Counterfactual Logic and the Necessity of Mathematics
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200626
Abstract:
This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by YliVakkuri and Hawthorne (2018), who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening (the inference from ˜If A were true, then C would be true' to ˜If A and B were true, then C would be true'), which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close by discussing the dispensability of counterfactual conditionals within the language of mathematics. Word Count:
On Stalnaker's Simple Theory of Propositions
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200619
Abstract:
Robert Stalnaker recently proposed a simple theory of propositions using the notion of a set of propositions being consistent, and conjectured that this theory is equivalent to the claim that propositions form a complete atomic Boolean algebra. This paper clarifies and confirms this conjecture. Stalnaker also noted that some of the principles of his theory may be given up, depending on the intended notion of proposition. This paper therefore also investigates weakened constraints on consistency and the corresponding classes of Boolean algebras. Word Count:
Rank  Word  Count 
0  propositions  3 
Excerpts:
...stalnaker recently proposed a simple theory of propositions using the notion of a set of ...
...using the notion of a set of propositions being consistent and conjectured that this theory ...
...theory is equivalent to the claim that propositions form a complete atomic boolean algebra this ...

1  theory  3 
Excerpts:
... robert stalnaker recently proposed a simple theory of propositions using the notion of a ...
...propositions being consistent and conjectured that this theory is equivalent to the claim that propositions ...
...that some of the principles of his theory may be given up depending on the ...

2  stalnaker  2 
Excerpts:
... robert stalnaker recently proposed a simple theory of propositions ...
...this paper clarifies and confirms this conjecture stalnaker also noted that some of the principles ...

3  boolean  2 
Excerpts:
...claim that propositions form a complete atomic boolean algebra this paper clarifies and confirms this ...
...on consistency and the corresponding classes of boolean algebras ...

4  notion  2 
Excerpts:
...a simple theory of propositions using the notion of a set of propositions being consistent ...
...be given up depending on the intended notion of proposition this paper therefore also investigates ...

5  robert  1 
Excerpts:
... robert stalnaker recently proposed a simple theory of ...

6  intended  1 
Excerpts:
...may be given up depending on the intended notion of proposition this paper therefore also ...

7  may  1 
Excerpts:
...some of the principles of his theory may be given up depending on the intended ...

8  given  1 
Excerpts:
...the principles of his theory may be given up depending on the intended notion of ...

9  up  1 
Excerpts:
...principles of his theory may be given up depending on the intended notion of proposition ...

Roads to Necessitarianism
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200616
Abstract:
We show that each of three natural sets of assumptions about the conditional entails necessitarianism: that anything possible is necessary. Since most agree that this conclusion is obviously false, this shows that at least one member of each set of assumptions must be rejected. All of these assumptions are, however, widely accepted and wellmotivated. This creates a puzzle which we leave open. Word Count:
Rank  Word  Count 
0  assumptions  3 
Excerpts:
...that each of three natural sets of assumptions about the conditional entails necessitarianism that anything ...
...least one member of each set of assumptions must be rejected all of these assumptions ...
...assumptions must be rejected all of these assumptions are however widely accepted and wellmotivated this ...

1  each  2 
Excerpts:
... we show that each of three natural sets of assumptions about ...
...shows that at least one member of each set of assumptions must be rejected all ...

2  show  1 
Excerpts:
... we show that each of three natural sets of ...

3  leave  1 
Excerpts:
...wellmotivated this creates a puzzle which we leave open ...

4  puzzle  1 
Excerpts:
...widely accepted and wellmotivated this creates a puzzle which we leave open ...

5  creates  1 
Excerpts:
...are however widely accepted and wellmotivated this creates a puzzle which we leave open ...

6  wellmotivated  1 
Excerpts:
...these assumptions are however widely accepted and wellmotivated this creates a puzzle which we leave ...

7  accepted  1 
Excerpts:
...all of these assumptions are however widely accepted and wellmotivated this creates a puzzle which ...

