Deflationism About Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191115
Abstract:
Logical consequence is typically construed as a metalinguistic relation between (sets of) sentences. Deflationism is an account of logic that challenges this orthodoxy. In Williamson's recent presentation of deflationism, logic's primary concern is with universal generalizations over absolutely everything. As well as an interesting account of logic in its own right, deflationism has also been recruited to decide between competing logics in resolving semantic paradoxes. This paper defends deflationism from its most important challenge to date, due to Ole Hjortland. It then presents two new problems for the view. Hjortland's objection is that deflationism cannot discriminate between distinct logics. I show that his example of classical logic and supervaluationism depends on equivocating about whether the language includes a definitely' operator. Moreover, I prove a result that blocks this line of objection no matter the choice of logics. I end by criticizing deflationism on two fronts. First, it cannot do the work it has been recruited to perform. That is, it cannot help adjudicate between competing logics. This is because a theory of logic cannot be as easily separated from a theory of truth as its proponents claim. Second, deflationism currently has no adequate answer to the following challenge: what does a sentence's universal generalization have to do with its logical truth? I argue that the most promising, stipulative response on behalf of the deflationist amounts to an unwarranted change of subject. Word Count:
Rank  Word  Count 
0  deflationism  7 
Excerpts:
...a metalinguistic relation between sets of sentences deflationism is an account of logic that challenges ...
...this orthodoxy in williamsons recent presentation of deflationism logics primary concern is with universal generalizations ...
...account of logic in its own right deflationism has also been recruited to decide between ...
...in resolving semantic paradoxes this paper defends deflationism from its most important challenge to date ...
...for the view hjortlands objection is that deflationism cannot discriminate between distinct logics i show ...
...choice of logics i end by criticizing deflationism on two fronts first it cannot do ...
...of truth as its proponents claim second deflationism currently has no adequate answer to the ...

1  logics  5 
Excerpts:
...orthodoxy in williamsons recent presentation of deflationism logics primary concern is with universal generalizations over ...
...also been recruited to decide between competing logics in resolving semantic paradoxes this paper defends ...
...is that deflationism cannot discriminate between distinct logics i show that his example of classical ...
...of objection no matter the choice of logics i end by criticizing deflationism on two ...
...is it cannot help adjudicate between competing logics this is because a theory of logic ...

2  logic  4 
Excerpts:
...of sentences deflationism is an account of logic that challenges this orthodoxy in williamsons recent ...
...as well as an interesting account of logic in its own right deflationism has also ...
...i show that his example of classical logic and supervaluationism depends on equivocating about whether ...
...logics this is because a theory of logic cannot be as easily separated from a ...

3  cannot  4 
Excerpts:
...the view hjortlands objection is that deflationism cannot discriminate between distinct logics i show that ...
...criticizing deflationism on two fronts first it cannot do the work it has been recruited ...
...been recruited to perform that is it cannot help adjudicate between competing logics this is ...
...this is because a theory of logic cannot be as easily separated from a theory ...

4  truth  2 
Excerpts:
...as easily separated from a theory of truth as its proponents claim second deflationism currently ...
...generalization have to do with its logical truth i argue that the most promising stipulative ...

5  universal  2 
Excerpts:
...of deflationism logics primary concern is with universal generalizations over absolutely everything as well as ...
...the following challenge what does a sentences universal generalization have to do with its logical ...

6  recruited  2 
Excerpts:
...its own right deflationism has also been recruited to decide between competing logics in resolving ...
...cannot do the work it has been recruited to perform that is it cannot help ...

7  competing  2 
Excerpts:
...has also been recruited to decide between competing logics in resolving semantic paradoxes this paper ...
...that is it cannot help adjudicate between competing logics this is because a theory of ...

8  logical  2 
Excerpts:
... logical consequence is typically construed as a metalinguistic ...
...universal generalization have to do with its logical truth i argue that the most promising ...

9  objection  2 
Excerpts:
...two new problems for the view hjortlands objection is that deflationism cannot discriminate between distinct ...
...a result that blocks this line of objection no matter the choice of logics i ...

Forcing and the Universe of Sets: Must We Lose Insight?
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191112
Abstract:
A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. Word Count:
Rank  Word  Count 
0  universist  3 
Excerpts:
...informs this debate by analysing ways the universist might interpret this discourse that seems to ...
...facie incoherence of such talk for the universist she nonetheless has reason to try and ...
...might be made we conclude that the universist has promising options for interpreting different forcing ...

1  forcing  2 
Excerpts:
...one of which is ontologically privileged often forcing constructions that add subsets to models are ...
...universist has promising options for interpreting different forcing constructions ...

2  analyse  2 
Excerpts:
...and provide interpretation of this discourse we analyse extant interpretations of such talk and analyse ...
...analyse extant interpretations of such talk and analyse various tradeoffs in naturality that might be ...

3  talk  2 
Excerpts:
...despite the prima facie incoherence of such talk for the universist she nonetheless has reason ...
...discourse we analyse extant interpretations of such talk and analyse various tradeoffs in naturality that ...

4  might  2 
Excerpts:
...this debate by analysing ways the universist might interpret this discourse that seems to necessitate ...
...and analyse various tradeoffs in naturality that might be made we conclude that the universist ...

5  constructions  2 
Excerpts:
...of which is ontologically privileged often forcing constructions that add subsets to models are cited ...
...has promising options for interpreting different forcing constructions ...

6  universe  2 
Excerpts:
...or not there is a single maximal universe of set theory universists maintain that there ...
...universists maintain that there is such a universe while multiversists argue that there are many ...

7  discourse  2 
Excerpts:
...analysing ways the universist might interpret this discourse that seems to necessitate the addition of ...
...to try and provide interpretation of this discourse we analyse extant interpretations of such talk ...

