Øystein Linnebo
Biographic Data
| ID | 1032040 |
|---|---|
| NAME | Øystein Linnebo |
| GIVEN NAMES | Øystein |
| FAMILY NAME | Linnebo |
| SIGNATURE | LINNEBO Ø |
| AFFILIATIONS | University of Oslo |
| ORCID | 0000-0002-3530-0295 |
| VERIFIED | Yes |
| TOTAL WORKS | 25 |
| TOTAL CITATIONS | 16 |
| AUTHOR COUNT | 25 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 2000 |
| LATEST PUBLICATION YEAR | 2025 |
| H-INDEX | 3 |
Why thin objects rather than ultra-thin
In Thin Objects, I articulated a thin conception of objecthood according to which the existence of objects need not make any substantive demands on reality. Agustín Rayo has developed and defended an even less demanding conception of objecthood, which drops the requirement of informative criteria of identity. The nature and extent of the disagreement is clarified, and two clusters of advantages of the thin conception are presented. In essence, by…
Weyl and two kinds of potential domains
According to Weyl, “‘inexhaustibility’ is essential to the infinite”. However, he distinguishes two kinds of inexhaustible, or merely potential, domains: those that are “extensionally determinate” and those that are not. This article clarifies Weyl's distinction and explains its enduring logical and philosophical significance. The distinction sheds lights on the contemporary debate about potentialism, which in turn affords a deeper understanding …
Riemann’s Scale
Replies
I am immensely grateful to the commentators for all of their thoughts and probing questions about TO. My replies will focus on one or two central points from each article. Inevitably, I need to be selective. First, for (§<) to hold, the facts that figure on the two sides of ‘ < ’ need to be distinct. I agree. Indeed, this is what distinguishes my asymmetric approach to abstraction from the more traditional symmetric approach espoused by Frege, th…
Précis
Thin Objects has two overarching ambitions. The first is to clarify and defend the idea that some objects are ‘thin’, in the sense that their existence does not make a substantive demand on reality. The second is to develop a systematic and well‐motivated account of permissible abstraction, thereby solving the so‐called ‘bad company problem’. Here I synthesise the book by briefly commenting on what I regard as its central themes
Abstraction and grounding
The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume's Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one‐to‐one: . The principal aim of thi…
Generality Explained
What explains the truth of a universal generalization? Two types of explanation can be distinguished. While an ‘instance-based explanation’ proceeds via some or all instances of the generalization, a ‘generic explanation’ is independent of the instances, relying instead on completely general facts about the properties or operations involved in the generalization. This intuitive distinction is analyzed by means of a truthmaker semantics, which als…
Introduction to special issue on ‘critical views of logic’
Critical views of logic are presented. These are views that are critical of logic in a sense akin to the way in which Kant is critical rather than dogmatic about traditional metaphysics. Such approaches differ from the Fregean ‘logic-first’ view. In accordance with the latter, logic is often regarded as epistemologically and methodologically fundamental. Hence, all disciplines – including mathematics – are considered as answerable to logic, rathe…
The Many and the One
Plural logic has become a well-established subject, especially in philosophical logic. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, h…
Peacocke on magnitudes and numbers
Peacocke’s recent The Primacy of Metaphysics covers a wide range of topics. This critical discussion focuses on the book’s novel account of extensive magnitudes and numbers. First, I further develop and defend Peacocke’s argument against nominalistic approaches to magnitudes and numbers. Then, I argue that his view is more Aristotelian than Platonist because reified magnitudes and numbers are accounted for via corresponding properties and these p…
Many and the One
Philosophy of Mathematics
Logic and Plurals
Logical analysis generally proceeds by paraphrasing sentences of natural language in a way that provides a more perspicuous representation of logically relevant features of those sentences. In linguistics, an influential approach to plurals is that of Godehard Link, who uses mereological sums to analyze plurals. This chapter introduces a formal language that may be used to regiment a wide range of natural language uses of plurals. George Boolos c…
Philosophy of Mathematics
Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that quest…
Plurals and modals
Consider one of several things. Is the one thing necessarily one of the several? This key question in the modal logic of plurals is clarified. Some defenses of an affirmative answer are developed and compared. Various remarks are made about the broader philosophical significance of the question.
