Ideas of Theodore Sider, by Theme

[American, fl. 2001, Professor at Rutgers University, New Jersey, then New York University.]

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1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Maybe what distinguishes philosophy from science is its pursuit of necessary truths
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Metaphysical enquiry can survive if its conclusions are tentative
Your metaphysics is 'cheating' if your ontology won't support the beliefs you accept
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysics as Science
Metaphysics is not about what exists or is true or essential; it is about the structure of reality
Extreme doubts about metaphysics also threaten to undermine the science of unobservables
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics as Conceptual
It seems unlikely that the way we speak will give insights into the universe
1. Philosophy / F. Analytic Philosophy / 2. Conceptual Analysis
Conceptual analysts trust particular intuitions much more than general ones
2. Reason / D. Definition / 12. Against Definition
Philosophical concepts are rarely defined, and are not understood by means of definitions
It seems possible for a correct definition to be factually incorrect, as in defining 'contact'
3. Truth / A. Truth Problems / 3. Value of Truth
We don't care about plain truth, but truth in joint-carving terms
3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
Orthodox truthmaker theories make entities fundamental, but that is poor for explanation
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
'Theorems' are formulas provable from no premises at all
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth tables assume truth functionality, and are just pictures of truth functions
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
Intuitively, deontic accessibility seems not to be reflexive, but to be serial
In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
System B introduces iterated modalities
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and KK)
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
We can treat modal worlds as different times
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
System B is needed to prove the Barcan Formula
The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic
Converse Barcan Formula: □∀αφ→∀α□φ
The Barcan schema implies if X might have fathered something, there is something X might have fathered
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
You can employ intuitionist logic without intuitionism about mathematics
4. Formal Logic / G. Formal Mereology / 1. Mereology
'Gunk' is an object in which proper parts all endlessly have further proper parts
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
Which should be primitive in mereology - part, or overlap?
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
There is a real issue over what is the 'correct' logic
'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or p'
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Classical logic is good for mathematics and science, but less good for natural language
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
The most popular account of logical consequence is the semantic or model-theoretic one
Maybe logical consequence is more a matter of provability than of truth-preservation
Maybe logical consequence is a primitive notion
Maybe logical consequence is impossibility of the premises being true and the consequent false
Modal accounts of logical consequence are simple necessity, or essential use of logical words
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
A 'theorem' is an axiom, or the last line of a legitimate proof
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
A 'total' function must always produce an output for a given domain
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
λ can treat 'is cold and hungry' as a single predicate
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
No assumptions in axiomatic proofs, so no conditional proof or reductio
Good axioms should be indisputable logical truths
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step'
Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Natural deduction helpfully allows reasoning with assumptions
'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
We can build proofs just from conclusions, rather than from plain formulae
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Valuations in PC assign truth values to formulas relative to variable assignments
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
The semantical notion of a logical truth is validity, being true in all interpretations
It is hard to say which are the logical truths in modal logic, especially for iterated modal operators
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation
5. Theory of Logic / K. Features of Logics / 4. Completeness
In a complete logic you can avoid axiomatic proofs, by using models to show consequences
5. Theory of Logic / K. Features of Logics / 6. Compactness
Compactness surprisingly says that no contradictions can emerge when the set goes infinite
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / e. Peano arithmetic 2nd-order
A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically
7. Existence / B. Change in Existence / 2. Processes
Four-dimensionalism sees things and processes as belonging in the same category
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
Supervenience is a modal connection
7. Existence / C. Structure of Existence / 6. Fundamentals / b. Types of fundamental
Is fundamentality in whole propositions (and holistic), or in concepts (and atomic)?
Tables and chairs have fundamental existence, but not fundamental natures
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
Unlike things, stuff obeys unrestricted composition and mereological essentialism
7. Existence / D. Theories of Reality / 8. States of Affairs
We must distinguish 'concrete' from 'abstract' and necessary states of affairs.
7. Existence / D. Theories of Reality / 9. Vagueness / e. Supervaluation for vagueness
Supervaluational logic is classical, except when it adds the 'Definitely' operator
We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings
A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation
A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification
7. Existence / D. Theories of Reality / 10. Ontological Commitment / d. Commitment of theories
Accept the ontology of your best theory - and also that it carves nature at the joints
8. Modes of Existence / A. Relations / 1. Nature of Relations
A relation is a feature of multiple objects taken together
8. Modes of Existence / B. Properties / 3. Types of Properties
A property is intrinsic if an object alone in the world can instantiate it
8. Modes of Existence / B. Properties / 6. Categorical Properties
Proper ontology should only use categorical (actual) properties, not hypothetical ones
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Predicates can be 'sparse' if there is a universal, or if there is a natural property or relation
9. Objects / A. Existence of Objects / 4. Individuation / e. Individuation by kind
If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
The stage view of objects is best for dealing with coincident entities
9. Objects / C. Structure of Objects / 5. Composition of an Object
'Composition as identity' says that an object just is the objects which compose it
9. Objects / D. Essence of Objects / 12. Essential Parts
Mereological essentialism says an object's parts are necessary for its existence
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essence (even if nonmodal) is not fundamental in metaphysics
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts'
Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time
4D says each spatiotemporal object must have a temporal part at every moment at which it exists
4D says intrinsic change is difference between successive parts
9. Objects / E. Objects over Time / 5. Temporal Parts
Temporal parts are instantaneous
How can an instantaneous stage believe anything, if beliefs take time?