8  widely  1 
Excerpts:
...rejected all of these assumptions are however widely accepted and wellmotivated this creates a puzzle ...

9  however  1 
Excerpts:
...be rejected all of these assumptions are however widely accepted and wellmotivated this creates a ...

Correction to: Deflationism About Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
Abstract:
The original version of this article unfortunately contains mistakes introduced by the publisher during the production process. The mistakes and corrections are described in the following list Word Count:
Rank  Word  Count 
0  mistakes  2 
Excerpts:
...original version of this article unfortunately contains mistakes introduced by the publisher during the production ...
...the publisher during the production process the mistakes and corrections are described in the following ...

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

2  version  1 
Excerpts:
... the original version of this article unfortunately contains mistakes introduced ...

3  article  1 
Excerpts:
... the original version of this article unfortunately contains mistakes introduced by the publisher ...

4  unfortunately  1 
Excerpts:
... the original version of this article unfortunately contains mistakes introduced by the publisher during ...

5  contains  1 
Excerpts:
...the original version of this article unfortunately contains mistakes introduced by the publisher during the ...

6  introduced  1 
Excerpts:
...version of this article unfortunately contains mistakes introduced by the publisher during the production process ...

7  publisher  1 
Excerpts:
...article unfortunately contains mistakes introduced by the publisher during the production process the mistakes and ...

8  during  1 
Excerpts:
...unfortunately contains mistakes introduced by the publisher during the production process the mistakes and corrections ...

9  production  1 
Excerpts:
...mistakes introduced by the publisher during the production process the mistakes and corrections are described ...

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: 20200601
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:
Reference and Truth
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
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  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 ...

2  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 ...

3  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 ...

4  compare  1 
Excerpts:
...shown to be sound prooftheoretically strong and compare well to the most renowned systems in ...

5  strong  1 
Excerpts:
...systems are shown to be sound prooftheoretically strong and compare well to the most renowned ...

6  prooftheoretically  1 
Excerpts:
...these systems are shown to be sound prooftheoretically strong and compare well to the most ...

7  sound  1 
Excerpts:
...of these systems are shown to be sound prooftheoretically strong and compare well to the ...

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

9  them  1 
Excerpts:
...prooftheoretic versions of those notions and use them to formulate axiomatic disquotational truth systems over ...

Indicative Conditionals and Graded Information
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
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  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 ...

5  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 ...

6  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 ...

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

9  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 ...

Realism and Empirical Equivalence
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
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  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 ...

2  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 ...

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  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 ...

8  underdetermination  3 
Excerpts:
...be refuted if one can establish an underdetermination thesis to the effect that every theory ...
...there is an obvious conflict between the underdetermination thesis and the nomiracles argument i show ...
...all notions of empirical equivalence support the underdetermination thesis the indispensability argument might be refuted ...

9  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 ...

Alethic Reference
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
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  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 ...

1  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 ...

2  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 ...

3  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 ...

4  put  1 
Excerpts:
... i put forward precise and appealing notions of reference ...

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

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

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

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

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

Deflationism About Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
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  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 ...

3  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 ...

4  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 ...

5  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 ...

6  do  2 
Excerpts:
...deflationism on two fronts first it cannot do the work it has been recruited to ...
...does a sentences universal generalization have to do with its logical truth i argue that ...

7  challenge  2 
Excerpts:
...paper defends deflationism from its most important challenge to date due to ole hjortland it ...
...has no adequate answer to the following challenge what does a sentences universal generalization have ...

8  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 ...

9  theory  2 
Excerpts:
...between competing logics this is because a theory of logic cannot be as easily separated ...
...cannot be as easily separated from a theory of truth as its proponents claim second ...

