Combining Texts

All the ideas for 'The Boundary Stones of Thought', 'Two-Dimensional Semantics' and 'The Theory of Relativity and A Priori Knowledge'

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57 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt]
3. Truth / A. Truth Problems / 1. Truth
The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt]
3. Truth / B. Truthmakers / 7. Making Modal Truths
'True at a possibility' means necessarily true if what is said had obtained [Rumfitt]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
'Absolute necessity' would have to rest on S5 [Rumfitt]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt]
Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
The iterated conception of set requires continual increase in axiom strength [Rumfitt]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt]
A set can be determinate, because of its concept, and still have vague membership [Rumfitt]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt]
Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt]
If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence is a relation that can extended into further statements [Rumfitt]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
Normal deduction presupposes the Cut Law [Rumfitt]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
When faced with vague statements, Bivalence is not a compelling principle [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths are just the assumption-free by-products of logical rules [Rumfitt]
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Infinitesimals do not stand in a determinate order relation to zero [Rumfitt]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt]
The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt]
10. Modality / A. Necessity / 3. Types of Necessity
Superficial necessity is true in all worlds; deep necessity is thus true, no matter which world is actual [Schroeter]
10. Modality / A. Necessity / 5. Metaphysical Necessity
Metaphysical modalities respect the actual identities of things [Rumfitt]
10. Modality / A. Necessity / 6. Logical Necessity
S5 is the logic of logical necessity [Rumfitt]
10. Modality / B. Possibility / 1. Possibility
Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt]
If two possibilities can't share a determiner, they are incompatible [Rumfitt]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
Contradictory claims about a necessary god both seem apriori coherent [Schroeter]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt]
11. Knowledge Aims / A. Knowledge / 2. Understanding
Medieval logicians said understanding A also involved understanding not-A [Rumfitt]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
2D semantics gives us apriori knowledge of our own meanings [Schroeter]
12. Knowledge Sources / B. Perception / 5. Interpretation
Kant showed that our perceptions are partly constructed from our concepts [Reichenbach]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt]
18. Thought / C. Content / 5. Twin Earth
Your view of water depends on whether you start from the actual Earth or its counterfactual Twin [Schroeter]
18. Thought / C. Content / 7. Narrow Content
Rationalists say knowing an expression is identifying its extension using an internal cognitive state [Schroeter]
19. Language / A. Nature of Meaning / 1. Meaning
Internalist meaning is about understanding; externalist meaning is about embedding in a situation [Schroeter]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
We understand conditionals, but disagree over their truth-conditions [Rumfitt]
19. Language / C. Assigning Meanings / 2. Semantics
Semantic theory assigns meanings to expressions, and metasemantics explains how this works [Schroeter]
19. Language / C. Assigning Meanings / 4. Compositionality
Semantic theories show how truth of sentences depends on rules for interpreting and joining their parts [Schroeter]
19. Language / C. Assigning Meanings / 7. Extensional Semantics
Simple semantics assigns extensions to names and to predicates [Schroeter]
'Federer' and 'best tennis player' can't mean the same, despite having the same extension [Schroeter]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
Possible worlds semantics uses 'intensions' - functions which assign extensions at each world [Schroeter]
Possible worlds make 'I' and that person's name synonymous, but they have different meanings [Schroeter]
Possible worlds semantics implies a constitutive connection between meanings and modal claims [Schroeter]
In the possible worlds account all necessary truths are same (because they all map to the True) [Schroeter]
19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics
Array worlds along the horizontal, and contexts (world,person,time) along the vertical [Schroeter]
If we introduce 'actually' into modal talk, we need possible worlds twice to express this [Schroeter]
Do we know apriori how we refer to names and natural kinds, but their modal profiles only a posteriori? [Schroeter]
2D fans defend it for conceptual analysis, for meaning, and for internalist reference [Schroeter]
2D semantics can't respond to contingent apriori claims, since there is no single proposition involved [Schroeter]
19. Language / F. Communication / 3. Denial
The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt]