Combining Philosophers

All the ideas for Ryan Wasserman, Gerhard Gentzen and Gideon Rosen

expand these ideas     |    start again     |     specify just one area for these philosophers


40 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Philosophers are often too fussy about words, dismissing perfectly useful ordinary terms [Rosen]
2. Reason / D. Definition / 1. Definitions
Figuring in the definition of a thing doesn't make it a part of that thing [Rosen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
The logical connectives are 'defined' by their introduction rules [Gentzen]
Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
Explanations fail to be monotonic [Rosen]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
Things could be true 'in virtue of' others as relations between truths, or between truths and items [Rosen]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
Facts are structures of worldly items, rather like sentences, individuated by their ingredients [Rosen]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
An 'intrinsic' property is one that depends on a thing and its parts, and not on its relations [Rosen]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
How we refer to abstractions is much less clear than how we refer to other things [Rosen]
9. Objects / A. Existence of Objects / 4. Impossible objects
A Meinongian principle might say that there is an object for any modest class of properties [Rosen]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman]
Constitution is not identity, because it is an asymmetric dependence relation [Wasserman]
There are three main objections to seeing constitution as different from identity [Wasserman]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman]
9. Objects / F. Identity among Objects / 3. Relative Identity
Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman]
10. Modality / A. Necessity / 5. Metaphysical Necessity
'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen]
Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen]
Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen]
The excellent notion of metaphysical 'necessity' cannot be defined [Rosen]
Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen]
Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen]
10. Modality / A. Necessity / 6. Logical Necessity
Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen]
10. Modality / B. Possibility / 3. Combinatorial possibility
Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Are necessary truths rooted in essences, or also in basic grounding laws? [Rosen]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen]
18. Thought / E. Abstraction / 2. Abstracta by Selection
The Way of Abstraction used to say an abstraction is an idea that was formed by abstracting [Rosen]
18. Thought / E. Abstraction / 5. Abstracta by Negation
Nowadays abstractions are defined as non-spatial, causally inert things [Rosen]
Chess may be abstract, but it has existed in specific space and time [Rosen]
Sets are said to be abstract and non-spatial, but a set of books can be on a shelf [Rosen]
18. Thought / E. Abstraction / 6. Abstracta by Conflation
Conflating abstractions with either sets or universals is a big claim, needing a big defence [Rosen]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Functional terms can pick out abstractions by asserting an equivalence relation [Rosen]
Abstraction by equivalence relationships might prove that a train is an abstract entity [Rosen]
19. Language / E. Analyticity / 1. Analytic Propositions
'Bachelor' consists in or reduces to 'unmarried' male, but not the other way around [Rosen]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen]
27. Natural Reality / F. Chemistry / 1. Chemistry
An acid is just a proton donor [Rosen]