Correction to: Agglomerative Algebras
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
The original version of the article unfortunately contained a few mistakes. Word Count:
Rank  Word  Count 
0  original  1 
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... the original version of the article unfortunately contained a ...

1  version  1 
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... the original version of the article unfortunately contained a few ...

2  article  1 
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... the original version of the article unfortunately contained a few mistakes ...

3  unfortunately  1 
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... the original version of the article unfortunately contained a few mistakes ...

4  contained  1 
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...the original version of the article unfortunately contained a few mistakes ...

5  few  1 
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...version of the article unfortunately contained a few mistakes ...

6  mistakes  1 
Excerpts:
...of the article unfortunately contained a few mistakes ...

Correction to: KripkeCompleteness and Cutelimination Theorems for Intuitionistic Paradefinite Logics With and Without QuasiExplosion
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
The original version of this article unfortunately contains several errors introduced by the typesetter during the publishing process. It has been corrected. Word Count:
Rank  Word  Count 
0  original  1 
Excerpts:
... the original version of this article unfortunately contains several ...

1  version  1 
Excerpts:
... the original version of this article unfortunately contains several errors ...

2  article  1 
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... the original version of this article unfortunately contains several errors introduced by the ...

3  unfortunately  1 
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... the original version of this article unfortunately contains several errors introduced by the typesetter ...

4  contains  1 
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...the original version of this article unfortunately contains several errors introduced by the typesetter during ...

5  several  1 
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...original version of this article unfortunately contains several errors introduced by the typesetter during the ...

6  errors  1 
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...version of this article unfortunately contains several errors introduced by the typesetter during the publishing ...

7  introduced  1 
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...of this article unfortunately contains several errors introduced by the typesetter during the publishing process ...

8  typesetter  1 
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...unfortunately contains several errors introduced by the typesetter during the publishing process it has been ...

9  during  1 
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...contains several errors introduced by the typesetter during the publishing process it has been corrected ...

Transfinite Metainferences
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
In Barrio et al. (Forthcoming) Barrio Pailos and Szmuc prove that there are systems of logic that agree with classical logic up to any finite metainferential level, and disagree with it thereafter. This article presents a generalized sense of metainference that extends into the transfinite, and proves analogous results to all transfinite orders. Word Count:
Rank  Word  Count 
0  transfinite  2 
Excerpts:
...sense of metainference that extends into the transfinite and proves analogous results to all transfinite ...
...transfinite and proves analogous results to all transfinite orders ...

1  barrio  2 
Excerpts:
... in barrio et al forthcoming barrio pailos and szmuc ...
... in barrio et al forthcoming barrio pailos and szmuc prove that there are ...

2  logic  2 
Excerpts:
...szmuc prove that there are systems of logic that agree with classical logic up to ...
...systems of logic that agree with classical logic up to any finite metainferential level and ...

3  thereafter  1 
Excerpts:
...finite metainferential level and disagree with it thereafter this article presents a generalized sense of ...

4  all  1 
Excerpts:
...the transfinite and proves analogous results to all transfinite orders ...

5  results  1 
Excerpts:
...extends into the transfinite and proves analogous results to all transfinite orders ...

6  analogous  1 
Excerpts:
...that extends into the transfinite and proves analogous results to all transfinite orders ...

7  proves  1 
Excerpts:
...metainference that extends into the transfinite and proves analogous results to all transfinite orders ...

8  into  1 
Excerpts:
...a generalized sense of metainference that extends into the transfinite and proves analogous results to ...

9  extends  1 
Excerpts:
...presents a generalized sense of metainference that extends into the transfinite and proves analogous results ...

KripkeCompleteness and Cutelimination Theorems for Intuitionistic Paradefinite Logics With and Without QuasiExplosion
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
Two intuitionistic paradefinite logics N4C and N4C+ are introduced as Gentzentype sequent calculi. These logics are regarded as a combination of Nelson's paraconsistent fourvalued logic N4 and Wansing's basic constructive connexive logic C. The proposed logics are also regarded as intuitionistic variants of Arieli, Avron, and Zamansky's ideal paraconistent fourvalued logic 4CC. The logic N4C has no quasiexplosion axiom that represents a relationship between conflation and paraconsistent negation, but the logic N4C+ has this axiom. The Kripkecompleteness and cutelimination theorems for N4C and N4C+ are proved. Word Count:
Rank  Word  Count 
0  logic  5 
Excerpts:
...as a combination of nelsons paraconsistent fourvalued logic n4 and wansings basic constructive connexive logic ...
...logic n4 and wansings basic constructive connexive logic c the proposed logics are also regarded ...
...arieli avron and zamanskys ideal paraconistent fourvalued logic 4cc the logic n4c has no quasiexplosion ...
...zamanskys ideal paraconistent fourvalued logic 4cc the logic n4c has no quasiexplosion axiom that represents ...
...between conflation and paraconsistent negation but the logic n4c+ has this axiom the kripkecompleteness and ...

1  logics  3 
Excerpts:
... two intuitionistic paradefinite logics n4c and n4c+ are introduced as gentzentype ...
...are introduced as gentzentype sequent calculi these logics are regarded as a combination of nelsons ...
...basic constructive connexive logic c the proposed logics are also regarded as intuitionistic variants of ...

2  n4c  3 
Excerpts:
... two intuitionistic paradefinite logics n4c and n4c+ are introduced as gentzentype sequent ...
...ideal paraconistent fourvalued logic 4cc the logic n4c has no quasiexplosion axiom that represents a ...
...axiom the kripkecompleteness and cutelimination theorems for n4c and n4c+ are proved ...

