Combining Texts

All the ideas for 'fragments/reports', 'Necessary Beings' and 'Thinking About Logic'

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67 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
You cannot understand what exists without understanding possibility and necessity [Hale]
2. Reason / D. Definition / 6. Definition by Essence
A canonical defintion specifies the type of thing, and what distinguish this specimen [Hale]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL
Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
Necessity is provability in S4, and true in all worlds in S5 [Read]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The two Barcan principles are easily proved in fairly basic modal logic [Hale]
With a negative free logic, we can dispense with the Barcan formulae [Hale]
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
Same say there are positive, negative and neuter free logics [Read]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
Realisms like the full Comprehension Principle, that all good concepts determine sets [Read]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Not all validity is captured in first-order logic [Read]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
The non-emptiness of the domain is characteristic of classical logic [Read]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Semantics must precede proof in higher-order logics, since they are incomplete [Read]
If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
We should exclude second-order logic, precisely because it captures arithmetic [Read]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read]
Logical consequence isn't just a matter of form; it depends on connections like round-square [Read]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
A theory is logically closed, which means infinite premisses [Read]
5. Theory of Logic / G. Quantification / 1. Quantification
Quantifiers are second-order predicates [Read]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
In second-order logic the higher-order variables range over all the properties of the objects [Read]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A logical truth is the conclusion of a valid inference with no premisses [Read]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Any first-order theory of sets is inadequate [Read]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Compactness does not deny that an inference can have infinitely many premisses [Read]
Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read]
Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read]
Compactness makes consequence manageable, but restricts expressive power [Read]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
Self-reference paradoxes seem to arise only when falsity is involved [Read]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read]
Second-order arithmetic covers all properties, ensuring categoricity [Read]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
Von Neumann numbers are helpful, but don't correctly describe numbers [Read]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
Interesting supervenience must characterise the base quite differently from what supervenes on it [Hale]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
There is no gap between a fact that p, and it is true that p; so we only have the truth-condtions for p [Hale]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Would a language without vagueness be usable at all? [Read]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
Supervaluations say there is a cut-off somewhere, but at no particular place [Read]
A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read]
Identities and the Indiscernibility of Identicals don't work with supervaluations [Read]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
A haecceity is a set of individual properties, essential to each thing [Read]
9. Objects / C. Structure of Objects / 5. Composition of an Object
If a chair could be made of slightly different material, that could lead to big changes [Hale]
10. Modality / A. Necessity / 2. Nature of Necessity
Equating necessity with truth in every possible world is the S5 conception of necessity [Read]
10. Modality / A. Necessity / 3. Types of Necessity
Absolute necessities are necessarily necessary [Hale]
'Absolute necessity' is when there is no restriction on the things which necessitate p [Hale]
Logical and metaphysical necessities differ in their vocabulary, and their underlying entities [Hale]
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity is something which is true, no matter what else is the case [Hale]
Maybe each type of logic has its own necessity, gradually becoming broader [Hale]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
Some people even claim that conditionals do not express propositions [Read]
The standard view of conditionals is that they are truth-functional [Read]
The point of conditionals is to show that one will accept modus ponens [Read]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
It seems that we cannot show that modal facts depend on non-modal facts [Hale]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
The big challenge for essentialist views of modality is things having necessary existence [Hale]
Essentialism doesn't explain necessity reductively; it explains all necessities in terms of a few basic natures [Hale]
If necessity derives from essences, how do we explain the necessary existence of essences? [Hale]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read]
What are these worlds, that being true in all of them makes something necessary? [Hale]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
How can modal Platonists know the truth of a modal proposition? [Read]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds make every proposition true or false, which endorses classical logic [Hale]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
A possible world is a determination of the truth-values of all propositions of a domain [Read]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
The mind abstracts ways things might be, which are nonetheless real [Read]
18. Thought / C. Content / 6. Broad Content
The molecules may explain the water, but they are not what 'water' means [Hale]
19. Language / C. Assigning Meanings / 4. Compositionality
Negative existentials with compositionality make the whole sentence meaningless [Read]
19. Language / D. Propositions / 1. Propositions
A proposition objectifies what a sentence says, as indicative, with secure references [Read]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]