A C Paseau
Biographic Data
| ID | 1296099 |
|---|---|
| NAME | A C Paseau |
| GIVEN NAMES | A C |
| FAMILY NAME | Paseau |
| SIGNATURE | PASEAU A C |
| AFFILIATIONS | University of Oxford |
| ORCID | 0000-0001-7610-8606 |
| VERIFIED | Yes |
| TOTAL WORKS | 12 |
| TOTAL CITATIONS | 11 |
| AUTHOR COUNT | 12 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 2003 |
| LATEST PUBLICATION YEAR | 2026 |
| H-INDEX | 2 |
What are the Formulas of a Logic
When describing a logic, the first thing one does is specify its language.The latter is made up of vocabulary items which, put together in the right way, make up well-formed formulas.Examples of well-formed formulas are 'Fx', 'p', ' yzRyz ' or ' (p q) '.But what exactly are these formulas?The analogous question for a natural language such as English asks what its sentences are.The answer must distinguish the language's written from its spoken for…
Ways of Being and Logicality
Ontological monists hold that there is only one way of being, while ontological pluralists hold that there are many; for example, concrete objects like tables and chairs exist in a different way from abstract objects like numbers and sets. Correspondingly, the monist will want the familiar existential quantifier as a primitive logical constant, whereas the pluralist will want distinct ones, such as for abstract and concrete existence. In this pap…
Non-metric Propositional Similarity
The idea that sentences can be closer or further apart in meaning is highly intuitive. Not only that, it is also a pillar of logic, semantic theory and the philosophy of science, and follows from other commitments about similarity. The present paper proposes a novel way of comparing the ‘distance’ between two pairs of propositions. We define ‘ $$p_1$$ p 1 is closer in meaning to $$p_2$$ p 2 than $$p_3$$ p 3 is to $$p_4$$ p 4 ’ and thereby give a …
Logos , logic and maximal infinity
Recent developments in the philosophy of logic suggest that the correct foundational logic is like God in that both are maximally infinite and only partially graspable by finite beings. This opens the door to a new argument for the existence of God, exploiting the link between God and logic through the intermediary of the Logos . This article explores the argument from the nature of God to the nature of logic, and sketches the converse argument f…
Propositionalism
Propositionalism is the claim that all logical relations can be captured by propositional logic. It is usually regarded as obviously false, because propositional logic seems too weak to capture the rich logical structure of language. I show that there is a clear sense in which propositional logic can match first-order logic, by producing formalizations that (i) are valid iff their first-order counterparts are, and (ii) also respect grammatical fo…
Arithmetic, enumerative induction and size bias
Number theory abounds with conjectures asserting that every natural number has some arithmetic property. An example is Goldbach’s Conjecture, which states that every even number greater than 2 is the sum of two primes. Enumerative inductive evidence for such conjectures usually consists of small cases. In the absence of supporting reasons, mathematicians mistrust such evidence for arithmetical generalisations, more so than most other forms of non…
A measure of inferential-role preservation
Fairness and Aggregation
Sometimes, two unfair distributions cancel out in aggregate. Paradoxically, two distributions each of which is fair in isolation may give rise to aggregate unfairness. When assessing the fairness of distributions, it therefore matters whether we assess transactions piecemeal or focus only on the overall result. This piece illustrates these difficulties for two leading theories of fairness (proportionality and shortfall minimization) before offeri…
Knowledge of Mathematics without Proof
Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support (for example, the Riemann hypothesis), they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present fo…
Defining Ultimate Ontological Basis and the Fundamental Layer
I explain why Ross Cameron's definition of ultimate ontological basis is incorrect, and propose a different definition in terms of ontological dependence, as well as a definition of reality's fundamental layer. These new definitions cover the conceptual possibility that self-dependent entities exist. They also apply to different conceptions of the relation of ontological dependence. © 2009 The Author
Naturalism in Mathematics and the Authority of Philosophy
Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I…
The Open-Endedness of the Set Concept and the Semantics of Set Theory
Knowledge of Mathematics without Proof
Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support (for example, the Riemann hypothesis), they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present fo…
Naturalism in Mathematics and the Authority of Philosophy
Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I…
Defining Ultimate Ontological Basis and the Fundamental Layer