Routley Star and Hyperintensionality
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200527
Abstract:
We compare the logic HYPE recently suggested by H. Leitgeb as a basic propositional logic to deal with hyperintensional contexts and HeytingOckham logic introduced in the course of studying logical aspects of the wellfounded semantics for logic programs with negation. The semantics of HeytingOckham logic makes use of the socalled Routley star negation. It is shown how the Routley star negation can be obtained from Dimiter Vakarelov's theory of negation and that propositional HYPE coincides with the logic characterized by the class of all involutive Routley star information frames. This result provides a much simplified semantics for HYPE and also a simplified axiomatization, which shows that HYPE is identical with the modal symmetric propositional calculus introduced by G. Moisil in 1942. Moreover, it is shown that HYPE can be faithfully embedded into a normal bimodal logic based on classical logic. Against this background, we discuss the notion of hyperintensionality. Word Count:
Rank  Word  Count 
0  logic  8 
Excerpts:
... we compare the logic hype recently suggested by h leitgeb as ...
...by h leitgeb as a basic propositional logic to deal with hyperintensional contexts and heytingockham ...
...to deal with hyperintensional contexts and heytingockham logic introduced in the course of studying logical ...
...logical aspects of the wellfounded semantics for logic programs with negation the semantics of heytingockham ...
...programs with negation the semantics of heytingockham logic makes use of the socalled routley star ...
...and that propositional hype coincides with the logic characterized by the class of all involutive ...
...be faithfully embedded into a normal bimodal logic based on classical logic against this background ...
...a normal bimodal logic based on classical logic against this background we discuss the notion ...

1  hype  5 
Excerpts:
... we compare the logic hype recently suggested by h leitgeb as a ...
...vakarelovs theory of negation and that propositional hype coincides with the logic characterized by the ...
...result provides a much simplified semantics for hype and also a simplified axiomatization which shows ...
...also a simplified axiomatization which shows that hype is identical with the modal symmetric propositional ...
...in 1942 moreover it is shown that hype can be faithfully embedded into a normal ...

2  negation  4 
Excerpts:
...the wellfounded semantics for logic programs with negation the semantics of heytingockham logic makes use ...
...makes use of the socalled routley star negation it is shown how the routley star ...
...it is shown how the routley star negation can be obtained from dimiter vakarelovs theory ...
...be obtained from dimiter vakarelovs theory of negation and that propositional hype coincides with the ...

3  routley  3 
Excerpts:
...heytingockham logic makes use of the socalled routley star negation it is shown how the ...
...star negation it is shown how the routley star negation can be obtained from dimiter ...
...characterized by the class of all involutive routley star information frames this result provides a ...

4  propositional  3 
Excerpts:
...suggested by h leitgeb as a basic propositional logic to deal with hyperintensional contexts and ...
...dimiter vakarelovs theory of negation and that propositional hype coincides with the logic characterized by ...
...hype is identical with the modal symmetric propositional calculus introduced by g moisil in 1942 ...

5  semantics  3 
Excerpts:
...of studying logical aspects of the wellfounded semantics for logic programs with negation the semantics ...
...semantics for logic programs with negation the semantics of heytingockham logic makes use of the ...
...frames this result provides a much simplified semantics for hype and also a simplified axiomatization ...

6  star  3 
Excerpts:
...logic makes use of the socalled routley star negation it is shown how the routley ...
...negation it is shown how the routley star negation can be obtained from dimiter vakarelovs ...
...by the class of all involutive routley star information frames this result provides a much ...

7  simplified  2 
Excerpts:
...information frames this result provides a much simplified semantics for hype and also a simplified ...
...simplified semantics for hype and also a simplified axiomatization which shows that hype is identical ...

8  shown  2 
Excerpts:
...the socalled routley star negation it is shown how the routley star negation can be ...
...g moisil in 1942 moreover it is shown that hype can be faithfully embedded into ...

9  heytingockham  2 
Excerpts:
...logic to deal with hyperintensional contexts and heytingockham logic introduced in the course of studying ...
...logic programs with negation the semantics of heytingockham logic makes use of the socalled routley ...

Rosenkranz's Logic of Justification and Unprovability
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200527
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:
Brouwer's Weak Counterexamples and the Creative Subject: A Critical Survey
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200509
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 ...