8  debate  2 
Excerpts:
... a central area of current philosophical debate in the foundations of mathematics concerns whether ...
...of the latter this paper informs this debate by analysing ways the universist might interpret ...

9  subsets  2 
Excerpts:
...ontologically privileged often forcing constructions that add subsets to models are cited as evidence in ...
...that seems to necessitate the addition of subsets to v we argue that despite the ...

Models for Hylomorphism
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191001
Abstract:
In a series of papers (Fine et al., 1982; Fine, NoÃ»s28(2), 137“158; 1994, Midwest Studies in Philosophy, 23, 61“74, 1999) Fine develops his hylomorphic theory of embodiments. In this article, we supply a formal semantics for this theory that is adequate to the principles laid down for it in (Midwest Studies in Philosophy, 23, 61“74, 1999). In Section 1, we lay out the theory of embodiments as Fine presents it. In Section 2, we argue on Cantorian grounds that the theory needs to be stabilized, and sketch some ways forward, discussing various choice points in modeling the view. In Section 3, we develop a formal semantics for the theory of embodiments by constructing embodiments in stages and restricting the domain of the secondorder quantifiers. In Section 4 we give a few illustrative examples to show how the models deliver Finean hylomorphic consequences. In Section 5, we prove that Fine's principles are sound with respect to this semantics. In Section 6 we present some inexpressibility results concerning Fine's various notions of parthood and show that in our formal semantics these notions are all expressible using a single mereological primitive. In Section 7, we prove several mereological results stemming from the model theory, showing that the mereology is surprisingly robust. In Section 8, we draw some philosophical lessons from the formal semantics, and in particular respond to Koslicki's (2008) main objection to Fine's theory. In the appendix we present proofs of the inexpressibility results of Section 6. Word Count:
The Harmony of Identity
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191001
Abstract:
The standard natural deduction rules for the identity predicate have seemed to some not to be harmonious. Stephen Read has suggested an alternative introduction rule that restores harmony but presupposes secondorder logic. Here it will be shown that the standard rules are in fact harmonious. To this end, natural deduction will be enriched with a theory of definitional identity. This leads to a novel conception of canonical derivation, on the basis of which the identity elimination rule can be justified in a prooftheoretical manner. Word Count:
Rank  Word  Count 
0  identity  3 
Excerpts:
...the standard natural deduction rules for the identity predicate have seemed to some not to ...
...be enriched with a theory of definitional identity this leads to a novel conception of ...
...derivation on the basis of which the identity elimination rule can be justified in a ...

1  harmonious  2 
Excerpts:
...have seemed to some not to be harmonious stephen read has suggested an alternative introduction ...
...that the standard rules are in fact harmonious to this end natural deduction will be ...

2  rule  2 
Excerpts:
...stephen read has suggested an alternative introduction rule that restores harmony but presupposes secondorder logic ...
...the basis of which the identity elimination rule can be justified in a prooftheoretical manner ...

3  standard  2 
Excerpts:
... the standard natural deduction rules for the identity predicate ...
...here it will be shown that the standard rules are in fact harmonious to this ...

4  will  2 
Excerpts:
...harmony but presupposes secondorder logic here it will be shown that the standard rules are ...
...fact harmonious to this end natural deduction will be enriched with a theory of definitional ...

5  natural  2 
Excerpts:
... the standard natural deduction rules for the identity predicate have ...
...are in fact harmonious to this end natural deduction will be enriched with a theory ...

6  rules  2 
Excerpts:
... the standard natural deduction rules for the identity predicate have seemed to ...
...it will be shown that the standard rules are in fact harmonious to this end ...

7  deduction  2 
Excerpts:
... the standard natural deduction rules for the identity predicate have seemed ...
...in fact harmonious to this end natural deduction will be enriched with a theory of ...

8  novel  1 
Excerpts:
...of definitional identity this leads to a novel conception of canonical derivation on the basis ...

9  conception  1 
Excerpts:
...definitional identity this leads to a novel conception of canonical derivation on the basis of ...

The Modal Logic of Bayesian Belief Revision
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191001
Abstract:
In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes' rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent's prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal companion of Medvedev's logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. Word Count:
Rank  Word  Count 
0  modal  5 
Excerpts:
...bayes rule we define a hierarchy of modal logics that capture the logical features of ...
...agents prior is defined inclusions among the modal logics in the hierarchy are determined by ...
...the hierarchy are determined by linking the modal logics in the hierarchy to the strongest ...
...logics in the hierarchy to the strongest modal companion of medvedevs logic of finite problems ...
...finite problems it is shown that the modal logic of belief revision determined by probabilities ...

1  hierarchy  4 
Excerpts:
...evidence using bayes rule we define a hierarchy of modal logics that capture the logical ...
...of bayesian belief revision elements in the hierarchy are distinguished by the cardinality of the ...
...inclusions among the modal logics in the hierarchy are determined by linking the modal logics ...
...by linking the modal logics in the hierarchy to the strongest modal companion of medvedevs ...

2  belief  4 
Excerpts:
... in bayesian belief revision a bayesian agent revises his prior ...
...revision a bayesian agent revises his prior belief by conditionalizing the prior on some evidence ...
...that capture the logical features of bayesian belief revision elements in the hierarchy are distinguished ...
...is shown that the modal logic of belief revision determined by probabilities on a finite ...

3  bayesian  3 
Excerpts:
... in bayesian belief revision a bayesian agent revises his ...
... in bayesian belief revision a bayesian agent revises his prior belief by conditionalizing ...
...logics that capture the logical features of bayesian belief revision elements in the hierarchy are ...

4  logics  3 
Excerpts:
...rule we define a hierarchy of modal logics that capture the logical features of bayesian ...
...prior is defined inclusions among the modal logics in the hierarchy are determined by linking ...
...hierarchy are determined by linking the modal logics in the hierarchy to the strongest modal ...