I explain why Ross Cameron's definition of ultimate ontological basis is incorrect, and propose a different definition in terms of ontological dependence, as well as a definition of reality's fundamental layer. These new definitions cover the conceptual possibility that self-dependent entities exist. They also apply to different conceptions of the relation of ontological dependence. © 2009 The Author
The Open-Endedness of the Set Concept and the Semantics of Set Theory
The Open-Endedness of the Set Concept and the Semantics of Set Theory
Naturalism in Mathematics and the Authority of Philosophy
Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I…
Defining Ultimate Ontological Basis and the Fundamental Layer
I explain why Ross Cameron's definition of ultimate ontological basis is incorrect, and propose a different definition in terms of ontological dependence, as well as a definition of reality's fundamental layer. These new definitions cover the conceptual possibility that self-dependent entities exist. They also apply to different conceptions of the relation of ontological dependence. © 2009 The Author
Fairness and Aggregation
Sometimes, two unfair distributions cancel out in aggregate. Paradoxically, two distributions each of which is fair in isolation may give rise to aggregate unfairness. When assessing the fairness of distributions, it therefore matters whether we assess transactions piecemeal or focus only on the overall result. This piece illustrates these difficulties for two leading theories of fairness (proportionality and shortfall minimization) before offeri…
Knowledge of Mathematics without Proof
Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support (for example, the Riemann hypothesis), they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present fo…
A measure of inferential-role preservation
Propositionalism
Propositionalism is the claim that all logical relations can be captured by propositional logic. It is usually regarded as obviously false, because propositional logic seems too weak to capture the rich logical structure of language. I show that there is a clear sense in which propositional logic can match first-order logic, by producing formalizations that (i) are valid iff their first-order counterparts are, and (ii) also respect grammatical fo…
Arithmetic, enumerative induction and size bias
Number theory abounds with conjectures asserting that every natural number has some arithmetic property. An example is Goldbach’s Conjecture, which states that every even number greater than 2 is the sum of two primes. Enumerative inductive evidence for such conjectures usually consists of small cases. In the absence of supporting reasons, mathematicians mistrust such evidence for arithmetical generalisations, more so than most other forms of non…
Non-metric Propositional Similarity
The idea that sentences can be closer or further apart in meaning is highly intuitive. Not only that, it is also a pillar of logic, semantic theory and the philosophy of science, and follows from other commitments about similarity. The present paper proposes a novel way of comparing the ‘distance’ between two pairs of propositions. We define ‘ $$p_1$$ p 1 is closer in meaning to $$p_2$$ p 2 than $$p_3$$ p 3 is to $$p_4$$ p 4 ’ and thereby give a …
Logos , logic and maximal infinity
Recent developments in the philosophy of logic suggest that the correct foundational logic is like God in that both are maximally infinite and only partially graspable by finite beings. This opens the door to a new argument for the existence of God, exploiting the link between God and logic through the intermediary of the Logos . This article explores the argument from the nature of God to the nature of logic, and sketches the converse argument f…
Ways of Being and Logicality
Ontological monists hold that there is only one way of being, while ontological pluralists hold that there are many; for example, concrete objects like tables and chairs exist in a different way from abstract objects like numbers and sets. Correspondingly, the monist will want the familiar existential quantifier as a primitive logical constant, whereas the pluralist will want distinct ones, such as for abstract and concrete existence. In this pap…
What are the Formulas of a Logic
When describing a logic, the first thing one does is specify its language.The latter is made up of vocabulary items which, put together in the right way, make up well-formed formulas.Examples of well-formed formulas are 'Fx', 'p', ' yzRyz ' or ' (p q) '.But what exactly are these formulas?The analogous question for a natural language such as English asks what its sentences are.The answer must distinguish the language's written from its spoken for…
Epistemology (10 works) · Mathematics (10 works) · Philosophy (10 works) · Philosophy and Theoretical Science (8 works) · Computer Science (7 works) · Argument (complex analysis) (4 works) · Epistemology, Ethics, and Metaphysics (4 works) · Logic, Reasoning, and Knowledge (4 works) · Advanced Algebra and Logic (3 works) · Artificial Intelligence (3 works)