Between Atomism and Superatomism
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200429
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 ...

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: 20200418
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 ...

Eulertype Diagrams and the Quantification of the Predicate
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200401
Abstract:
Logicians have often suggested that the use of Eulertype diagrams has influenced the idea of the quantification of the predicate. This is mainly due to the fact that Eulertype diagrams display more information than is required in traditional syllogistics. The paper supports this argument and extends it by a further step: Eulertype diagrams not only illustrate the quantification of the predicate, but also solve problems of traditional proof theory, which prevented an overall quantification of the predicate. Thus, Eulertype diagrams can be called the natural basis of syllogistic reasoning and can even go beyond. In the paper, these arguments are presented in connection with the book Nucleus Logicae Weisaniae by Johann Christian Lange from 1712. Word Count:
Rank  Word  Count 
0  eulertype  4 
Excerpts:
...have often suggested that the use of eulertype diagrams has influenced the idea of the ...
...is mainly due to the fact that eulertype diagrams display more information than is required ...
...and extends it by a further step eulertype diagrams not only illustrate the quantification of ...
...an overall quantification of the predicate thus eulertype diagrams can be called the natural basis ...

1  diagrams  4 
Excerpts:
...often suggested that the use of eulertype diagrams has influenced the idea of the quantification ...
...mainly due to the fact that eulertype diagrams display more information than is required in ...
...extends it by a further step eulertype diagrams not only illustrate the quantification of the ...
...overall quantification of the predicate thus eulertype diagrams can be called the natural basis of ...

2  quantification  3 
Excerpts:
...diagrams has influenced the idea of the quantification of the predicate this is mainly due ...
...step eulertype diagrams not only illustrate the quantification of the predicate but also solve problems ...
...traditional proof theory which prevented an overall quantification of the predicate thus eulertype diagrams can ...

3  predicate  3 
Excerpts:
...the idea of the quantification of the predicate this is mainly due to the fact ...
...not only illustrate the quantification of the predicate but also solve problems of traditional proof ...
...which prevented an overall quantification of the predicate thus eulertype diagrams can be called the ...

4  traditional  2 
Excerpts:
...display more information than is required in traditional syllogistics the paper supports this argument and ...
...the predicate but also solve problems of traditional proof theory which prevented an overall quantification ...

5  logicians  1 
Excerpts:
... logicians have often suggested that the use of ...

6  thus  1 
Excerpts:
...prevented an overall quantification of the predicate thus eulertype diagrams can be called the natural ...

7  called  1 
Excerpts:
...the predicate thus eulertype diagrams can be called the natural basis of syllogistic reasoning and ...

8  natural  1 
Excerpts:
...thus eulertype diagrams can be called the natural basis of syllogistic reasoning and can even ...

9  basis  1 
Excerpts:
...eulertype diagrams can be called the natural basis of syllogistic reasoning and can even go ...

Classical Logic and the Strict Tolerant Hierarchy
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200401
Abstract:
In their recent article A Hierarchy of Classical and Paraconsistent Logics', Eduardo Barrio, Federico Pailos and Damien Szmuc (BPS hereafter) present novel and striking results about metainferential validity in various three valued logics. In the process, they have thrown open the door to a hitherto unrecognized domain of nonclassical logics with surprising intrinsic properties, as well as subtle and interesting relations to various familiar logics, including classical logic. One such result is that, for each natural number n, there is a logic which agrees with classical logic on tautologies, inferences, metainferences, metametainferences, metameta...(n  3 times)metainferences, but that disagrees with classical logic on n + 1metainferences. They suggest that this shows that classical logic can only be characterized by defining its valid inferences at all orders. In this article, I invoke some simple symmetric generalizations of BPS's results to show that the problem is worse than they suggest, since in fact there are logics that agree with classical logic on inferential validity to all orders but still intuitively differ from it. I then discuss the relevance of these results for truth theory and the classification problem. Word Count:
Rank  Word  Count 
0  logic  6 
Excerpts:
...relations to various familiar logics including classical logic one such result is that for each ...
...each natural number n there is a logic which agrees with classical logic on tautologies ...
...is a logic which agrees with classical logic on tautologies inferences metainferences metametainferences metametan ...
...3 timesmetainferences but that disagrees with classical logic on n + 1metainferences they suggest that ...
...they suggest that this shows that classical logic can only be characterized by defining its ...
...there are logics that agree with classical logic on inferential validity to all orders but ...

