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All the ideas for 'Confessions', 'Hilbert's Programme' and 'Nominalism and Substitutional Quantifiers'

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38 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)]
Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)]
5. Theory of Logic / G. Quantification / 1. Quantification
Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)]
Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)]
Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)]
A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
The study of mathematical foundations needs new non-mathematical concepts [Kreisel]
7. Existence / A. Nature of Existence / 2. Types of Existence
I prefer a lack of form to mean non-existence, than to think of some quasi-existence [Augustine]
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
Is being just referent of the verb 'to be'? [Marcus (Barcan)]
7. Existence / D. Theories of Reality / 1. Ontologies
Three main questions seem to be whether a thing is, what it is, and what sort it is [Augustine]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
Nominalists say predication is relations between individuals, or deny that it refers [Marcus (Barcan)]
9. Objects / A. Existence of Objects / 3. Objects in Thought
If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)]
9. Objects / F. Identity among Objects / 2. Defining Identity
Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Mind and memory are the same, as shown in 'bear it in mind' or 'it slipped from mind' [Augustine]
Memory contains innumerable principles of maths, as well as past sense experiences [Augustine]
We would avoid remembering sorrow or fear if that triggered the emotions afresh [Augustine]
I can distinguish different smells even when I am not experiencing them [Augustine]
Why does joy in my mind make me happy, but joy in my memory doesn't? [Augustine]
15. Nature of Minds / A. Nature of Mind / 6. Anti-Individualism
Memory is so vast that I cannot recognise it as part of my mind [Augustine]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
Without memory I could not even speak of myself [Augustine]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
If the future does not exist, how can prophets see it? [Augustine]
18. Thought / B. Mechanics of Thought / 5. Mental Files
Memories are preserved separately, according to category [Augustine]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
Everyone wants happiness [Augustine]
27. Natural Reality / C. Space / 3. Points in Space
The natural conception of points ducks the problem of naming or constructing each point [Kreisel]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
Maybe time is an extension of the mind [Augustine]
To be aware of time it can only exist in the mind, as memory or anticipation [Augustine, by Bardon]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
How can ten days ahead be a short time, if it doesn't exist? [Augustine]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
If the past is no longer, and the future is not yet, how can they exist? [Augustine]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
The whole of the current year is not present, so how can it exist? [Augustine]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
I know what time is, until someone asks me to explain it [Augustine]
27. Natural Reality / D. Time / 2. Passage of Time / h. Change in time
I disagree with the idea that time is nothing but cosmic movement [Augustine]
27. Natural Reality / E. Cosmology / 3. The Beginning
Heaven and earth must be created, because they are subject to change [Augustine]
28. God / A. Divine Nature / 5. God and Time
If God existed before creation, why would a perfect being desire to change things? [Augustine, by Bardon]
If God is outside time in eternity, can He hear prayers? [Augustine]