3  n4c+  3 
Excerpts:
... two intuitionistic paradefinite logics n4c and n4c+ are introduced as gentzentype sequent ...
...ideal paraconistent fourvalued logic 4cc the logic n4c has no quasiexplosion axiom that represents a ...
...axiom the kripkecompleteness and cutelimination theorems for n4c and n4c+ are proved ...

4  intuitionistic  2 
Excerpts:
... two intuitionistic paradefinite logics n4c and n4c+ are introduced ...
...the proposed logics are also regarded as intuitionistic variants of arieli avron and zamanskys ideal ...

5  regarded  2 
Excerpts:
...as gentzentype sequent calculi these logics are regarded as a combination of nelsons paraconsistent fourvalued ...
...logic c the proposed logics are also regarded as intuitionistic variants of arieli avron and ...

6  axiom  2 
Excerpts:
...4cc the logic n4c has no quasiexplosion axiom that represents a relationship between conflation and ...
...negation but the logic n4c+ has this axiom the kripkecompleteness and cutelimination theorems for n4c ...

7  paraconsistent  2 
Excerpts:
...are regarded as a combination of nelsons paraconsistent fourvalued logic n4 and wansings basic constructive ...
...that represents a relationship between conflation and paraconsistent negation but the logic n4c+ has this ...

8  fourvalued  2 
Excerpts:
...regarded as a combination of nelsons paraconsistent fourvalued logic n4 and wansings basic constructive connexive ...
...of arieli avron and zamanskys ideal paraconistent fourvalued logic 4cc the logic n4c has no ...

9  ideal  1 
Excerpts:
...intuitionistic variants of arieli avron and zamanskys ideal paraconistent fourvalued logic 4cc the logic n4c ...

Inferences and Metainferences in ST
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the stricttolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+'s external logic and they question whether ST+'s solution to the semantic paradoxes is fundamentally different from LP+'s. Here we establish that by parity of reasoning, ST+ can be related to LP+'s dual logic K3+. We clarify the distinction between internal and external logic and argue that while ST+'s nonclassicality can be granted, its selfdual character does not tie it to LP+ more closely than to K3+. Word Count:
Rank  Word  Count 
0  logic  5 
Excerpts:
...correspondence between metainferences holding in the stricttolerant logic of transparent truth st+ and inferences holding ...
...truth st+ and inferences holding in the logic of paradox lp+ they argue that lp+ ...
...they argue that lp+ is st+s external logic and they question whether st+s solution to ...
...st+ can be related to lp+s dual logic k3+ we clarify the distinction between internal ...
...clarify the distinction between internal and external logic and argue that while st+s nonclassicality can ...

1  lp+  3 
Excerpts:

2  st+s  3 
Excerpts:

3  st+  2 
Excerpts:

4  establish  2 
Excerpts:
...a recent paper barrio tajer and rosenblatt establish a correspondence between metainferences holding in the ...
...is fundamentally different from lp+s here we establish that by parity of reasoning st+ can ...

5  holding  2 
Excerpts:
...and rosenblatt establish a correspondence between metainferences holding in the stricttolerant logic of transparent truth ...
...logic of transparent truth st+ and inferences holding in the logic of paradox lp+ they ...

6  k3+  2 
Excerpts:

7  external  2 
Excerpts:
...lp+ they argue that lp+ is st+s external logic and they question whether st+s solution ...
...we clarify the distinction between internal and external logic and argue that while st+s nonclassicality ...

8  lp+s  2 
Excerpts:

9  parity  1 
Excerpts:
...from lp+s here we establish that by parity of reasoning st+ can be related to ...

Brouwer's Weak Counterexamples and the Creative Subject: A Critical Survey
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
I survey Brouwer's weak counterexamples to classical theorems, with a view to discovering (i) what useful mathematical work is done by weak counterexamples; (ii) whether they are rigorous mathematical proofs or just plausibility arguments; (iii) the role of Brouwer's notion of the creative subject in them, and whether the creative subject is really necessary for them; (iv) what axioms for the creative subject are needed; (v) what relation there is between these arguments and Brouwer's theory of choice sequences. I refute one of Brouwer's claims with a weak counterexample of my own. I also examine Brouwer's 1927 proof of the negative continuity theorem, which appears to be a weak counterexample reliant on both the creative subject and the concept of choice sequence; I argue that it provides a good justification for the weak continuity principle, but it is not a weak counterexample and it does not depend essentially on the creative subject. Word Count:
Rank  Word  Count 
0  weak  6 
Excerpts:
... i survey brouwers weak counterexamples to classical theorems with a view ...
...what useful mathematical work is done by weak counterexamples ii whether they are rigorous mathematical ...
...refute one of brouwers claims with a weak counterexample of my own i also examine ...
...continuity theorem which appears to be a weak counterexample reliant on both the creative subject ...
...it provides a good justification for the weak continuity principle but it is not a ...
...continuity principle but it is not a weak counterexample and it does not depend essentially ...

1  brouwers  5 
Excerpts:
... i survey brouwers weak counterexamples to classical theorems with a ...
...just plausibility arguments iii the role of brouwers notion of the creative subject in them ...
...relation there is between these arguments and brouwers theory of choice sequences i refute one ...
...of choice sequences i refute one of brouwers claims with a weak counterexample of my ...
...counterexample of my own i also examine brouwers 1927 proof of the negative continuity theorem ...

