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All the ideas for 'Grundgesetze der Arithmetik 1 (Basic Laws)', 'Person and Object' and 'Philosophical Logic: Intro to Advanced Topics'

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49 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Many philosophers aim to understand metaphysics by studying ourselves [Chisholm]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
I use variables to show that each item remains the same entity throughout [Chisholm]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward]
Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
My Basic Law V is a law of pure logic [Frege]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
Events are states of affairs that occur at certain places and times [Chisholm]
7. Existence / D. Theories of Reality / 9. States of Affairs
The mark of a state of affairs is that it is capable of being accepted [Chisholm]
A state of affairs pertains to a thing if it implies that it has some property [Chisholm]
I propose that events and propositions are two types of states of affairs [Chisholm]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Some properties, such as 'being a widow', can be seen as 'rooted outside the time they are had' [Chisholm]
Some properties can never be had, like being a round square [Chisholm]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
If some dogs are brown, that entails the properties of 'being brown' and 'being canine' [Chisholm]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Maybe we can only individuate things by relating them to ourselves [Chisholm]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
Being the tallest man is an 'individual concept', but not a haecceity [Chisholm]
A haecceity is a property had necessarily, and strictly confined to one entity [Chisholm]
9. Objects / C. Structure of Objects / 7. Substratum
A peach is sweet and fuzzy, but it doesn't 'have' those qualities [Chisholm]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
If x is ever part of y, then y is necessarily such that x is part of y at any time that y exists [Chisholm, by Simons]
9. Objects / D. Essence of Objects / 3. Individual Essences
A traditional individual essence includes all of a thing's necessary characteristics [Chisholm]
9. Objects / E. Objects over Time / 7. Intermittent Objects
Intermittence is seen in a toy fort, which is dismantled then rebuilt with the same bricks [Chisholm, by Simons]
9. Objects / F. Identity among Objects / 5. Self-Identity
The property of being identical with me is an individual concept [Chisholm]
9. Objects / F. Identity among Objects / 9. Sameness
There is 'loose' identity between things if their properties, or truths about them, might differ [Chisholm]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
Do sense-data have structure, location, weight, and constituting matter? [Chisholm]
12. Knowledge Sources / B. Perception / 8. Adverbial Theory
'I feel depressed' is more like 'he runs slowly' than like 'he has a red book' [Chisholm]
If we can say a man senses 'redly', why not also 'rectangularly'? [Chisholm]
So called 'sense-data' are best seen as 'modifications' of the person experiencing them [Chisholm]
14. Science / D. Explanation / 1. Explanation / a. Explanation
Explanations have states of affairs as their objects [Chisholm]
16. Persons / B. Nature of the Self / 3. Self as Non-physical
I am picked out uniquely by my individual essence, which is 'being identical with myself' [Chisholm]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
Sartre says the ego is 'opaque'; I prefer to say that it is 'transparent' [Chisholm]
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
People use 'I' to refer to themselves, with the meaning of their own individual essence [Chisholm]
16. Persons / E. Rejecting the Self / 1. Self as Indeterminate
Bad theories of the self see it as abstract, or as a bundle, or as a process [Chisholm]
16. Persons / F. Free Will / 5. Against Free Will
Determinism claims that every event has a sufficient causal pre-condition [Chisholm]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
Frege took the study of concepts to be part of logic [Frege, by Shapiro]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
There are mere omissions (through ignorance, perhaps), and people can 'commit an omission' [Chisholm]
26. Natural Theory / A. Speculations on Nature / 1. Nature
The concept of physical necessity is basic to both causation, and to the concept of nature [Chisholm]
26. Natural Theory / C. Causation / 2. Types of cause
Some propose a distinct 'agent causation', as well as 'event causation' [Chisholm]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
A 'law of nature' is just something which is physically necessary [Chisholm]