5  revision  3 
Excerpts:
... in bayesian belief revision a bayesian agent revises his prior belief ...
...capture the logical features of bayesian belief revision elements in the hierarchy are distinguished by ...
...shown that the modal logic of belief revision determined by probabilities on a finite set ...

6  prior  3 
Excerpts:
...belief revision a bayesian agent revises his prior belief by conditionalizing the prior on some ...
...revises his prior belief by conditionalizing the prior on some evidence using bayes rule we ...
...of elementary propositions on which the agents prior is defined inclusions among the modal logics ...

7  set  2 
Excerpts:
...are distinguished by the cardinality of the set of elementary propositions on which the agents ...
...revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable ...

8  determined  2 
Excerpts:
...the modal logics in the hierarchy are determined by linking the modal logics in the ...
...that the modal logic of belief revision determined by probabilities on a finite set of ...

9  logic  2 
Excerpts:
...to the strongest modal companion of medvedevs logic of finite problems it is shown that ...
...problems it is shown that the modal logic of belief revision determined by probabilities on ...

The FmlaFmla Axiomatizations of the Exactly True and Nonfalsity Logics and Some of Their Cousins
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191001
Abstract:
In this paper we present a solution of the axiomatization problem for the FmlaFmla versions of the Pietz and Rivieccio exactly true logic and the nonfalsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific prooftheoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the resulting logic, and the other is introduced as an extension of this basic relation. The proposed biconsequences systems allow for a standard Henkinstyle canonical model used in the completeness proof. The deductive equivalence of these biconsequence systems to the corresponding binary consequence systems is proved. We also outline a family of the biconsequence systems generated on the basis of the firstdegree entailment logic up to the classic consequence. Word Count:
Rank  Word  Count 
0  systems  5 
Excerpts:
...the completeness of the corresponding binary consequence systems we introduce a specific prooftheoretic formalism which ...
...of this basic relation the proposed biconsequences systems allow for a standard henkinstyle canonical model ...
...proof the deductive equivalence of these biconsequence systems to the corresponding binary consequence systems is ...
...biconsequence systems to the corresponding binary consequence systems is proved we also outline a family ...
...also outline a family of the biconsequence systems generated on the basis of the firstdegree ...

1  logic  4 
Excerpts:
...of the pietz and rivieccio exactly true logic and the nonfalsity logic dual to it ...
...rivieccio exactly true logic and the nonfalsity logic dual to it to prove the completeness ...
...treated as the basic for the resulting logic and the other is introduced as an ...
...on the basis of the firstdegree entailment logic up to the classic consequence ...

2  consequence  4 
Excerpts:
...prove the completeness of the corresponding binary consequence systems we introduce a specific prooftheoretic formalism ...
...allows us to deal simultaneously with two consequence relations within one logical system these relations ...
...these biconsequence systems to the corresponding binary consequence systems is proved we also outline a ...
...firstdegree entailment logic up to the classic consequence ...

3  biconsequence  2 
Excerpts:
...completeness proof the deductive equivalence of these biconsequence systems to the corresponding binary consequence systems ...
...we also outline a family of the biconsequence systems generated on the basis of the ...

4  completeness  2 
Excerpts:
...logic dual to it to prove the completeness of the corresponding binary consequence systems we ...
...standard henkinstyle canonical model used in the completeness proof the deductive equivalence of these biconsequence ...

5  corresponding  2 
Excerpts:
...it to prove the completeness of the corresponding binary consequence systems we introduce a specific ...
...equivalence of these biconsequence systems to the corresponding binary consequence systems is proved we also ...

6  basic  2 
Excerpts:
...one of them is treated as the basic for the resulting logic and the other ...
...is introduced as an extension of this basic relation the proposed biconsequences systems allow for ...

7  relations  2 
Excerpts:
...us to deal simultaneously with two consequence relations within one logical system these relations are ...
...consequence relations within one logical system these relations are hierarchically organized so that one of ...

8  binary  2 
Excerpts:
...to prove the completeness of the corresponding binary consequence systems we introduce a specific prooftheoretic ...
...of these biconsequence systems to the corresponding binary consequence systems is proved we also outline ...

9  classic  1 
Excerpts:
...the firstdegree entailment logic up to the classic consequence ...

BuraliForti as a Purely Logical Paradox
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191001
Abstract:
Russell's paradox is purely logical in the following sense: a contradiction can be formally deduced from the proposition that there is a set of all nonselfmembered sets, in pure firstorder logic'the firstorder logical form of this proposition is inconsistent. This explains why Russell's paradox is portable'why versions of the paradox arise in contexts unrelated to set theory, from propositions with the same logical form as the claim that there is a set of all nonselfmembered sets. BuraliForti's paradox, like Russell's paradox, is portable. I offer the following explanation for this fact: BuraliForti's paradox, like Russell's, is purely logical. Concretely, I show that if we enrich the language
\(\mathcal {L}\)
of firstorder logic with a wellfoundedness quantifier W and adopt certain minimal inference rules for this quantifier, then a contradiction can be formally deduced from the proposition that there is a greatest ordinal. Moreover, a proposition with the same logical form as the claim that there is a greatest ordinal can be found at the heart of several other paradoxes that resemble BuraliForti's. The reductio of BuraliForti can be repeated verbatim to establish the inconsistency of these other propositions. Hence, the portability of the BuraliForti's paradox is explained in the same way as the portability of Russell's: both paradoxes involve an inconsistent logical form'Russell's involves an inconsistent form expressible in
\(\mathcal {L}\)
and BuraliForti's involves an inconsistent form expressible in
\(\mathcal {L} + \mathsf {W}\)
. Word Count:
Rank  Word  Count 
0  paradox  7 
Excerpts:
... russells paradox is purely logical in the following sense ...
...proposition is inconsistent this explains why russells paradox is portablewhy versions of the paradox arise ...
...russells paradox is portablewhy versions of the paradox arise in contexts unrelated to set theory ...
...a set of all nonselfmembered sets buralifortis paradox like russells paradox is portable i offer ...
...all nonselfmembered sets buralifortis paradox like russells paradox is portable i offer the following explanation ...
...the following explanation for this fact buralifortis paradox like russells is purely logical concretely i ...
...propositions hence the portability of the buralifortis paradox is explained in the same way as ...