2  creative  5 
Excerpts:
...the role of brouwers notion of the creative subject in them and whether the creative ...
...creative subject in them and whether the creative subject is really necessary for them iv ...
...for them iv what axioms for the creative subject are needed v what relation there ...
...a weak counterexample reliant on both the creative subject and the concept of choice sequence ...
...it does not depend essentially on the creative subject ...

3  subject  5 
Excerpts:
...role of brouwers notion of the creative subject in them and whether the creative subject ...
...subject in them and whether the creative subject is really necessary for them iv what ...
...them iv what axioms for the creative subject are needed v what relation there is ...
...weak counterexample reliant on both the creative subject and the concept of choice sequence i ...
...does not depend essentially on the creative subject ...

4  counterexample  3 
Excerpts:
...one of brouwers claims with a weak counterexample of my own i also examine brouwers ...
...theorem which appears to be a weak counterexample reliant on both the creative subject and ...
...principle but it is not a weak counterexample and it does not depend essentially on ...

5  them  2 
Excerpts:
...brouwers notion of the creative subject in them and whether the creative subject is really ...
...the creative subject is really necessary for them iv what axioms for the creative subject ...

6  counterexamples  2 
Excerpts:
... i survey brouwers weak counterexamples to classical theorems with a view to ...
...useful mathematical work is done by weak counterexamples ii whether they are rigorous mathematical proofs ...

7  arguments  2 
Excerpts:
...are rigorous mathematical proofs or just plausibility arguments iii the role of brouwers notion of ...
...v what relation there is between these arguments and brouwers theory of choice sequences i ...

8  choice  2 
Excerpts:
...between these arguments and brouwers theory of choice sequences i refute one of brouwers claims ...
...the creative subject and the concept of choice sequence i argue that it provides a ...

9  mathematical  2 
Excerpts:
...a view to discovering i what useful mathematical work is done by weak counterexamples ii ...
...weak counterexamples ii whether they are rigorous mathematical proofs or just plausibility arguments iii the ...

Rosenkranz's Logic of Justification and Unprovability
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
Rosenkranz has recently proposed a logic for propositional, nonfactive, allthingsconsidered justification, which is based on a logic for the notion of being in a position to know (Rosenkranz Mind, 127(506), 309“338 2018). Starting from three quite weak assumptions in addition to some of the core principles that are already accepted by Rosenkranz, I prove that, if one has positive introspective and modally robust knowledge of the axioms of minimal arithmetic, then one is in a position to know that a sentence is not provable in minimal arithmetic or that the negation of that sentence is not provable in minimal arithmetic. This serves as the formal background for an example that calls into question the correctness of Rosenkranz's logic of justification. Word Count:
Predicate Change
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
Like belief revision, conceptual change has rational aspects. The paper discusses this for predicate change. We determine the meaning of predicates by a set of imaginable instances, i.e., conceptually consistent entities that fall under the predicate. Predicate change is then an alteration of which possible entities are instances of a concept. The recent exclusion of Pluto from the category of planets is an example of such a predicate change. In order to discuss predicate change, we define a monadic predicate logic with three different kinds of lawful belief: analytic laws, which hold for all possible instances; doxastic laws, which hold for the most plausible instances; and typicality laws, which hold for typical instances. We introduce predicate changing operations that alter the analytic laws of the language and show that the expressive power is not affected by the predicate change. One can translate the new laws into old laws and vice versa. Moreover, we discuss rational restrictions of predicate change. These limit its possible influence on doxastic and typicality laws. Based on the results, we argue that predicate change can be quite conservative and sometimes even hardly recognisable. Word Count:
Rank  Word  Count 
0  predicate  10 
Excerpts:
...rational aspects the paper discusses this for predicate change we determine the meaning of predicates ...
...conceptually consistent entities that fall under the predicate predicate change is then an alteration of ...
...consistent entities that fall under the predicate predicate change is then an alteration of which ...
...planets is an example of such a predicate change in order to discuss predicate change ...
...a predicate change in order to discuss predicate change we define a monadic predicate logic ...
...discuss predicate change we define a monadic predicate logic with three different kinds of lawful ...
...which hold for typical instances we introduce predicate changing operations that alter the analytic laws ...
...expressive power is not affected by the predicate change one can translate the new laws ...
...versa moreover we discuss rational restrictions of predicate change these limit its possible influence on ...
...based on the results we argue that predicate change can be quite conservative and sometimes ...

1  change  8 
Excerpts:
... like belief revision conceptual change has rational aspects the paper discusses this ...
...aspects the paper discusses this for predicate change we determine the meaning of predicates by ...
...entities that fall under the predicate predicate change is then an alteration of which possible ...
...is an example of such a predicate change in order to discuss predicate change we ...
...predicate change in order to discuss predicate change we define a monadic predicate logic with ...
...power is not affected by the predicate change one can translate the new laws into ...
...moreover we discuss rational restrictions of predicate change these limit its possible influence on doxastic ...
...on the results we argue that predicate change can be quite conservative and sometimes even ...

2  laws  7 
Excerpts:
...three different kinds of lawful belief analytic laws which hold for all possible instances doxastic ...
...which hold for all possible instances doxastic laws which hold for the most plausible instances ...
...for the most plausible instances and typicality laws which hold for typical instances we introduce ...
...predicate changing operations that alter the analytic laws of the language and show that the ...
...predicate change one can translate the new laws into old laws and vice versa moreover ...
...can translate the new laws into old laws and vice versa moreover we discuss rational ...
...its possible influence on doxastic and typicality laws based on the results we argue that ...

