Combining Texts

All the ideas for 'fragments/reports', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'Truthmakers and Converse Barcan Formula'

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26 ideas

2. Reason / D. Definition / 2. Aims of Definition
Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
2. Reason / D. Definition / 7. Contextual Definition
We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
2. Reason / D. Definition / 11. Ostensive Definition
Only what is logically complex can be defined; what is simple must be pointed to [Frege]
3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
The truthmaker principle requires some specific named thing to make the difference [Williamson]
3. Truth / B. Truthmakers / 7. Making Modal Truths
Truthmaker is incompatible with modal semantics of varying domains [Williamson]
The converse Barcan formula will not allow contingent truths to have truthmakers [Williamson]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
If metaphysical possibility is not a contingent matter, then S5 seems to suit it best [Williamson]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson]
Converse Barcan: could something fail to meet a condition, if everything meets that condition? [Williamson]
5. Theory of Logic / G. Quantification / 1. Quantification
Not all quantification is either objectual or substitutional [Williamson]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
Not all quantification is objectual or substitutional [Williamson]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities [Frege, by Dummett]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
A number is a class of classes of the same cardinality [Frege, by Dummett]
Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
Only applicability raises arithmetic from a game to a science [Frege]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
If 'fact' is a noun, can we name the fact that dogs bark 'Mary'? [Williamson]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
The first demand of logic is of a sharp boundary [Frege]
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
Our ability to count objects across possibilities favours the Barcan formulas [Williamson]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
18. Thought / E. Abstraction / 8. Abstractionism Critique
If we abstract the difference between two houses, they don't become the same house [Frege]
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]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
A thing can't be the only necessary existent, because its singleton set would be as well [Williamson]