1  logical  6 
Excerpts:
... russells paradox is purely logical in the following sense a contradiction can ...
...nonselfmembered sets in pure firstorder logicthe firstorder logical form of this proposition is inconsistent this ...
...set theory from propositions with the same logical form as the claim that there is ...
...fact buralifortis paradox like russells is purely logical concretely i show that if we enrich ...
...ordinal moreover a proposition with the same logical form as the claim that there is ...
...of russells both paradoxes involve an inconsistent logical formrussells involves an inconsistent form expressible in ...

2  russells  5 
Excerpts:
... russells paradox is purely logical in the following ...
...this proposition is inconsistent this explains why russells paradox is portablewhy versions of the paradox ...
...of all nonselfmembered sets buralifortis paradox like russells paradox is portable i offer the following ...
...explanation for this fact buralifortis paradox like russells is purely logical concretely i show that ...
...the same way as the portability of russells both paradoxes involve an inconsistent logical formrussells ...

3  buralifortis  5 
Excerpts:
...is a set of all nonselfmembered sets buralifortis paradox like russells paradox is portable i ...
...offer the following explanation for this fact buralifortis paradox like russells is purely logical concretely ...
...heart of several other paradoxes that resemble buralifortis the reductio of buraliforti can be repeated ...
...other propositions hence the portability of the buralifortis paradox is explained in the same way ...
... and buralifortis involves an inconsistent form expressible in
...

4  form  5 
Excerpts:
...sets in pure firstorder logicthe firstorder logical form of this proposition is inconsistent this explains ...
...theory from propositions with the same logical form as the claim that there is a ...
...moreover a proposition with the same logical form as the claim that there is a ...
...an inconsistent logical formrussells involves an inconsistent form expressible in
...
... and buralifortis involves an inconsistent form expressible in
...

5  proposition  4 
Excerpts:
...contradiction can be formally deduced from the proposition that there is a set of all ...
...firstorder logicthe firstorder logical form of this proposition is inconsistent this explains why russells paradox ...
...contradiction can be formally deduced from the proposition that there is a greatest ordinal moreover ...
...there is a greatest ordinal moreover a proposition with the same logical form as the ...

6  inconsistent  4 
Excerpts:
...firstorder logical form of this proposition is inconsistent this explains why russells paradox is portablewhy ...
...portability of russells both paradoxes involve an inconsistent logical formrussells involves an inconsistent form expressible ...
...involve an inconsistent logical formrussells involves an inconsistent form expressible in
...
... and buralifortis involves an inconsistent form expressible in
...

7  same  3 
Excerpts:
...to set theory from propositions with the same logical form as the claim that there ...
...greatest ordinal moreover a proposition with the same logical form as the claim that there ...
...the buralifortis paradox is explained in the same way as the portability of russells both ...

8  mathcal  3 
Excerpts:
... mathcal l
...
... mathcal l
...
... mathcal l + mathsf w
...

9  firstorder  3 
Excerpts:
...set of all nonselfmembered sets in pure firstorder logicthe firstorder logical form of this proposition ...
...all nonselfmembered sets in pure firstorder logicthe firstorder logical form of this proposition is inconsistent ...
... of firstorder logic with a wellfoundedness quantifier w and ...

Symmetric Contingency Logic with Unlimitedly Many Modalities
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191001
Abstract:
The completeness of the axiomatization of contingency logic over symmetric frames has been thought of as a nontrivial job, the unimodal case of which cannot be generalized to the finitely multimodal case, which in turn cannot be generalized to the infinitely multimodal case. This paper deals with the completeness of symmetric contingency logic with unlimitedly many modalities, no matter whether the set of modalities is finite or infinite. Word Count:
Rank  Word  Count 
0  case  3 
Excerpts:
...of as a nontrivial job the unimodal case of which cannot be generalized to the ...
...cannot be generalized to the finitely multimodal case which in turn cannot be generalized to ...
...cannot be generalized to the infinitely multimodal case this paper deals with the completeness of ...

1  completeness  2 
Excerpts:
... the completeness of the axiomatization of contingency logic over ...
...multimodal case this paper deals with the completeness of symmetric contingency logic with unlimitedly many ...

2  generalized  2 
Excerpts:
...the unimodal case of which cannot be generalized to the finitely multimodal case which in ...
...multimodal case which in turn cannot be generalized to the infinitely multimodal case this paper ...

3  multimodal  2 
Excerpts:
...which cannot be generalized to the finitely multimodal case which in turn cannot be generalized ...
...turn cannot be generalized to the infinitely multimodal case this paper deals with the completeness ...

4  modalities  2 
Excerpts:
...of symmetric contingency logic with unlimitedly many modalities no matter whether the set of modalities ...
...modalities no matter whether the set of modalities is finite or infinite ...

5  cannot  2 
Excerpts:
...nontrivial job the unimodal case of which cannot be generalized to the finitely multimodal case ...
...the finitely multimodal case which in turn cannot be generalized to the infinitely multimodal case ...