3  instances  5 
Excerpts:
...of predicates by a set of imaginable instances ie conceptually consistent entities that fall under ...
...an alteration of which possible entities are instances of a concept the recent exclusion of ...
...analytic laws which hold for all possible instances doxastic laws which hold for the most ...
...laws which hold for the most plausible instances and typicality laws which hold for typical ...
...and typicality laws which hold for typical instances we introduce predicate changing operations that alter ...

4  hold  3 
Excerpts:
...kinds of lawful belief analytic laws which hold for all possible instances doxastic laws which ...
...for all possible instances doxastic laws which hold for the most plausible instances and typicality ...
...most plausible instances and typicality laws which hold for typical instances we introduce predicate changing ...

5  possible  3 
Excerpts:
...change is then an alteration of which possible entities are instances of a concept the ...
...belief analytic laws which hold for all possible instances doxastic laws which hold for the ...
...restrictions of predicate change these limit its possible influence on doxastic and typicality laws based ...

6  analytic  2 
Excerpts:
...with three different kinds of lawful belief analytic laws which hold for all possible instances ...
...introduce predicate changing operations that alter the analytic laws of the language and show that ...

7  rational  2 
Excerpts:
... like belief revision conceptual change has rational aspects the paper discusses this for predicate ...
...laws and vice versa moreover we discuss rational restrictions of predicate change these limit its ...

8  belief  2 
Excerpts:
... like belief revision conceptual change has rational aspects the ...
...logic with three different kinds of lawful belief analytic laws which hold for all possible ...

9  typicality  2 
Excerpts:
...hold for the most plausible instances and typicality laws which hold for typical instances we ...
...limit its possible influence on doxastic and typicality laws based on the results we argue ...

A StateofAffairsSemantic Solution to the Problem of Extensionality in Free Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
If one takes seriously the idea that a scientific language must be extensional, and accepts Quine's notion of truthvaluerelated extensionality, and also recognizes that a scientific language must allow for singular terms that do not refer to existing objects, then there is a problem, since this combination of assumptions must be inconsistent. I will argue for a particular solution to the problem, namely, changing what is meant by the word ˜extensionality', so that it would not be the truthvalue that had to be preserved under the substitution of coextensional expressions, but the state of affairs that the sentence described. The question is whether or not elementary sentences containing empty singular terms, such as ˜Vulcan rotates', are extensional in the substitutivity sense. Five conditions are specified under which extensionality in the substitutivity sense of such sentences can be secured. It is demonstrated that such sentences are stateofaffairsasextensionrelated extensional. This implies (in accordance with the basic idea of stateofaffairs semantics) that such sentences are also truthvaluerelated extensional in Quine's sense, but not truthvalueasextensionrelated extensional. Word Count:
Between Atomism and Superatomism
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is wellfounded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these two theses in terms of its relative strength: strong atomism, the claim that every maximal proper parthood chain terminates. Although strong atomism is equivalent to superatomism in classical extensional mereology, it is strictly weaker than it in strictly weaker systems in which parthood is a partial order. And it is strictly stronger than standard atomism in classical extensional mereology and, given the axiom of choice, in such strictly weaker systems as well. Though strong atomism has not, to my knowledge, been explicitly identified, Shiver appears to have it in mind, though it is unclear whether he recognizes that it is not equivalent to standard atomism in each of the mereologies he considers. I prove these logical relationships which hold amongst these three atomistic principles, and argue that, whether one adopts classical extensional mereology or a system strictly weaker than it in which parthood is a partial order, standard atomism is a more defensible addition to one's mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis. Word Count:
Rank  Word  Count 
0  atomism  9 
Excerpts:
...two explicitly and one implicitly first standard atomism is the claim that everything is composed ...
...of atoms and is very often how atomism is characterized in the literature second superatomism ...
...discussed as a stronger alternative to standard atomism third there is a principle that lies ...
...in terms of its relative strength strong atomism the claim that every maximal proper parthood ...
...maximal proper parthood chain terminates although strong atomism is equivalent to superatomism in classical extensional ...
...and it is strictly stronger than standard atomism in classical extensional mereology and given the ...
...strictly weaker systems as well though strong atomism has not to my knowledge been explicitly ...
...that it is not equivalent to standard atomism in each of the mereologies he considers ...
...which parthood is a partial order standard atomism is a more defensible addition to ones ...

1  standard  5 
Excerpts:
...literature two explicitly and one implicitly first standard atomism is the claim that everything is ...
...been discussed as a stronger alternative to standard atomism third there is a principle that ...
...order and it is strictly stronger than standard atomism in classical extensional mereology and given ...
...recognizes that it is not equivalent to standard atomism in each of the mereologies he ...
...in which parthood is a partial order standard atomism is a more defensible addition to ...

2  parthood  5 
Excerpts:
...literature second superatomism is the claim that parthood is wellfounded which implies that every proper ...
...is wellfounded which implies that every proper parthood chain terminates and has been discussed as ...
...atomism the claim that every maximal proper parthood chain terminates although strong atomism is equivalent ...
...it in strictly weaker systems in which parthood is a partial order and it is ...
...system strictly weaker than it in which parthood is a partial order standard atomism is ...

3  strictly  5 
Excerpts:
...superatomism in classical extensional mereology it is strictly weaker than it in strictly weaker systems ...
...it is strictly weaker than it in strictly weaker systems in which parthood is a ...
...is a partial order and it is strictly stronger than standard atomism in classical extensional ...
...given the axiom of choice in such strictly weaker systems as well though strong atomism ...
...adopts classical extensional mereology or a system strictly weaker than it in which parthood is ...

4  weaker  4 
Excerpts:
...in classical extensional mereology it is strictly weaker than it in strictly weaker systems in ...
...is strictly weaker than it in strictly weaker systems in which parthood is a partial ...
...the axiom of choice in such strictly weaker systems as well though strong atomism has ...
...classical extensional mereology or a system strictly weaker than it in which parthood is a ...

5  mereology  4 
Excerpts:
...is equivalent to superatomism in classical extensional mereology it is strictly weaker than it in ...
...stronger than standard atomism in classical extensional mereology and given the axiom of choice in ...
...argue that whether one adopts classical extensional mereology or a system strictly weaker than it ...
...is a more defensible addition to ones mereology than either of the other two principles ...

6  strong  3 
Excerpts:
...theses in terms of its relative strength strong atomism the claim that every maximal proper ...
...every maximal proper parthood chain terminates although strong atomism is equivalent to superatomism in classical ...
...such strictly weaker systems as well though strong atomism has not to my knowledge been ...

7  atomistic  3 
Excerpts:
... there are at least three vaguely atomistic principles that have come up in the ...
...logical relationships which hold amongst these three atomistic principles and argue that whether one adopts ...
...regarded as the best formulation of the atomistic thesis ...

8  principles  3 
Excerpts:
...there are at least three vaguely atomistic principles that have come up in the literature ...
...relationships which hold amongst these three atomistic principles and argue that whether one adopts classical ...
...mereology than either of the other two principles and it should be regarded as the ...

9  extensional  3 
Excerpts:
...atomism is equivalent to superatomism in classical extensional mereology it is strictly weaker than it ...
...strictly stronger than standard atomism in classical extensional mereology and given the axiom of choice ...
...and argue that whether one adopts classical extensional mereology or a system strictly weaker than ...

Collective Opinion as Tendency Towards Consensus
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201107
Abstract:
Group beliefs in social networks are often construed as arising from individual beliefs through processes of update and aggregation. In this paper, we explore an alternative ˜arational' perspective. More specifically, we focus on group attitudes as neutral tendencies toward alignment of opinions driven by influence patterns among agents modeled in a Markov dynamics. In addition, we investigate logical patterns in the resulting potential group beliefs or, in more neutral arational terminology: collective opinion structures. Word Count:
Plurals and Mereology
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201026
Abstract:
In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We identify four main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and wellmotivated framework for the analysis of plurals. Word Count:
Rank  Word  Count 
0  approach  4 
Excerpts:
... in linguistics the dominant approach to the semantics of plurals appeals to ...
...of plurals appeals to mereology however this approach has received strong criticisms from philosophical logicians ...
...offer a precise characterization of the mereological approach and the semantic background in which the ...
...the strengths and shortcomings of the mereological approach and plural logic our conclusion is that ...

1  framework  2 
Excerpts:
...philosophical logicians who subscribe to an alternative framework based on plural logic in the first ...
...the former remains a viable and wellmotivated framework for the analysis of plurals ...

2  mereological  2 
Excerpts:
...we offer a precise characterization of the mereological approach and the semantic background in which ...
...compare the strengths and shortcomings of the mereological approach and plural logic our conclusion is ...

3  part  2 
Excerpts:
...based on plural logic in the first part of the article we offer a precise ...
...can be meaningfully reconstructed in the second part we deal with the criticisms and assess ...

4  philosophical  2 
Excerpts:
...this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework ...
...criticisms and assess their logical linguistic and philosophical significance we identify four main objections and ...

5  criticisms  2 
Excerpts:
...mereology however this approach has received strong criticisms from philosophical logicians who subscribe to an ...
...the second part we deal with the criticisms and assess their logical linguistic and philosophical ...

6  plural  2 
Excerpts:
...subscribe to an alternative framework based on plural logic in the first part of the ...
...and shortcomings of the mereological approach and plural logic our conclusion is that the former ...

7  logic  2 
Excerpts:
...to an alternative framework based on plural logic in the first part of the article ...
...shortcomings of the mereological approach and plural logic our conclusion is that the former remains ...

8  plurals  2 
Excerpts:
...the dominant approach to the semantics of plurals appeals to mereology however this approach has ...
...and wellmotivated framework for the analysis of plurals ...

9  significance  1 
Excerpts:
...and assess their logical linguistic and philosophical significance we identify four main objections and show ...

What is the Meaning of Proofs?
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201022
Abstract:
The origins of prooftheoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further and ask about the meaning of a proof as a whole? In this paper we address this question and lay out a framework to distinguish sense and denotation of proofs. Two questions are central here. First of all, if we have two (syntactically) different derivations, does this always lead to a difference, firstly, in sense, and secondly, in denotation? The other question is about the relation between different kinds of proof systems (here: natural deduction vs. sequent calculi) with respect to this distinction. Do the different forms of representing a proof necessarily correspond to a difference in how the inferential steps are given? In our framework it will be possible to identify denotation as well as sense of proofs not only within one proof system but also between different kinds of proof systems. Thus, we give an account to distinguish a mere syntactic divergence from a divergence in meaning and a divergence in meaning from a divergence of proof objects analogous to Frege's distinction for singular terms and sentences. Word Count:
Rank  Word  Count 
0  proof  6 
Excerpts:
...and ask about the meaning of a proof as a whole in this paper we ...
...about the relation between different kinds of proof systems here natural deduction vs sequent calculi ...
...do the different forms of representing a proof necessarily correspond to a difference in how ...
...sense of proofs not only within one proof system but also between different kinds of ...
...system but also between different kinds of proof systems thus we give an account to ...
...divergence in meaning from a divergence of proof objects analogous to freges distinction for singular ...

