Ideas of Ian Rumfitt, by Theme
[British, fl. 2014, Pupil of Dummett. At University College, Oxford. Then at Birkbeck, then Birmingham, then All Souls Oxford]
green numbers give full details |
back to list of philosophers |
expand these ideas
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
|
18835
|
Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics
|
3. Truth / A. Truth Problems / 1. Truth
|
18819
|
The idea that there are unrecognised truths is basic to our concept of truth
|
3. Truth / B. Truthmakers / 7. Making Modal Truths
|
18826
|
'True at a possibility' means necessarily true if what is said had obtained
|
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
|
18803
|
Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables
|
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
|
12204
|
The logic of metaphysical necessity is S5
|
|
18814
|
'Absolute necessity' would have to rest on S5
|
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
|
18799
|
Intuitionists can accept Double Negation Elimination for decidable propositions
|
|
18798
|
It is the second-order part of intuitionistic logic which actually negates some classical theorems
|
4. Formal Logic / F. Set Theory ST / 1. Set Theory
|
18830
|
Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
|
18843
|
The iterated conception of set requires continual increase in axiom strength
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
|
18836
|
A set may well not consist of its members; the empty set, for example, is a problem
|
|
18837
|
A set can be determinate, because of its concept, and still have vague membership
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
|
18845
|
If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom
|
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
|
11211
|
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter
|
|
18815
|
Logic is higher-order laws which can expand the range of any sort of deduction
|
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
|
9390
|
Logic guides thinking, but it isn't a substitute for it
|
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
|
18804
|
The case for classical logic rests on its rules, much more than on the Principle of Bivalence
|
|
18805
|
Classical logic rules cannot be proved, but various lines of attack can be repelled
|
|
18827
|
If truth-tables specify the connectives, classical logic must rely on Bivalence
|
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
|
12195
|
Soundness in argument varies with context, and may be achieved very informally indeed
|
|
12199
|
There is a modal element in consequence, in assessing reasoning from suppositions
|
|
12201
|
We reject deductions by bad consequence, so logical consequence can't be deduction
|
|
18813
|
Logical consequence is a relation that can extended into further statements
|
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
|
18808
|
Normal deduction presupposes the Cut Law
|
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
|
18840
|
When faced with vague statements, Bivalence is not a compelling principle
|
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
|
12194
|
Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B'
|
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
|
11210
|
Standardly 'and' and 'but' are held to have the same sense by having the same truth table
|
|
11212
|
The sense of a connective comes from primitively obvious rules of inference
|
|
18802
|
In specifying a logical constant, use of that constant is quite unavoidable
|
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
|
12198
|
Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths)
|
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
|
18800
|
Introduction rules give deduction conditions, and Elimination says what can be deduced
|
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
|
18809
|
Logical truths are just the assumption-free by-products of logical rules
|
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
|
18807
|
Monotonicity means there is a guarantee, rather than mere inductive support
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
|
18842
|
Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
|
17462
|
A single object must not be counted twice, which needs knowledge of distinctness (negative identity)
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
|
18834
|
Infinitesimals do not stand in a determinate order relation to zero
|
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
|
18846
|
Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry)
|
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
|
17461
|
Some 'how many?' answers are not predications of a concept, like 'how many gallons?'
|
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
|
9389
|
Vague membership of sets is possible if the set is defined by its concept, not its members
|
|
18839
|
An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases
|
|
18838
|
The extension of a colour is decided by a concept's place in a network of contraries
|
10. Modality / A. Necessity / 3. Types of Necessity
|
14532
|
A distinctive type of necessity is found in logical consequence [Hale/Hoffmann,A]
|
10. Modality / A. Necessity / 5. Metaphysical Necessity
|
18816
|
Metaphysical modalities respect the actual identities of things
|
10. Modality / A. Necessity / 6. Logical Necessity
|
12193
|
Logical necessity is when 'necessarily A' implies 'not-A is contradictory'
|
|
12200
|
A logically necessary statement need not be a priori, as it could be unknowable
|
|
12202
|
Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not
|
|
18825
|
S5 is the logic of logical necessity
|
10. Modality / B. Possibility / 1. Possibility
|
18828
|
If two possibilities can't share a determiner, they are incompatible
|
|
18824
|
Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right
|
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
|
12203
|
If a world is a fully determinate way things could have been, can anyone consider such a thing?
|
|
18821
|
Possibilities are like possible worlds, but not fully determinate or complete
|
11. Knowledge Aims / A. Knowledge / 2. Understanding
|
18831
|
Medieval logicians said understanding A also involved understanding not-A
|
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
|
18820
|
In English 'evidence' is a mass term, qualified by 'little' and 'more'
|
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
|
18817
|
We understand conditionals, but disagree over their truth-conditions
|
19. Language / F. Communication / 3. Denial
|
11214
|
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence
|
|
18829
|
The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A
|