6  logic  2 
Excerpts:
...the completeness of the axiomatization of contingency logic over symmetric frames has been thought of ...
...deals with the completeness of symmetric contingency logic with unlimitedly many modalities no matter whether ...

7  symmetric  2 
Excerpts:
...of the axiomatization of contingency logic over symmetric frames has been thought of as a ...
...this paper deals with the completeness of symmetric contingency logic with unlimitedly many modalities no ...

8  contingency  2 
Excerpts:
... the completeness of the axiomatization of contingency logic over symmetric frames has been thought ...
...paper deals with the completeness of symmetric contingency logic with unlimitedly many modalities no matter ...

9  axiomatization  1 
Excerpts:
... the completeness of the axiomatization of contingency logic over symmetric frames has ...

A Calculus of Regions Respecting Both Measure and Topology
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20191001
Abstract:
Say that space is ˜gunky' if every part of space has a proper part. Traditional theories of gunk, dating back to the work of Whitehead in the early part of last century, modeled space in the Boolean algebra of regular closed (or regular open) subsets of Euclidean space. More recently a complaint was brought against that tradition in Arntzenius (2008) and Russell (2008): Lebesgue measure is not even finitely additive over the algebra, and there is no countably additive measure on the algebra. Arntzenius advocated modeling gunk in measure algebras instead'in particular, in the algebra of Borel subsets of Euclidean space, modulo sets of Lebesgue measure zero. But while this algebra carries a natural, countably additive measure, it has some unattractive topological features. In this paper, we show how to construct a model of gunk that has both nice rudimentary measuretheoretic and topological properties. We then show that in modeling gunk in this way we can distinguish between finite dimensions, and that nothing in lost in terms of our ability to identify points as locations in space. Word Count:
Indicative Conditionals and Graded Information
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190904
Abstract:
I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: if p then q' is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the pworlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of spheres. Worlds in the inner sphere are considered possible; worlds outside of it are ruled out, but to different degrees. In this way, even when a state supports not p', it is still possible to suppose p consistently. I argue that this account does better than its predecessors with respect to a set of desiderata concerning inferences with conditionals. In particular, it captures three important facts: (i) that a conditional is logically independent from its antecedent; (ii) that a sequence of antecedents behaves like a single conjunctive antecedent (the importexport equivalence); and (iii) that conditionals restrict the quantification domain of epistemic modals. I also discuss two ways to construe the role of a premise, and propose a generalized notion of entailment that keeps the two apart. Word Count:
Rank  Word  Count 
0  state  4 
Excerpts:
...conditionals are interpreted relative to an information state in accordance with the ramsey test idea ...
...p then q is supported at a state s iff q is supported at the ...
...iff q is supported at the hypothetical state sp obtained by restricting s to the ...
...degrees in this way even when a state supports not p it is still possible ...

1  conditionals  4 
Excerpts:
... i propose an account of indicative conditionals that combines features of minimal change semantics ...
...and information semantics as in information semantics conditionals are interpreted relative to an information state ...
...a set of desiderata concerning inferences with conditionals in particular it captures three important facts ...
...antecedent the importexport equivalence and iii that conditionals restrict the quantification domain of epistemic modals ...

2  information  4 
Excerpts:
...combines features of minimal change semantics and information semantics as in information semantics conditionals are ...
...change semantics and information semantics as in information semantics conditionals are interpreted relative to an ...
...semantics conditionals are interpreted relative to an information state in accordance with the ramsey test ...
...by restricting s to the pworlds however information states are not modeled as simple sets ...

3  worlds  3 
Excerpts:
...are not modeled as simple sets of worlds but by means of a lewisian system ...
...means of a lewisian system of spheres worlds in the inner sphere are considered possible ...
...in the inner sphere are considered possible worlds outside of it are ruled out but ...

4  p  3 
Excerpts:
...accordance with the ramsey test idea if p then q is supported at a state ...
...way even when a state supports not p it is still possible to suppose p ...
...p it is still possible to suppose p consistently i argue that this account does ...

5  semantics  3 
Excerpts:
...conditionals that combines features of minimal change semantics and information semantics as in information semantics ...
...features of minimal change semantics and information semantics as in information semantics conditionals are interpreted ...
...semantics and information semantics as in information semantics conditionals are interpreted relative to an information ...

6  q  2 
Excerpts:
...the ramsey test idea if p then q is supported at a state s iff ...
...is supported at a state s iff q is supported at the hypothetical state sp ...

7  possible  2 
Excerpts:
...worlds in the inner sphere are considered possible worlds outside of it are ruled out ...
...state supports not p it is still possible to suppose p consistently i argue that ...

8  propose  2 
Excerpts:
... i propose an account of indicative conditionals that combines ...
...construe the role of a premise and propose a generalized notion of entailment that keeps ...

9  antecedent  2 
Excerpts:
...a conditional is logically independent from its antecedent ii that a sequence of antecedents behaves ...
...of antecedents behaves like a single conjunctive antecedent the importexport equivalence and iii that conditionals ...

Reference and Truth
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190829
Abstract:
I apply the notions of alethic reference introduced in previous work in the construction of several classical semantic truth theories. Furthermore, I provide prooftheoretic versions of those notions and use them to formulate axiomatic disquotational truth systems over classical logic. Some of these systems are shown to be sound, prooftheoretically strong, and compare well to the most renowned systems in the literature. Word Count:
Rank  Word  Count 
0  systems  3 
Excerpts:
...use them to formulate axiomatic disquotational truth systems over classical logic some of these systems ...
...systems over classical logic some of these systems are shown to be sound prooftheoretically strong ...
...and compare well to the most renowned systems in the literature ...

1  truth  2 
Excerpts:
...in the construction of several classical semantic truth theories furthermore i provide prooftheoretic versions of ...
...and use them to formulate axiomatic disquotational truth systems over classical logic some of these ...