1  meaning  4 
Excerpts:
...in the question of what constitutes the meaning of the logical connectives and its response ...
...a step further and ask about the meaning of a proof as a whole in ...
...mere syntactic divergence from a divergence in meaning and a divergence in meaning from a ...
...divergence in meaning and a divergence in meaning from a divergence of proof objects analogous ...

2  different  4 
Excerpts:
...of all if we have two syntactically different derivations does this always lead to a ...
...other question is about the relation between different kinds of proof systems here natural deduction ...
...with respect to this distinction do the different forms of representing a proof necessarily correspond ...
...within one proof system but also between different kinds of proof systems thus we give ...

3  divergence  4 
Excerpts:
...an account to distinguish a mere syntactic divergence from a divergence in meaning and a ...
...distinguish a mere syntactic divergence from a divergence in meaning and a divergence in meaning ...
...from a divergence in meaning and a divergence in meaning from a divergence of proof ...
...and a divergence in meaning from a divergence of proof objects analogous to freges distinction ...

4  sense  3 
Excerpts:
...and lay out a framework to distinguish sense and denotation of proofs two questions are ...
...always lead to a difference firstly in sense and secondly in denotation the other question ...
...possible to identify denotation as well as sense of proofs not only within one proof ...

5  question  3 
Excerpts:
...origins of prooftheoretic semantics lie in the question of what constitutes the meaning of the ...
...whole in this paper we address this question and lay out a framework to distinguish ...
...sense and secondly in denotation the other question is about the relation between different kinds ...

6  denotation  3 
Excerpts:
...out a framework to distinguish sense and denotation of proofs two questions are central here ...
...difference firstly in sense and secondly in denotation the other question is about the relation ...
...framework it will be possible to identify denotation as well as sense of proofs not ...

7  distinguish  2 
Excerpts:
...question and lay out a framework to distinguish sense and denotation of proofs two questions ...
...systems thus we give an account to distinguish a mere syntactic divergence from a divergence ...

8  kinds  2 
Excerpts:
...question is about the relation between different kinds of proof systems here natural deduction vs ...
...one proof system but also between different kinds of proof systems thus we give an ...

9  proofs  2 
Excerpts:
...framework to distinguish sense and denotation of proofs two questions are central here first of ...
...identify denotation as well as sense of proofs not only within one proof system but ...

On Negation for Nonclassical Set Theories
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201022
Abstract:
We present a case study for the debate between the American and the Australian plans, analyzing a crucial aspect of negation: expressivity within a theory. We discuss the case of nonclassical set theories, presenting three different negations and testing their expressivity within algebravalued structures for ZFlike set theories. We end by proposing a minimal definitional account of negation, inspired by the algebraic framework discussed. Word Count:
Rank  Word  Count 
0  theories  2 
Excerpts:
...we discuss the case of nonclassical set theories presenting three different negations and testing their ...
...expressivity within algebravalued structures for zflike set theories we end by proposing a minimal definitional ...

1  negation  2 
Excerpts:
...australian plans analyzing a crucial aspect of negation expressivity within a theory we discuss the ...
...by proposing a minimal definitional account of negation inspired by the algebraic framework discussed ...

2  case  2 
Excerpts:
... we present a case study for the debate between the american ...
...expressivity within a theory we discuss the case of nonclassical set theories presenting three different ...

3  set  2 
Excerpts:
...theory we discuss the case of nonclassical set theories presenting three different negations and testing ...
...their expressivity within algebravalued structures for zflike set theories we end by proposing a minimal ...

4  within  2 
Excerpts:
...analyzing a crucial aspect of negation expressivity within a theory we discuss the case of ...
...three different negations and testing their expressivity within algebravalued structures for zflike set theories we ...

5  expressivity  2 
Excerpts:
...plans analyzing a crucial aspect of negation expressivity within a theory we discuss the case ...
...presenting three different negations and testing their expressivity within algebravalued structures for zflike set theories ...

6  their  1 
Excerpts:
...theories presenting three different negations and testing their expressivity within algebravalued structures for zflike set ...

7  algebravalued  1 
Excerpts:
...different negations and testing their expressivity within algebravalued structures for zflike set theories we end ...

8  structures  1 
Excerpts:
...negations and testing their expressivity within algebravalued structures for zflike set theories we end by ...

9  zflike  1 
Excerpts:
...testing their expressivity within algebravalued structures for zflike set theories we end by proposing a ...

More Aboutness in Imagination
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201008
Abstract:
In Berto's logic for aboutness in imagination, the output content of an imaginative episode must be part of the initial content of the episode (Berto, Philos Stud 175:1871“1886, 2018). This condition predicts expressions of perfectly legitimate imaginative episodes to be false. Thus, this condition is too strict. Relaxing the condition to correctly model these cases requires to consider a language with predicates and constants. The paper extends Berto's semantics for aboutness in imagination to a semantics for such a language. The new semantics models contents of formulas along the lines of Hawke's issuebased theory of topics (Hawke, Australas J Philos 96:697“723, 2017), while remaining faithful to the (in)validities discussed by Berto. Several relations between issues and topics are defined, which allow to overcome shortcomings of Hawke's initial framework. These relations are then discussed with respect to their usefulness in the truth condition for the imagination operator. Word Count:
A Relevant Logic of Questions
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201001
Abstract:
This paper introduces the inquisitive extension of R, denoted as InqR, which is a relevant logic of questions based on the logic R as the background logic of declaratives. A semantics for InqR is developed, and it is shown that this semantics is, in a precisely defined sense, dual to RoutleyMeyer semantics for R. Moreover, InqR is axiomatized and completeness of the axiomatic system is established. The philosophical interpretation of the duality between RoutleyMeyer semantics and the semantics for InqR is also discussed. Word Count:
Rank  Word  Count 
0  semantics  5 
Excerpts:
...as the background logic of declaratives a semantics for inqr is developed and it is ...
...developed and it is shown that this semantics is in a precisely defined sense dual ...
...a precisely defined sense dual to routleymeyer semantics for r moreover inqr is axiomatized and ...
...philosophical interpretation of the duality between routleymeyer semantics and the semantics for inqr is also ...
...the duality between routleymeyer semantics and the semantics for inqr is also discussed ...