1  classical  6 
Excerpts:
...in their recent article a hierarchy of classical and paraconsistent logics eduardo barrio federico pailos ...
...interesting relations to various familiar logics including classical logic one such result is that for ...
...there is a logic which agrees with classical logic on tautologies inferences metainferences metametainferences metametan ...
... 3 timesmetainferences but that disagrees with classical logic on n + 1metainferences they suggest ...
...1metainferences they suggest that this shows that classical logic can only be characterized by defining ...
...fact there are logics that agree with classical logic on inferential validity to all orders ...

2  logics  5 
Excerpts:
...article a hierarchy of classical and paraconsistent logics eduardo barrio federico pailos and damien szmuc ...
...about metainferential validity in various three valued logics in the process they have thrown open ...
...to a hitherto unrecognized domain of nonclassical logics with surprising intrinsic properties as well as ...
...subtle and interesting relations to various familiar logics including classical logic one such result is ...
...they suggest since in fact there are logics that agree with classical logic on inferential ...

3  results  3 
Excerpts:
...szmuc bps hereafter present novel and striking results about metainferential validity in various three valued ...
...invoke some simple symmetric generalizations of bpss results to show that the problem is worse ...
...i then discuss the relevance of these results for truth theory and the classification problem ...

4  inferences  2 
Excerpts:
...which agrees with classical logic on tautologies inferences metainferences metametainferences metametan 3 timesmetainferences but ...
...only be characterized by defining its valid inferences at all orders in this article i ...

5  article  2 
Excerpts:
... in their recent article a hierarchy of classical and paraconsistent logics ...
...valid inferences at all orders in this article i invoke some simple symmetric generalizations of ...

6  problem  2 
Excerpts:
...of bpss results to show that the problem is worse than they suggest since in ...
...results for truth theory and the classification problem ...

7  n  2 
Excerpts:
...result is that for each natural number n there is a logic which agrees with ...
...but that disagrees with classical logic on n + 1metainferences they suggest that this shows ...

8  various  2 
Excerpts:
...and striking results about metainferential validity in various three valued logics in the process they ...
...well as subtle and interesting relations to various familiar logics including classical logic one such ...

9  validity  2 
Excerpts:
...present novel and striking results about metainferential validity in various three valued logics in the ...
...that agree with classical logic on inferential validity to all orders but still intuitively differ ...

An Accuracy Argument in Favor of Ranking Theory
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200401
Abstract:
Fitelson and McCarthy (2014) have proposed an accuracy measure for confidence orders which favors probability measures and DempsterShafer belief functions as accounts of degrees of belief and excludes ranking functions. Their accuracy measure only penalizes mistakes in confidence comparisons. We propose an alternative accuracy measure that also rewards correct confidence comparisons. Thus we conform to both of William James' maxims: Believe truth! Shun error!' We combine the two maxims, penalties and rewards, into one criterion that we call prioritized accuracy optimization (PAO). That is, PAO punishes wrong comparisons (preferring the false to the true) and rewards right comparisons (preferring the true to the false). And it requires to prioritize being right und avoiding to be wrong in a specific way. Thus PAO is both, a scoring rule and a decision rule. It turns out that precisely confidence orders representable by twosided ranking functions satisfy PAO. The point is not to argue that PAO is the better accuracy goal. The point is only that ranking theory can also be supported by accuracy considerations. Thus, those considerations by themselves cannot decide about rational formats for degrees of belief, but are part and parcel of an overall normative assessment of those formats. Word Count:
Rank  Word  Count 
0  accuracy  6 
Excerpts:
...fitelson and mccarthy 2014 have proposed an accuracy measure for confidence orders which favors probability ...
...of belief and excludes ranking functions their accuracy measure only penalizes mistakes in confidence comparisons ...
...in confidence comparisons we propose an alternative accuracy measure that also rewards correct confidence comparisons ...
...into one criterion that we call prioritized accuracy optimization pao that is pao punishes wrong ...
...to argue that pao is the better accuracy goal the point is only that ranking ...
...ranking theory can also be supported by accuracy considerations thus those considerations by themselves cannot ...

