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All the ideas for 'Higher-Order Logic', 'Summula philosophiae naturalis' and 'A Future for Presentism'

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29 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
Is Sufficient Reason self-refuting (no reason to accept it!), or is it a legitimate explanatory tool? [Bourne]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
The redundancy theory conflates metalinguistic bivalence with object-language excluded middle [Bourne]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Some say that second-order logic is mathematics, not logic [Shapiro]
If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
7. Existence / E. Categories / 5. Category Anti-Realism
Ockham was an anti-realist about the categories [William of Ockham, by Pasnau]
8. Modes of Existence / A. Relations / 1. Nature of Relations
All relations between spatio-temporal objects are either spatio-temporal, or causal [Bourne]
It is a necessary condition for the existence of relations that both of the relata exist [Bourne]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau]
Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
The idea of simultaneity in Special Relativity is full of verificationist assumptions [Bourne]
Relativity denies simultaneity, so it needs past, present and future (unlike Presentism) [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
Special Relativity allows an absolute past, future, elsewhere and simultaneity [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
No-Futurists believe in past and present, but not future, and say the world grows as facts increase [Bourne]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
How can presentists talk of 'earlier than', and distinguish past from future? [Bourne]
Presentism seems to deny causation, because the cause and the effect can never coexist [Bourne]
Since presentists treat the presentness of events as basic, simultaneity should be define by that means [Bourne]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
Time is tensed or tenseless; the latter says all times and objects are real, and there is no passage of time [Bourne]
B-series objects relate to each other; A-series objects relate to the present [Bourne]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
Time flows, past is fixed, future is open, future is feared but not past, we remember past, we plan future [Bourne]