2  classical  2 
Excerpts:
...previous work in the construction of several classical semantic truth theories furthermore i provide prooftheoretic ...
...to formulate axiomatic disquotational truth systems over classical logic some of these systems are shown ...

3  notions  2 
Excerpts:
... i apply the notions of alethic reference introduced in previous work ...
...furthermore i provide prooftheoretic versions of those notions and use them to formulate axiomatic disquotational ...

4  logic  1 
Excerpts:
...formulate axiomatic disquotational truth systems over classical logic some of these systems are shown to ...

5  over  1 
Excerpts:
...them to formulate axiomatic disquotational truth systems over classical logic some of these systems are ...

6  disquotational  1 
Excerpts:
...notions and use them to formulate axiomatic disquotational truth systems over classical logic some of ...

7  formulate  1 
Excerpts:
...of those notions and use them to formulate axiomatic disquotational truth systems over classical logic ...

8  axiomatic  1 
Excerpts:
...those notions and use them to formulate axiomatic disquotational truth systems over classical logic some ...

9  shown  1 
Excerpts:
...classical logic some of these systems are shown to be sound prooftheoretically strong and compare ...

Rabern's Semantics for Metaphysical and Epistemic Modalities and the Nesting Problem
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190827
Abstract:
In a recent paper, Brian Rabern suggests a semantics for languages with two kinds of modality, standard Kripkean metaphysical modality as well as epistemic modality. This semantics presents an alternative to twodimensionalism, which was developed in the last decades. Both Rabern's semantics and twodimensionalism are subject to a puzzle that Chalmers and Rabern (Analysis, 74(2), 210“224 2014) call the nesting problem. I will investigate how Rabern's semantics answers this puzzle. Word Count:
Realism and Empirical Equivalence
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190827
Abstract:
The main purpose of this paper is to investigate various notions of empirical equivalence in relation to the two main arguments for realism in the philosophy of science, namely the nomiracles argument and the indispensability argument. According to realism, one should believe in the existence of the theoretical entities (such as numbers and electrons) postulated by empirically adequate theories. According to the nomiracles argument, one should do so because truth is the the best explanation of empirical adequacy. According to the indispensability argument, one should do so because the theoretical terms employed in the formulation of an empirically adequate theory are practically indispensable for the formulation of its empirical content. The nomiracles argument might be refuted if one can establish an underdetermination thesis to the effect that every theory has empirically equivalent rivals that are incompatible with each other. Insofar as truth cannot explain the empirical adequacy of two incompatible theories, there is an obvious conflict between the underdetermination thesis and the nomiracles argument. I show that, under certain assumptions, some but not all notions of empirical equivalence support the underdetermination thesis. The indispensability argument might be refuted if one can establish a dispensability thesis to the effect that, for any theory with a practical formulation (e.g. for any axiomatizable theory), there is an empirically equivalent theory with a practical formulation in purely empirical terms. I show that (using axiomatizability as the measure of practicality) some but not all notions of empirical equivalence support this thesis. Word Count:
Rank  Word  Count 
0  empirical  7 
Excerpts:
...paper is to investigate various notions of empirical equivalence in relation to the two main ...
...truth is the the best explanation of empirical adequacy according to the indispensability argument one ...
...practically indispensable for the formulation of its empirical content the nomiracles argument might be refuted ...
...other insofar as truth cannot explain the empirical adequacy of two incompatible theories there is ...
...assumptions some but not all notions of empirical equivalence support the underdetermination thesis the indispensability ...
...theory with a practical formulation in purely empirical terms i show that using axiomatizability as ...
...practicality some but not all notions of empirical equivalence support this thesis ...

1  thesis  5 
Excerpts:
...refuted if one can establish an underdetermination thesis to the effect that every theory has ...
...is an obvious conflict between the underdetermination thesis and the nomiracles argument i show that ...
...notions of empirical equivalence support the underdetermination thesis the indispensability argument might be refuted if ...
...refuted if one can establish a dispensability thesis to the effect that for any theory ...
...all notions of empirical equivalence support this thesis ...

2  theory  5 
Excerpts:
...in the formulation of an empirically adequate theory are practically indispensable for the formulation of ...
...underdetermination thesis to the effect that every theory has empirically equivalent rivals that are incompatible ...
...thesis to the effect that for any theory with a practical formulation eg for any ...
...a practical formulation eg for any axiomatizable theory there is an empirically equivalent theory with ...
...axiomatizable theory there is an empirically equivalent theory with a practical formulation in purely empirical ...

3  empirically  4 
Excerpts:
...such as numbers and electrons postulated by empirically adequate theories according to the nomiracles argument ...
...terms employed in the formulation of an empirically adequate theory are practically indispensable for the ...
...to the effect that every theory has empirically equivalent rivals that are incompatible with each ...
...for any axiomatizable theory there is an empirically equivalent theory with a practical formulation in ...

4  formulation  4 
Excerpts:
...because the theoretical terms employed in the formulation of an empirically adequate theory are practically ...
...adequate theory are practically indispensable for the formulation of its empirical content the nomiracles argument ...
...that for any theory with a practical formulation eg for any axiomatizable theory there is ...
...an empirically equivalent theory with a practical formulation in purely empirical terms i show that ...

5  nomiracles  4 
Excerpts:
...in the philosophy of science namely the nomiracles argument and the indispensability argument according to ...
...by empirically adequate theories according to the nomiracles argument one should do so because truth ...
...the formulation of its empirical content the nomiracles argument might be refuted if one can ...
...conflict between the underdetermination thesis and the nomiracles argument i show that under certain assumptions ...

6  equivalence  3 
Excerpts:
...is to investigate various notions of empirical equivalence in relation to the two main arguments ...
...some but not all notions of empirical equivalence support the underdetermination thesis the indispensability argument ...
...some but not all notions of empirical equivalence support this thesis ...