1  pao  5 
Excerpts:
...criterion that we call prioritized accuracy optimization pao that is pao punishes wrong comparisons preferring ...
...call prioritized accuracy optimization pao that is pao punishes wrong comparisons preferring the false to ...
...be wrong in a specific way thus pao is both a scoring rule and a ...
...orders representable by twosided ranking functions satisfy pao the point is not to argue that ...
...the point is not to argue that pao is the better accuracy goal the point ...

2  comparisons  4 
Excerpts:
...accuracy measure only penalizes mistakes in confidence comparisons we propose an alternative accuracy measure that ...
...accuracy measure that also rewards correct confidence comparisons thus we conform to both of william ...
...optimization pao that is pao punishes wrong comparisons preferring the false to the true and ...
...false to the true and rewards right comparisons preferring the true to the false and ...

3  confidence  4 
Excerpts:
...2014 have proposed an accuracy measure for confidence orders which favors probability measures and dempstershafer ...
...their accuracy measure only penalizes mistakes in confidence comparisons we propose an alternative accuracy measure ...
...alternative accuracy measure that also rewards correct confidence comparisons thus we conform to both of ...
...decision rule it turns out that precisely confidence orders representable by twosided ranking functions satisfy ...

4  belief  3 
Excerpts:
...orders which favors probability measures and dempstershafer belief functions as accounts of degrees of belief ...
...belief functions as accounts of degrees of belief and excludes ranking functions their accuracy measure ...
...decide about rational formats for degrees of belief but are part and parcel of an ...

5  rewards  3 
Excerpts:
...propose an alternative accuracy measure that also rewards correct confidence comparisons thus we conform to ...
...we combine the two maxims penalties and rewards into one criterion that we call prioritized ...
...preferring the false to the true and rewards right comparisons preferring the true to the ...

6  ranking  3 
Excerpts:
...accounts of degrees of belief and excludes ranking functions their accuracy measure only penalizes mistakes ...
...that precisely confidence orders representable by twosided ranking functions satisfy pao the point is not ...
...accuracy goal the point is only that ranking theory can also be supported by accuracy ...

7  functions  3 
Excerpts:
...which favors probability measures and dempstershafer belief functions as accounts of degrees of belief and ...
...of degrees of belief and excludes ranking functions their accuracy measure only penalizes mistakes in ...
...precisely confidence orders representable by twosided ranking functions satisfy pao the point is not to ...

8  thus  3 
Excerpts:
...measure that also rewards correct confidence comparisons thus we conform to both of william james ...
...to be wrong in a specific way thus pao is both a scoring rule and ...
...can also be supported by accuracy considerations thus those considerations by themselves cannot decide about ...

9  measure  3 
Excerpts:
...and mccarthy 2014 have proposed an accuracy measure for confidence orders which favors probability measures ...
...belief and excludes ranking functions their accuracy measure only penalizes mistakes in confidence comparisons we ...
...confidence comparisons we propose an alternative accuracy measure that also rewards correct confidence comparisons thus ...