Temporal parts exist, but are not prior building blocks for objects
Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts
9. Objects / E. Objects over Time / 9. Ship of Theseus
The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The identity of indiscernibles is necessarily true, if being a member of some set counts as a property
9. Objects / F. Identity among Objects / 8. Leibniz's Law
If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity
10. Modality / A. Necessity / 3. Types of Necessity
'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist
10. Modality / A. Necessity / 5. Metaphysical Necessity
Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible
10. Modality / A. Necessity / 6. Logical Necessity
Logical truths must be necessary if anything is
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Humeans say that we decide what is necessary
Modal terms in English are entirely contextual, with no modality outside the language
10. Modality / C. Sources of Modality / 3. Necessity by Convention
Conventionalism doesn't seem to apply to examples of the necessary a posteriori
If truths are necessary 'by convention', that seems to make them contingent
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
Humeans says mathematics and logic are necessary because that is how our concept of necessity works
10. Modality / C. Sources of Modality / 5. Modality from Actuality
The world does not contain necessity and possibility - merely how things are
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Transworld identity is not a problem in de dicto sentences, which needn't identify an individual
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterparts rest on similarity, so there are many such relations in different contexts
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost
14. Science / B. Scientific Theories / 2. Aim of Science
A theory which doesn't fit nature is unexplanatory, even if it is true
14. Science / B. Scientific Theories / 8. Ramsey Sentences
If I used ramsey sentences to eliminate fundamentality from my theory, that would be a real loss
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
Problem predicates in induction don't reflect the structure of nature
Two applications of 'grue' do not guarantee a similarity between two things
14. Science / C. Induction / 6. Bayes's Theorem
Bayes produces weird results if the prior probabilities are bizarre
14. Science / D. Explanation / 1. Explanation / a. Explanation
Explanations must cite generalisations
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
If the ultimate explanation is a list of entities, no laws, patterns or mechanisms can be cited
15. Nature of Minds / B. Properties of Minds / 4. Intentionality / a. Nature of intentionality
Intentionality is too superficial to appear in the catalogue of ultimate physics
19. Language / B. Meaning / 4. Meaning as Use
Prior to conventions, not all green things were green?
19. Language / C. Semantics / 7. Two-Dimensional Semantics
'Water' is two-dimensionally inconstant, with different intensions in different worlds
19. Language / F. Analytic/Synthetic / 3. Analytic Truths
Conventions are contingent and analytic truths are necessary, so that isn't their explanation
19. Language / F. Analytic/Synthetic / 4. Analytic/Synthetic Critique
Analyticity has lost its traditional role, which relied on truth by convention
26. Natural Theory / B. Concepts of Nature / 3. Space / c. Substantival space
Space has real betweenness and congruence structure (though it is not the Euclidean concepts)
26. Natural Theory / B. Concepts of Nature / 4. Time / a. Time
The central question in the philosophy of time is: How alike are time and space?
26. Natural Theory / B. Concepts of Nature / 4. Time / b. Tensed (A) time
Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance
26. Natural Theory / B. Concepts of Nature / 4. Time / c. Tenseless (B) time
The B-series involves eternalism, and the reduction of tense
The B-theory is adequate, except that it omits to say which time is present
26. Natural Theory / B. Concepts of Nature / 4. Time / f. Presentism
Presentists must deny truths about multiple times
For Presentists there must always be a temporal vantage point for any description
26. Natural Theory / B. Concepts of Nature / 4. Time / g. Eternalism
The spotlight theorists accepts eternal time, but with a spotlight of the present moving across it
26. Natural Theory / B. Concepts of Nature / 4. Time / h. Growing block of time
Between presentism and eternalism is the 'growing block' view - the past is real, the future is not
26. Natural Theory / B. Concepts of Nature / 5. Space-Time
Space is 3D and lacks a direction; time seems connected to causation
26. Natural Theory / D. Laws of Nature / 12. Against Laws of Nature
The notion of law doesn't seem to enhance physical theories
Many of the key theories of modern physics do not appear to be 'laws'
27. Natural Reality / A. Physics / 2. Movement
Maybe motion is a dynamical quantity intrinsic to a thing at a particular time