Two types of abstraction for structuralism
If numbers were identified with any of their standard set-theoretic realizations, then they would have various non-arithmetical properties that mathematicians are reluctant to ascribe to them. Dedekind and later structuralists conclude that we should refrain from ascribing to numbers such ‘foreign’ properties. We first rehearse why it is hard to provide an acceptable formulation of this conclusion. Then we investigate some forms of abstraction me…
Entanglement and non-factorizability
Metaontological Minimalism
Can there be objects that are 'thin' in the sense that very little is required for their existence? A number of philosophers have thought so. For instance, many Fregeans believe it suffices for the existence of directions that there be lines standing in the relation of parallelism; other philosophers believe it suffices for a mathematical theory to have a model that the theory be coherent. This article explains the appeal of thin objects, discuss…
New Model Naturalism
Bad company tamed
Which Abstraction Principles are Acceptable? Some Limitative Results
Neo-Fregean logicism attempts to base mathematics on abstraction principles. Since not all abstraction principles are acceptable, the neo-Fregeans need an account of which ones are. One of the most promising accounts is in terms of the notion of stability; roughly, that an abstraction principle is acceptable just in case it is satisfiable in all domains of sufficiently large cardinality. We present two counterexamples to stability as a sufficient…
Modality and Tense
Modality and Tense brings together eleven of Kit Fine's articles on these topics, spanning the past three decades. The collection does not include his influential work on essence and dependence or his technical work on modality. Aided by a terrific introduction that sets the stage and provides a useful summary, the collection is quite well unified. The result is a demanding book that abounds in insight, penetrating analysis and subtle distinction…
Structuralism and the Notion of Dependence
The notion of dependence figures prominently in recent discussions of non‐eliminative mathematical structuralism. Structuralists often argue that mathematical objects from one and the same structure depend on one another and on the structure to which they belong. Their opponents often argue that there cannot be any such dependence. I first show that the structuralists' claims about dependence are more important to their view than is generally rec…
Early Analytic Philosophy
These essays present new analyses of the central figures of analytic philosophy -- Frege, Russell, Moore, Wittgenstein, and Carnap -- from the beginnings of the analytic movement into the 1930s. The papers do not reflect a single perspective, but rather express divergent interpretations of this controversial intellectual milieu
Early Analytic Philosophy
Two types of abstraction for structuralism
If numbers were identified with any of their standard set-theoretic realizations, then they would have various non-arithmetical properties that mathematicians are reluctant to ascribe to them. Dedekind and later structuralists conclude that we should refrain from ascribing to numbers such ‘foreign’ properties. We first rehearse why it is hard to provide an acceptable formulation of this conclusion. Then we investigate some forms of abstraction me…
Metaontological Minimalism
Can there be objects that are 'thin' in the sense that very little is required for their existence? A number of philosophers have thought so. For instance, many Fregeans believe it suffices for the existence of directions that there be lines standing in the relation of parallelism; other philosophers believe it suffices for a mathematical theory to have a model that the theory be coherent. This article explains the appeal of thin objects, discuss…
Bad company tamed
Which Abstraction Principles are Acceptable? Some Limitative Results
Neo-Fregean logicism attempts to base mathematics on abstraction principles. Since not all abstraction principles are acceptable, the neo-Fregeans need an account of which ones are. One of the most promising accounts is in terms of the notion of stability; roughly, that an abstraction principle is acceptable just in case it is satisfiable in all domains of sufficiently large cardinality. We present two counterexamples to stability as a sufficient…
Structuralism and the Notion of Dependence
The notion of dependence figures prominently in recent discussions of non‐eliminative mathematical structuralism. Structuralists often argue that mathematical objects from one and the same structure depend on one another and on the structure to which they belong. Their opponents often argue that there cannot be any such dependence. I first show that the structuralists' claims about dependence are more important to their view than is generally rec…
Early Analytic Philosophy
These essays present new analyses of the central figures of analytic philosophy -- Frege, Russell, Moore, Wittgenstein, and Carnap -- from the beginnings of the analytic movement into the 1930s. The papers do not reflect a single perspective, but rather express divergent interpretations of this controversial intellectual milieu
Early Analytic Philosophy
Modality and Tense
Modality and Tense brings together eleven of Kit Fine's articles on these topics, spanning the past three decades. The collection does not include his influential work on essence and dependence or his technical work on modality. Aided by a terrific introduction that sets the stage and provides a useful summary, the collection is quite well unified. The result is a demanding book that abounds in insight, penetrating analysis and subtle distinction…
Structuralism and the Notion of Dependence
The notion of dependence figures prominently in recent discussions of non‐eliminative mathematical structuralism. Structuralists often argue that mathematical objects from one and the same structure depend on one another and on the structure to which they belong. Their opponents often argue that there cannot be any such dependence. I first show that the structuralists' claims about dependence are more important to their view than is generally rec…
New Model Naturalism
Bad company tamed
Which Abstraction Principles are Acceptable? Some Limitative Results
Neo-Fregean logicism attempts to base mathematics on abstraction principles. Since not all abstraction principles are acceptable, the neo-Fregeans need an account of which ones are. One of the most promising accounts is in terms of the notion of stability; roughly, that an abstraction principle is acceptable just in case it is satisfiable in all domains of sufficiently large cardinality. We present two counterexamples to stability as a sufficient…
Metaontological Minimalism
Can there be objects that are 'thin' in the sense that very little is required for their existence? A number of philosophers have thought so. For instance, many Fregeans believe it suffices for the existence of directions that there be lines standing in the relation of parallelism; other philosophers believe it suffices for a mathematical theory to have a model that the theory be coherent. This article explains the appeal of thin objects, discuss…
Entanglement and non-factorizability
Two types of abstraction for structuralism
If numbers were identified with any of their standard set-theoretic realizations, then they would have various non-arithmetical properties that mathematicians are reluctant to ascribe to them. Dedekind and later structuralists conclude that we should refrain from ascribing to numbers such ‘foreign’ properties. We first rehearse why it is hard to provide an acceptable formulation of this conclusion. Then we investigate some forms of abstraction me…
Plurals and modals
Consider one of several things. Is the one thing necessarily one of the several? This key question in the modal logic of plurals is clarified. Some defenses of an affirmative answer are developed and compared. Various remarks are made about the broader philosophical significance of the question.