Intuitionism and the Modal Logic of Vagueness
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200401
Abstract:
Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the socalled paradoxes of higherorder vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist's characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ˜it is clearly the case that'. S4M opens the way to an account of higherorder vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus (IPC) and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson's objections to intuitionistic treatments of vagueness. Word Count:
Blame it on me
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200401
Abstract:
In this paper, we develop a formalisation of the main ideas of the work of Van de Poel on responsibility. Using the basic concepts through which the meanings of responsibility are defined, we construct a logic which enables to express sentences like individual i is accountable for Ï†', individual i is blameworthy for Ï†' and individual i has the obligation to see to it that Ï†'. This formalization clarifies the definitions of responsibility given by Van de Poel and highlights their differences and similarities. It also helps to assess the consistency of the formalisation of responsibility, not only by showing that definitions are not inconsistent, but also by providing a formal demonstration of the relation between three main meanings of responsibility (accountability, blameworthiness, and obligation). The formal account can be used to derive new properties of the concepts. With the help of the formalisation, we detect the occurrence of the problem of many hands (PMH) by defining a logical framework for reasoning about collective and individual responsibility. This logic extends the Coalition Epistemic Dynamic Logic (CEDL) by adding a notion of group knowledge (and generalize the definitions of individual responsibility to groups of agents), agent ability and knowing how to its semantics. Word Count:
Rank  Word  Count 
0  responsibility  7 
Excerpts:
...the work of van de poel on responsibility using the basic concepts through which the ...
...basic concepts through which the meanings of responsibility are defined we construct a logic which ...
...Ï† this formalization clarifies the definitions of responsibility given by van de poel and highlights ...
...assess the consistency of the formalisation of responsibility not only by showing that definitions are ...
...the relation between three main meanings of responsibility accountability blameworthiness and obligation the formal account ...
...framework for reasoning about collective and individual responsibility this logic extends the coalition epistemic dynamic ...
...knowledge and generalize the definitions of individual responsibility to groups of agents agent ability and ...

1  individual  5 
Excerpts:
...logic which enables to express sentences like individual i is accountable for Ï† individual i ...
...like individual i is accountable for Ï† individual i is blameworthy for Ï† and individual ...
...individual i is blameworthy for Ï† and individual i has the obligation to see to ...
...logical framework for reasoning about collective and individual responsibility this logic extends the coalition epistemic ...
...group knowledge and generalize the definitions of individual responsibility to groups of agents agent ability ...

2  Ï†  3 
Excerpts:
...sentences like individual i is accountable for Ï† individual i is blameworthy for Ï† and ...
...for Ï† individual i is blameworthy for Ï† and individual i has the obligation to ...
...the obligation to see to it that Ï† this formalization clarifies the definitions of responsibility ...

3  logic  3 
Excerpts:
...of responsibility are defined we construct a logic which enables to express sentences like individual ...
...reasoning about collective and individual responsibility this logic extends the coalition epistemic dynamic logic cedl ...
...this logic extends the coalition epistemic dynamic logic cedl by adding a notion of group ...

4  definitions  3 
Excerpts:
...it that Ï† this formalization clarifies the definitions of responsibility given by van de poel ...
...of responsibility not only by showing that definitions are not inconsistent but also by providing ...
...notion of group knowledge and generalize the definitions of individual responsibility to groups of agents ...

5  formalisation  3 
Excerpts:
... in this paper we develop a formalisation of the main ideas of the work ...
...helps to assess the consistency of the formalisation of responsibility not only by showing that ...
...the concepts with the help of the formalisation we detect the occurrence of the problem ...

6  obligation  2 
Excerpts:
...for Ï† and individual i has the obligation to see to it that Ï† this ...
...main meanings of responsibility accountability blameworthiness and obligation the formal account can be used to ...

7  concepts  2 
Excerpts:
...de poel on responsibility using the basic concepts through which the meanings of responsibility are ...
...used to derive new properties of the concepts with the help of the formalisation we ...

8  meanings  2 
Excerpts:
...using the basic concepts through which the meanings of responsibility are defined we construct a ...
...demonstration of the relation between three main meanings of responsibility accountability blameworthiness and obligation the ...

9  formal  2 
Excerpts:
...not inconsistent but also by providing a formal demonstration of the relation between three main ...
...of responsibility accountability blameworthiness and obligation the formal account can be used to derive new ...