1  inqr  4 
Excerpts:
...the inquisitive extension of r denoted as inqr which is a relevant logic of questions ...
...background logic of declaratives a semantics for inqr is developed and it is shown that ...
...dual to routleymeyer semantics for r moreover inqr is axiomatized and completeness of the axiomatic ...
...between routleymeyer semantics and the semantics for inqr is also discussed ...

2  r  3 
Excerpts:
...this paper introduces the inquisitive extension of r denoted as inqr which is a relevant ...
...logic of questions based on the logic r as the background logic of declaratives a ...
...defined sense dual to routleymeyer semantics for r moreover inqr is axiomatized and completeness of ...

3  logic  3 
Excerpts:
...denoted as inqr which is a relevant logic of questions based on the logic r ...
...relevant logic of questions based on the logic r as the background logic of declaratives ...
...on the logic r as the background logic of declaratives a semantics for inqr is ...

4  routleymeyer  2 
Excerpts:
...in a precisely defined sense dual to routleymeyer semantics for r moreover inqr is axiomatized ...
...the philosophical interpretation of the duality between routleymeyer semantics and the semantics for inqr is ...

5  introduces  1 
Excerpts:
... this paper introduces the inquisitive extension of r denoted as ...

6  dual  1 
Excerpts:
...semantics is in a precisely defined sense dual to routleymeyer semantics for r moreover inqr ...

7  duality  1 
Excerpts:
...is established the philosophical interpretation of the duality between routleymeyer semantics and the semantics for ...

8  interpretation  1 
Excerpts:
...the axiomatic system is established the philosophical interpretation of the duality between routleymeyer semantics and ...

9  philosophical  1 
Excerpts:
...of the axiomatic system is established the philosophical interpretation of the duality between routleymeyer semantics ...

Infinitesimal Gunk
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201001
Abstract:
In this paper, I advance an original view of the structure of space called Infinitesimal Gunk. This view says that every region of space can be further divided and some regions have infinitesimal size, where infinitesimals are understood in the framework of Robinson's (1966) nonstandard analysis. This view, I argue, provides a novel reply to the inconsistency arguments proposed by Arntzenius (2008) and Russell (2008), which have troubled a more familiar gunky approach. Moreover, it has important advantages over the alternative views these authors suggested. Unlike Arntzenius's proposal, it does not introduce regions with no interior. It also has a much richer measure theory than Russell's proposal and does not retreat to mere finite additivity. Word Count:
Rank  Word  Count 
0  does  2 
Excerpts:
...these authors suggested unlike arntzeniuss proposal it does not introduce regions with no interior it ...
...richer measure theory than russells proposal and does not retreat to mere finite additivity ...

1  proposal  2 
Excerpts:
...alternative views these authors suggested unlike arntzeniuss proposal it does not introduce regions with no ...
...a much richer measure theory than russells proposal and does not retreat to mere finite ...

2  space  2 
Excerpts:
...an original view of the structure of space called infinitesimal gunk this view says that ...
...this view says that every region of space can be further divided and some regions ...

3  infinitesimal  2 
Excerpts:
...view of the structure of space called infinitesimal gunk this view says that every region ...
...be further divided and some regions have infinitesimal size where infinitesimals are understood in the ...

4  regions  2 
Excerpts:
...space can be further divided and some regions have infinitesimal size where infinitesimals are understood ...
...unlike arntzeniuss proposal it does not introduce regions with no interior it also has a ...

5  approach  1 
Excerpts:
...which have troubled a more familiar gunky approach moreover it has important advantages over the ...

6  moreover  1 
Excerpts:
...have troubled a more familiar gunky approach moreover it has important advantages over the alternative ...

7  important  1 
Excerpts:
...more familiar gunky approach moreover it has important advantages over the alternative views these authors ...

8  advantages  1 
Excerpts:
...familiar gunky approach moreover it has important advantages over the alternative views these authors suggested ...

9  over  1 
Excerpts:
...gunky approach moreover it has important advantages over the alternative views these authors suggested unlike ...

Probability Modals and Infinite Domains
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201001
Abstract:
Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of probabilistic' semantics are often motivated by their ability to explain intuitions about inferences involving likely' and probably''intuitions that Angelika Kratzer's canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to undercut this motivation: they present a worldordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of worldordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard's semantics yields an adequate logic only if models are restricted to Noetherian preorders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data. Word Count:
Rank  Word  Count 
0  semantics  10 
Excerpts:
...the mathematical theory of probability to the semantics of natural language probability talk these sorts ...
...language probability talk these sorts of probabilistic semantics are often motivated by their ability to ...
...likely and probablyintuitions that angelika kratzers canonical semantics fails to accommodate through a semantics based ...
...canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds ...
...undercut this motivation they present a worldordering semantics that yields essentially the same logic as ...
...yields essentially the same logic as probabilistic semantics in this paper i argue that the ...
...that the challenge remains defenders of worldordering semantics have yet to offer a plausible semantics ...
...semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood ...
...logic of comparative likelihood holliday amp icards semantics yields an adequate logic only if models ...
...of epistemic possibilities as a result probabilistic semantics remains the better explanation of the data ...