Philosophy of Mathematics
Logic and Plurals
Logical analysis generally proceeds by paraphrasing sentences of natural language in a way that provides a more perspicuous representation of logically relevant features of those sentences. In linguistics, an influential approach to plurals is that of Godehard Link, who uses mereological sums to analyze plurals. This chapter introduces a formal language that may be used to regiment a wide range of natural language uses of plurals. George Boolos c…
Philosophy of Mathematics
Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that quest…
The Many and the One
Plural logic has become a well-established subject, especially in philosophical logic. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, h…
Peacocke on magnitudes and numbers
Peacocke’s recent The Primacy of Metaphysics covers a wide range of topics. This critical discussion focuses on the book’s novel account of extensive magnitudes and numbers. First, I further develop and defend Peacocke’s argument against nominalistic approaches to magnitudes and numbers. Then, I argue that his view is more Aristotelian than Platonist because reified magnitudes and numbers are accounted for via corresponding properties and these p…
Many and the One
Generality Explained
What explains the truth of a universal generalization? Two types of explanation can be distinguished. While an ‘instance-based explanation’ proceeds via some or all instances of the generalization, a ‘generic explanation’ is independent of the instances, relying instead on completely general facts about the properties or operations involved in the generalization. This intuitive distinction is analyzed by means of a truthmaker semantics, which als…
Introduction to special issue on ‘critical views of logic’
Critical views of logic are presented. These are views that are critical of logic in a sense akin to the way in which Kant is critical rather than dogmatic about traditional metaphysics. Such approaches differ from the Fregean ‘logic-first’ view. In accordance with the latter, logic is often regarded as epistemologically and methodologically fundamental. Hence, all disciplines – including mathematics – are considered as answerable to logic, rathe…
Riemann’s Scale
Replies
I am immensely grateful to the commentators for all of their thoughts and probing questions about TO. My replies will focus on one or two central points from each article. Inevitably, I need to be selective. First, for (§<) to hold, the facts that figure on the two sides of ‘ < ’ need to be distinct. I agree. Indeed, this is what distinguishes my asymmetric approach to abstraction from the more traditional symmetric approach espoused by Frege, th…
Précis
Thin Objects has two overarching ambitions. The first is to clarify and defend the idea that some objects are ‘thin’, in the sense that their existence does not make a substantive demand on reality. The second is to develop a systematic and well‐motivated account of permissible abstraction, thereby solving the so‐called ‘bad company problem’. Here I synthesise the book by briefly commenting on what I regard as its central themes
Abstraction and grounding
The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume's Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one‐to‐one: . The principal aim of thi…
Weyl and two kinds of potential domains
According to Weyl, “‘inexhaustibility’ is essential to the infinite”. However, he distinguishes two kinds of inexhaustible, or merely potential, domains: those that are “extensionally determinate” and those that are not. This article clarifies Weyl's distinction and explains its enduring logical and philosophical significance. The distinction sheds lights on the contemporary debate about potentialism, which in turn affords a deeper understanding …
Why thin objects rather than ultra-thin
In Thin Objects, I articulated a thin conception of objecthood according to which the existence of objects need not make any substantive demands on reality. Agustín Rayo has developed and defended an even less demanding conception of objecthood, which drops the requirement of informative criteria of identity. The nature and extent of the disagreement is clarified, and two clusters of advantages of the thin conception are presented. In essence, by…
Philosophy (22 works) · Epistemology (19 works) · Philosophy and Theoretical Science (13 works) · Computer Science (12 works) · Philosophy and History of Science (7 works) · Abstraction (5 works) · Linguistics (5 works) · Logic, Reasoning, and Knowledge (5 works) · Mathematics (5 works) · Metaphysics (5 works)