7  should  3 
Excerpts:
...the indispensability argument according to realism one should believe in the existence of the theoretical ...
...theories according to the nomiracles argument one should do so because truth is the the ...
...adequacy according to the indispensability argument one should do so because the theoretical terms employed ...

8  notions  3 
Excerpts:
...of this paper is to investigate various notions of empirical equivalence in relation to the ...
...under certain assumptions some but not all notions of empirical equivalence support the underdetermination thesis ...
...measure of practicality some but not all notions of empirical equivalence support this thesis ...

9  indispensability  3 
Excerpts:
...science namely the nomiracles argument and the indispensability argument according to realism one should believe ...
...explanation of empirical adequacy according to the indispensability argument one should do so because the ...
...empirical equivalence support the underdetermination thesis the indispensability argument might be refuted if one can ...

Alethic Reference
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190816
Abstract:
I put forward precise and appealing notions of reference, selfreference, and wellfoundedness for sentences of the language of firstorder Peano arithmetic extended with a truth predicate. These notions are intended to play a central role in the study of the reference patterns that underlie expressions leading to semantic paradox and, thus, in the construction of philosophically wellmotivated semantic theories of truth. Word Count:
Rank  Word  Count 
0  reference  2 
Excerpts:
...put forward precise and appealing notions of reference selfreference and wellfoundedness for sentences of the ...
...central role in the study of the reference patterns that underlie expressions leading to semantic ...

1  semantic  2 
Excerpts:
...reference patterns that underlie expressions leading to semantic paradox and thus in the construction of ...
...thus in the construction of philosophically wellmotivated semantic theories of truth ...

2  truth  2 
Excerpts:
...of firstorder peano arithmetic extended with a truth predicate these notions are intended to play ...
...construction of philosophically wellmotivated semantic theories of truth ...

3  notions  2 
Excerpts:
... i put forward precise and appealing notions of reference selfreference and wellfoundedness for sentences ...
...arithmetic extended with a truth predicate these notions are intended to play a central role ...

4  expressions  1 
Excerpts:
...study of the reference patterns that underlie expressions leading to semantic paradox and thus in ...

5  role  1 
Excerpts:
...notions are intended to play a central role in the study of the reference patterns ...

6  underlie  1 
Excerpts:
...the study of the reference patterns that underlie expressions leading to semantic paradox and thus ...

7  patterns  1 
Excerpts:
...role in the study of the reference patterns that underlie expressions leading to semantic paradox ...

8  study  1 
Excerpts:
...to play a central role in the study of the reference patterns that underlie expressions ...

9  leading  1 
Excerpts:
...of the reference patterns that underlie expressions leading to semantic paradox and thus in the ...

Holism, Meaning Similarity and Inferential Space'a Measurement Theoretic Approach
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190801
Abstract:
Proponents of meaning holism often invoke notions of meaning similarity and semantic spatiality in order to counter accusations that holism renders language unstable and chaotic. However, talk of such notions often falls short of being explicit and formal. In this paper I present an algebraically couched theory of inferential similarity and spatiality, motivated by measurement theory, and I apply it to the discussion of meaning holism. I argue that the proposed theory offers new and improved conceptual resources for facing the challenges raised against the thesis. Word Count:
Rank  Word  Count 
0  theory  3 
Excerpts:
...this paper i present an algebraically couched theory of inferential similarity and spatiality motivated by ...
...inferential similarity and spatiality motivated by measurement theory and i apply it to the discussion ...
...meaning holism i argue that the proposed theory offers new and improved conceptual resources for ...

1  holism  3 
Excerpts:
... proponents of meaning holism often invoke notions of meaning similarity and ...
...spatiality in order to counter accusations that holism renders language unstable and chaotic however talk ...
...apply it to the discussion of meaning holism i argue that the proposed theory offers ...

2  meaning  3 
Excerpts:
... proponents of meaning holism often invoke notions of meaning similarity ...
...of meaning holism often invoke notions of meaning similarity and semantic spatiality in order to ...
...i apply it to the discussion of meaning holism i argue that the proposed theory ...

3  spatiality  2 
Excerpts:
...invoke notions of meaning similarity and semantic spatiality in order to counter accusations that holism ...
...algebraically couched theory of inferential similarity and spatiality motivated by measurement theory and i apply ...

4  similarity  2 
Excerpts:
...meaning holism often invoke notions of meaning similarity and semantic spatiality in order to counter ...
...present an algebraically couched theory of inferential similarity and spatiality motivated by measurement theory and ...

5  notions  2 
Excerpts:
... proponents of meaning holism often invoke notions of meaning similarity and semantic spatiality in ...
...unstable and chaotic however talk of such notions often falls short of being explicit and ...

6  often  2 
Excerpts:
... proponents of meaning holism often invoke notions of meaning similarity and semantic ...
...and chaotic however talk of such notions often falls short of being explicit and formal ...

7  discussion  1 
Excerpts:
...theory and i apply it to the discussion of meaning holism i argue that the ...

8  proposed  1 
Excerpts:
...of meaning holism i argue that the proposed theory offers new and improved conceptual resources ...

9  apply  1 
Excerpts:
...spatiality motivated by measurement theory and i apply it to the discussion of meaning holism ...

