Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Carnap and Logical Truth' and 'Essence and Modality'

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36 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
My account shows how the concept works, rather than giving an analysis [Fine,K]
2. Reason / D. Definition / 4. Real Definition
Modern philosophy has largely abandoned real definitions, apart from sortals [Fine,K]
2. Reason / D. Definition / 6. Definition by Essence
Defining a term and giving the essence of an object don't just resemble - they are the same [Fine,K]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Arithmetical undecidability is always settled at the next stage up [Koellner]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
An object is dependent if its essence prevents it from existing without some other object [Fine,K]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine]
9. Objects / D. Essence of Objects / 2. Types of Essence
Essences are either taken as real definitions, or as necessary properties [Fine,K]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
Essentially having a property is naturally expressed as 'the property it must have to be what it is' [Fine,K]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
Simple modal essentialism refers to necessary properties of an object [Fine,K]
Essentialist claims can be formulated more clearly with quantified modal logic [Fine,K]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Metaphysical necessity is a special case of essence, not vice versa [Fine,K]
Essence as necessary properties produces a profusion of essential properties [Fine,K, by Lowe]
The nature of singleton Socrates has him as a member, but not vice versa [Fine,K]
It is not part of the essence of Socrates that a huge array of necessary truths should hold [Fine,K]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
An essential property of something must be bound up with what it is to be that thing [Fine,K, by Rami]
9. Objects / D. Essence of Objects / 9. Essence and Properties
Essential properties are part of an object's 'definition' [Fine,K, by Rami]
9. Objects / E. Objects over Time / 12. Origin as Essential
If Socrates lacks necessary existence, then his nature cannot require his parents' existence [Fine,K]
10. Modality / A. Necessity / 6. Logical Necessity
Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
The subject of a proposition need not be the source of its necessity [Fine,K]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
Conceptual necessities rest on the nature of all concepts [Fine,K]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
Socrates is necessarily distinct from the Eiffel Tower, but that is not part of his essence [Fine,K]
Metaphysical necessities are true in virtue of the nature of all objects [Fine,K]
12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention
Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine]
19. Language / E. Analyticity / 2. Analytic Truths
Analytic truth may only be true in virtue of the meanings of certain terms [Fine,K]
The meaning of 'bachelor' is irrelevant to the meaning of 'unmarried man' [Fine,K]