing relations between the constituent states, and thereby gives an account of “truth at a possible world” in terms of exact truthmaking.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"64 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Counterpart Theory and Actuality","authors":"","doi":"10.1007/s10992-024-09745-8","DOIUrl":"https://doi.org/10.1007/s10992-024-09745-8","url":null,"abstract":"<h3>Abstract</h3> <p>Lewis (<em>The Journal of Philosophy</em>, <em>65</em>(5), 113–126, <span>1968</span>) attempts to provide an account of modal talk in terms of the resources of <em>counterpart theory</em>, a first-order theory that eschews transworld identity. First, a regimentation of natural language modal claims into sentences of a formal first-order modal language L is assumed. Second, a translation scheme from L-sentences to sentences of the language of the theory is provided. According to Hazen (<em>The Journal of Philosophy</em>, <em>76</em>(6), 319–338, <span>1979</span>) and Fara & Williamson (<em>Mind</em>, <em>114</em>(453), 1–30, <span>2005</span>), the account cannot handle certain natural language modal claims involving a notion of <em>actuality</em>. The challenge has two parts. First, in order to handle such claims, the initial formal modal language that natural language modal claims are regimented into must extend L with something like an actuality operator. Second, certain ways that Lewis’ translation scheme for L might be extended to accommodate an actuality operator are unacceptable. Meyer (<em>Mind</em>, <em>122</em>(485), 27–42, <span>2013</span>) attempts to defend Lewis’ approach. First, Meyer holds that in order to handle such claims, the formal modal language L<span> <span>(^*)</span> </span> that we initially regiment our natural language claims into need not contain an actuality operator. Instead, we can make do with other resources. Next, Meyer provides an alternative translation scheme from L<span> <span>(^*)</span> </span>-sentences to sentences of an enriched language of counterpart theory. Unfortunately, Meyer’s approach fails to provide an appropriate counterpart theoretic account of natural language modal claims. In this paper, I demonstrate that failure.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"24 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"One Variable Relevant Logics are S5ish","authors":"Nicholas Ferenz","doi":"10.1007/s10992-024-09753-8","DOIUrl":"https://doi.org/10.1007/s10992-024-09753-8","url":null,"abstract":"<p>Here I show that the one-variable fragment of several first-order relevant logics corresponds to certain <b>S5</b>ish extensions of the underlying propositional relevant logic. In particular, given a fairly standard translation between modal and one-variable languages and a permuting propositional relevant logic <b>L</b>, a formula <span>(mathcal {A})</span> of the one-variable fragment is a theorem of <b>LQ</b> (<b>QL</b>) iff its translation is a theorem of <b>L5</b> (<b>L.5</b>). The proof is model-theoretic. In one direction, semantics based on the Mares-Goldblatt [15] semantics for quantified <b>L</b> are transformed into ternary (plus two binary) relational semantics for <b>S5</b>-like extensions of <b>L</b> (for a general presentation, see Seki [26, 27]). In the other direction, a valuation is given for the full first-order relevant logic based on <b>L</b> into a model for a suitable <b>S5</b> extension of <b>L</b>. I also discuss this work’s relation to finding a complete axiomatization of the constant domain, non-general frame ternary relational semantics for which <b>RQ</b> is incomplete [11].</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"27 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
