Combining Texts

All the ideas for 'fragments/reports', 'Logic for Philosophy' and 'On What There Is'

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76 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
'Theorems' are formulas provable from no premises at all [Sider]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth tables assume truth functionality, and are just pictures of truth functions [Sider]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider]
In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
System B introduces iterated modalities [Sider]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider]
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
We can treat modal worlds as different times [Sider]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
Converse Barcan Formula: □∀αφ→∀α□φ [Sider]
The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider]
System B is needed to prove the Barcan Formula [Sider]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
You can employ intuitionist logic without intuitionism about mathematics [Sider]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
The most popular account of logical consequence is the semantic or model-theoretic one [Sider]
Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]
Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider]
Maybe logical consequence is a primitive notion [Sider]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
A 'theorem' is an axiom, or the last line of a legitimate proof [Sider]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
We study bound variables not to know reality, but to know what reality language asserts [Quine]
When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
A 'total' function must always produce an output for a given domain [Sider]
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein]
Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
Names can be converted to descriptions, and Russell showed how to eliminate those [Quine]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
λ can treat 'is cold and hungry' as a single predicate [Sider]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Good axioms should be indisputable logical truths [Sider]
No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider]
Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Natural deduction helpfully allows reasoning with assumptions [Sider]
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
We can build proofs just from conclusions, rather than from plain formulae [Sider]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Valuations in PC assign truth values to formulas relative to variable assignments [Sider]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
The semantical notion of a logical truth is validity, being true in all interpretations [Sider]
It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider]
5. Theory of Logic / K. Features of Logics / 4. Completeness
In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualism holds that there are universals but they are mind-made [Quine]
7. Existence / A. Nature of Existence / 2. Types of Existence
For Quine, there is only one way to exist [Quine, by Shapiro]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
The idea of a thing and the idea of existence are two sides of the same coin [Quine, by Crane]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Quine rests existence on bound variables, because he thinks singular terms can be analysed away [Quine, by Hale]
7. Existence / D. Theories of Reality / 1. Ontologies
Quine's ontology is wrong; his question is scientific, and his answer is partly philosophical [Fine,K on Quine]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider]
Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider]
A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider]
We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
What actually exists does not, of course, depend on language [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
To be is to be the value of a variable, which amounts to being in the range of reference of a pronoun [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
Fictional quantification has no ontology, so we study ontology through scientific theories [Quine, by Orenstein]
An ontology is like a scientific theory; we accept the simplest scheme that fits disorderly experiences [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
If commitment rests on first-order logic, we obviously lose the ontology concerning predication [Maudlin on Quine]
If to be is to be the value of a variable, we must already know the values available [Jacquette on Quine]
8. Modes of Existence / A. Relations / 1. Nature of Relations
A relation is a feature of multiple objects taken together [Sider]
8. Modes of Existence / D. Universals / 1. Universals
Realism, conceptualism and nominalism in medieval universals reappear in maths as logicism, intuitionism and formalism [Quine]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
There is no entity called 'redness', and that some things are red is ultimate and irreducible [Quine]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
Quine has argued that predicates do not have any ontological commitment [Quine, by Armstrong]
9. Objects / A. Existence of Objects / 1. Physical Objects
Treating scattered sensations as single objects simplifies our understanding of experience [Quine]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider]
10. Modality / A. Necessity / 3. Types of Necessity
'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider]
10. Modality / A. Necessity / 5. Metaphysical Necessity
Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider]
10. Modality / A. Necessity / 6. Logical Necessity
Logical truths must be necessary if anything is [Sider]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider]
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
Quine's indispensability argument said arguments for abstracta were a posteriori [Quine, by Yablo]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Can an unactualized possible have self-identity, and be distinct from other possibles? [Quine]
Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider]
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
We can never translate our whole language of objects into phenomenalism [Quine]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
There is an attempt to give a verificationist account of meaning, without the error of reducing everything to sensations [Dennett on Quine]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
I do not believe there is some abstract entity called a 'meaning' which we can 'have' [Quine]
The word 'meaning' is only useful when talking about significance or about synonymy [Quine]
19. Language / C. Assigning Meanings / 3. Predicates
Quine relates predicates to their objects, by being 'true of' them [Quine, by Davidson]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]