Notes on Stratified Semantics
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190801
Abstract:
In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature (see, e.g. Mares, Studia Logica 51(1), 1“20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71(1), 163“187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are (Fine, Journal of Philosophical Logic 17(1), 27“59, 1988; Mares, Studia Logica 51(1), 1“20, 1992), both of which are quite dense and technically challenging. Second, there are a number of prima facie reasons to be worried about stratified semantics. The purpose of this paper is to revitalize research on stratified semantics. I will do so by giving a ˜user friendly' presentation of the semantics, and by giving reasons to think that the prima facie reasons to be worried about it are too simplistic. Word Count:
On Generalization of Definitional Equivalence to NonDisjoint Languages
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190801
Abstract:
For simplicity, most of the literature introduces the concept of definitional equivalence only for disjoint languages. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to nondisjoint languages and they show that their generalization is not equivalent to intertranslatability in general. In this paper, we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce another formalization of definitional equivalence due to AndrÃ©ka and NÃ©meti which is equivalent to the Barrett“Halvorson generalization in the case of disjoint languages. We show that the AndrÃ©ka“NÃ©meti generalization is the smallest equivalence relation containing the Barrett“Halvorson generalization and it is equivalent to intertranslatability, which is another definition for definitional equivalence, even for nondisjoint languages. Finally, we investigate which definitions for definitional equivalences remain equivalent when we generalize them for theories in nondisjoint languages. Word Count:
Agglomerative Algebras
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190801
Abstract:
This paper investigates a generalization of Boolean algebras which I call agglomerative algebras. It also outlines two conceptions of propositions according to which they form an agglomerative algebra but not a Boolean algebra with respect to conjunction and negation. Word Count:
Rank  Word  Count 
0  algebra  2 
Excerpts:
...according to which they form an agglomerative algebra but not a boolean algebra with respect ...
...an agglomerative algebra but not a boolean algebra with respect to conjunction and negation ...

1  agglomerative  2 
Excerpts:
...generalization of boolean algebras which i call agglomerative algebras it also outlines two conceptions of ...
...propositions according to which they form an agglomerative algebra but not a boolean algebra with ...

2  algebras  2 
Excerpts:
...this paper investigates a generalization of boolean algebras which i call agglomerative algebras it also ...
...of boolean algebras which i call agglomerative algebras it also outlines two conceptions of propositions ...

3  boolean  2 
Excerpts:
... this paper investigates a generalization of boolean algebras which i call agglomerative algebras it ...
...form an agglomerative algebra but not a boolean algebra with respect to conjunction and negation ...

4  form  1 
Excerpts:
...conceptions of propositions according to which they form an agglomerative algebra but not a boolean ...

5  respect  1 
Excerpts:
...algebra but not a boolean algebra with respect to conjunction and negation ...

6  conjunction  1 
Excerpts:
...not a boolean algebra with respect to conjunction and negation ...

7  negation  1 
Excerpts:
...boolean algebra with respect to conjunction and negation ...

8  according  1 
Excerpts:
...it also outlines two conceptions of propositions according to which they form an agglomerative algebra ...

9  conceptions  1 
Excerpts:
...call agglomerative algebras it also outlines two conceptions of propositions according to which they form ...

Six Problems in Pure Inductive Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190801
Abstract:
We present six significant open problems in Pure Inductive Logic, together with their background and current status, with the intention of raising awareness and leading ultimately to their resolution. Word Count:
Rank  Word  Count 
0  their  2 
Excerpts:
...problems in pure inductive logic together with their background and current status with the intention ...
...of raising awareness and leading ultimately to their resolution ...

1  intention  1 
Excerpts:
...their background and current status with the intention of raising awareness and leading ultimately to ...

2  status  1 
Excerpts:
...logic together with their background and current status with the intention of raising awareness and ...

3  current  1 
Excerpts:
...inductive logic together with their background and current status with the intention of raising awareness ...

4  raising  1 
Excerpts:
...and current status with the intention of raising awareness and leading ultimately to their resolution ...

5  awareness  1 
Excerpts:
...current status with the intention of raising awareness and leading ultimately to their resolution ...

6  resolution  1 
Excerpts:
...raising awareness and leading ultimately to their resolution ...

7  ultimately  1 
Excerpts:
...the intention of raising awareness and leading ultimately to their resolution ...

8  leading  1 
Excerpts:
...with the intention of raising awareness and leading ultimately to their resolution ...

9  background  1 
Excerpts:
...in pure inductive logic together with their background and current status with the intention of ...

A New Game Equivalence, its Logic and Algebra
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20190801
Abstract:
We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games. Word Count:
Rank  Word  Count 
0  logic  3 
Excerpts:
...we provide a representation theorem a complete logic and a new game algebra for basic ...
...connections with imperfect information games and epistemic logic we also identify some new open problems ...
...also identify some new open problems concerning logic and games ...

1  new  3 
Excerpts:
... we present a new notion of game equivalence that captures basic ...
...representation theorem a complete logic and a new game algebra for basic powers in doing ...
...and epistemic logic we also identify some new open problems concerning logic and games ...

2  games  2 
Excerpts:
...so we establish connections with imperfect information games and epistemic logic we also identify some ...
...some new open problems concerning logic and games ...

3  basic  2 
Excerpts:
...new notion of game equivalence that captures basic powers of interacting players we provide a ...
...logic and a new game algebra for basic powers in doing so we establish connections ...

4  powers  2 
Excerpts:
...notion of game equivalence that captures basic powers of interacting players we provide a representation ...
...and a new game algebra for basic powers in doing so we establish connections with ...

5  game  2 
Excerpts:
... we present a new notion of game equivalence that captures basic powers of interacting ...
...theorem a complete logic and a new game algebra for basic powers in doing so ...

6  imperfect  1 
Excerpts:
...in doing so we establish connections with imperfect information games and epistemic logic we also ...

7  connections  1 
Excerpts:
...basic powers in doing so we establish connections with imperfect information games and epistemic logic ...

8  concerning  1 
Excerpts:
...we also identify some new open problems concerning logic and games ...

9  establish  1 
Excerpts:
...for basic powers in doing so we establish connections with imperfect information games and epistemic ...