1  logic  3 
Excerpts:
...worldordering semantics that yields essentially the same logic as probabilistic semantics in this paper i ...
...offer a plausible semantics that captures the logic of comparative likelihood holliday amp icards semantics ...
...holliday amp icards semantics yields an adequate logic only if models are restricted to noetherian ...

2  probabilistic  3 
Excerpts:
...natural language probability talk these sorts of probabilistic semantics are often motivated by their ability ...
...that yields essentially the same logic as probabilistic semantics in this paper i argue that ...
...domains of epistemic possibilities as a result probabilistic semantics remains the better explanation of the ...

3  recent  2 
Excerpts:
... recent years have witnessed a proliferation of attempts ...
...and a qualitative ranking of propositions however recent work by wesley holliday and thomas icard ...

4  holliday  2 
Excerpts:
...of propositions however recent work by wesley holliday and thomas icard has been widely thought ...
...that captures the logic of comparative likelihood holliday amp icards semantics yields an adequate logic ...

5  worldordering  2 
Excerpts:
...to undercut this motivation they present a worldordering semantics that yields essentially the same logic ...
...argue that the challenge remains defenders of worldordering semantics have yet to offer a plausible ...

6  yields  2 
Excerpts:
...motivation they present a worldordering semantics that yields essentially the same logic as probabilistic semantics ...
...of comparative likelihood holliday amp icards semantics yields an adequate logic only if models are ...

7  remains  2 
Excerpts:
...this paper i argue that the challenge remains defenders of worldordering semantics have yet to ...
...epistemic possibilities as a result probabilistic semantics remains the better explanation of the data ...

8  noetherian  2 
Excerpts:
...logic only if models are restricted to noetherian preorders but i argue that the noetherian ...
...noetherian preorders but i argue that the noetherian restriction faces problems in cases involving infinitely ...

9  involving  2 
Excerpts:
...their ability to explain intuitions about inferences involving likely and probablyintuitions that angelika kratzers canonical ...
...the noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities as ...

Revising Probabilities and Full Beliefs
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201001
Abstract:
A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a proposition if and only if she considers the probability that it is false to be so close to zero that she chooses to disregard that probability. She treats such a proposition as having the probability 1, but, importantly, she is still willing and able to revise that probability assignment if she receives information that gives her sufficient reasons to do so. Such a proposition is (presently) undoubted, but not undoubtable (incorrigible). In the formal model it is assigned a probability 1 ˆ’ Î´, where Î´ is an infinitesimal number. The proposed model employs probabilistic belief states that contain several underlying probability functions representing alternative probabilistic states of the world. Furthermore, a distinction is made between update and revision, in the same way as in the literature on (dichotomous) belief change. The formal properties of the model are investigated, including properties relevant for learning from experience. The set of propositions whose probabilities are infinitesimally close to 1 forms a (logically closed) belief set. Operations that change the probabilistic belief state give rise to changes in this belief set, which have much in common with traditional operations of belief change. Word Count:
A Paraconsistent Conditional Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201001
Abstract:
We develop a paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection functions which are variants of Chellas' conditional models. The acceptance and rejection conditions are substituted for truth conditions of conditionals. The paraconsistent conditional logic is axiomatized by a sequent system
\(\mathcal {C}\)
which is an extension of the BelnapDunn fourvalued logic with a conditional operator. Some acceptive extensions of
\(\mathcal {C}\)
are shown to be sound and complete. We also show the finite acceptive model property and decidability of these logics. Word Count:
Rank  Word  Count 
0  logic  3 
Excerpts:
... we develop a paraconsistent logic by introducing new models for conditionals with ...
...truth conditions of conditionals the paraconsistent conditional logic is axiomatized by a sequent system
...
...is an extension of the belnapdunn fourvalued logic with a conditional operator some acceptive extensions ...

1  acceptive  3 
Excerpts:
...by introducing new models for conditionals with acceptive and rejective selection functions which are variants ...
...fourvalued logic with a conditional operator some acceptive extensions of
...
...and complete we also show the finite acceptive model property and decidability of these logics ...

2  conditional  3 
Excerpts:
...selection functions which are variants of chellas conditional models the acceptance and rejection conditions are ...
...for truth conditions of conditionals the paraconsistent conditional logic is axiomatized by a sequent system ...
...of the belnapdunn fourvalued logic with a conditional operator some acceptive extensions of
...

3  mathcal  2 
Excerpts:
...system
mathcal c
...
...of
mathcal c
...

4  models  2 
Excerpts:
...develop a paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection ...
...functions which are variants of chellas conditional models the acceptance and rejection conditions are substituted ...

5  conditionals  2 
Excerpts:
...paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection functions which ...
...conditions are substituted for truth conditions of conditionals the paraconsistent conditional logic is axiomatized by ...

6  paraconsistent  2 
Excerpts:
... we develop a paraconsistent logic by introducing new models for conditionals ...
...substituted for truth conditions of conditionals the paraconsistent conditional logic is axiomatized by a sequent ...

7  c  2 
Excerpts:

8  conditions  2 
Excerpts:
...chellas conditional models the acceptance and rejection conditions are substituted for truth conditions of conditionals ...
...and rejection conditions are substituted for truth conditions of conditionals the paraconsistent conditional logic is ...

9  extensions  1 
Excerpts:
...logic with a conditional operator some acceptive extensions of
...

