Combining Philosophers

All the ideas for Michael Bratman, Alfred Tarski and Richard Dedekind

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111 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Some say metaphysics is a highly generalised empirical study of objects [Tarski]
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Disputes that fail to use precise scientific terminology are all meaningless [Tarski]
2. Reason / D. Definition / 1. Definitions
For a definition we need the words or concepts used, the rules, and the structure of the language [Tarski]
2. Reason / D. Definition / 9. Recursive Definition
Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter]
3. Truth / A. Truth Problems / 2. Defining Truth
In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski]
Tarski proved that truth cannot be defined from within a given theory [Tarski, by Halbach]
Tarski proved that any reasonably expressive language suffers from the liar paradox [Tarski, by Horsten]
'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless [Tarski]
Definitions of truth should not introduce a new version of the concept, but capture the old one [Tarski]
A definition of truth should be materially adequate and formally correct [Tarski]
A rigorous definition of truth is only possible in an exactly specified language [Tarski]
We may eventually need to split the word 'true' into several less ambiguous terms [Tarski]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Tarski's Theorem renders any precise version of correspondence impossible [Tarski, by Halbach]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Scheme (T) is not a definition of truth [Tarski]
Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Tarski, by Horsten]
Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Tarski, by Halbach]
Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson on Tarski]
Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson on Tarski]
Tarski made truth relative, by only defining truth within some given artificial language [Tarski, by O'Grady]
Tarski has to avoid stating how truths relate to states of affairs [Kirkham on Tarski]
Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Tarski, by Hossack]
'"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski]
It is convenient to attach 'true' to sentences, and hence the language must be specified [Tarski]
In the classical concept of truth, 'snow is white' is true if snow is white [Tarski]
Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate' [Tarski]
Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction [Tarski]
We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true [Tarski]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski]
Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt]
We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten]
For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham]
Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham]
Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson]
The best truth definition involves other semantic notions, like satisfaction (relating terms and objects) [Tarski]
Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [Tarski]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
We can't use a semantically closed language, or ditch our logic, so a meta-language is needed [Tarski]
The metalanguage must contain the object language, logic, and defined semantics [Tarski]
3. Truth / F. Semantic Truth / 2. Semantic Truth
Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach]
Tarski defined truth for particular languages, but didn't define it across languages [Davidson on Tarski]
Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach on Tarski]
Tarski's 'truth' is a precise relation between the language and its semantics [Tarski, by Walicki]
Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith on Tarski]
Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Tarski, by Haack]
A physicalist account must add primitive reference to Tarski's theory [Field,H on Tarski]
Physicalists should explain reference nonsemantically, rather than getting rid of it [Tarski, by Field,H]
Tarski had a theory of truth, and a theory of theories of truth [Tarski, by Read]
If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs [Field,H on Tarski]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Tarski's had the first axiomatic theory of truth that was minimally adequate [Tarski, by Horsten]
Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Tarski, by Halbach]
Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson]
We need an undefined term 'true' in the meta-language, specified by axioms [Tarski]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
Truth can't be eliminated from universal claims, or from particular unspecified claims [Tarski]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Semantics is a very modest discipline which solves no real problems [Tarski]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
An infinite set maps into its own proper subset [Dedekind, by Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Set theory and logic are fairy tales, but still worth studying [Tarski]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
There is no clear boundary between the logical and the non-logical [Tarski]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall]
Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
X follows from sentences K iff every model of K also models X [Tarski]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
A name denotes an object if the object satisfies a particular sentential function [Tarski]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Tarski built a compositional semantics for predicate logic, from dependent satisfactions [Tarski, by McGee]
Tarksi invented the first semantics for predicate logic, using this conception of truth [Tarski, by Kirkham]
Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski]
A language containing its own semantics is inconsistent - but we can use a second language [Tarski]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski]
Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach]
A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski]
5. Theory of Logic / K. Features of Logics / 2. Consistency
Using the definition of truth, we can prove theories consistent within sound logics [Tarski]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Tarski, by Fisher]
The Liar makes us assert a false sentence, so it must be taken seriously [Tarski]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
Numbers are free creations of the human mind, to understand differences [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman]
Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck]
Order, not quantity, is central to defining numbers [Dedekind, by Monk]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
We want the essence of continuity, by showing its origin in arithmetic [Dedekind]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
A cut between rational numbers creates and defines an irrational number [Dedekind]
Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell]
Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock]
I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting we see the human ability to relate, correspond and represent [Dedekind]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
Arithmetic is just the consequence of counting, which is the successor operation [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
If x changes by less and less, it must approach a limit [Dedekind]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
I am a deeply convinced nominalist [Tarski]
9. Objects / A. Existence of Objects / 3. Objects in Thought
A thing is completely determined by all that can be thought concerning it [Dedekind]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett]
We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait]
19. Language / E. Analyticity / 1. Analytic Propositions
Sentences are 'analytical' if every sequence of objects models them [Tarski]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
Intentions must be mutually consistent, affirm appropriate means, and fit the agent's beliefs [Bratman, by Wilson/Schpall]
Intentions are normative, requiring commitment and further plans [Bratman, by Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / b. Types of intention
Intention is either the aim of an action, or a long-term constraint on what we can do [Bratman, by Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / c. Reducing intentions
Bratman rejected reducing intentions to belief-desire, because they motivate, and have their own standards [Bratman, by Wilson/Schpall]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
Taste is the capacity to judge an object or representation which is thought to be beautiful [Tarski, by Schellekens]