Combining Philosophers

All the ideas for George Engelbretsen, James Robert Brown and Michael della Rocca

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48 ideas

2. Reason / D. Definition / 2. Aims of Definition
Definitions should be replaceable by primitives, and should not be creative [Brown,JR]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
If facts are the truthmakers, they are not in the world [Engelbretsen]
There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
Traditional term logic struggled to express relations [Engelbretsen]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Na´ve logical sets
Na´ve set theory assumed that there is a set for every condition [Brown,JR]
Nowadays conditions are only defined on existing sets [Brown,JR]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The 'iterative' view says sets start with the empty set and build up [Brown,JR]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
A flock of birds is not a set, because a set cannot go anywhere [Brown,JR]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
If a proposition is false, then its negation is true [Brown,JR]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical syntax is actually close to surface linguistic form [Engelbretsen]
Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics is the only place where we are sure we are right [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / n. Pi
π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Mathematics represents the world through structurally similar models. [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
There is no limit to how many ways something can be proved in mathematics [Brown,JR]
Computers played an essential role in proving the four-colour theorem of maps [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Set theory may represent all of mathematics, without actually being mathematics [Brown,JR]
When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
To see a structure in something, we must already have the idea of the structure [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
The irrationality of root-2 was achieved by intellect, not experience [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Numbers are not abstracted from particulars, because each number is a particular [Brown,JR]
There is an infinity of mathematical objects, so they can't be physical [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Empiricists base numbers on objects, Platonists base them on properties [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Does some mathematics depend entirely on notation? [Brown,JR]
For nomalists there are no numbers, only numerals [Brown,JR]
The most brilliant formalist was Hilbert [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
There are no constructions for many highly desirable results in mathematics [Brown,JR]
Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
David's 'Napoleon' is about something concrete and something abstract [Brown,JR]
7. Existence / D. Theories of Reality / 7. Facts / a. Facts
Facts are not in the world - they are properties of the world [Engelbretsen]
7. Existence / E. Categories / 4. Category Realism
Individuals are arranged in inclusion categories that match our semantics [Engelbretsen]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
The distinction between necessary and essential properties can be ignored [Rocca]
18. Thought / E. Abstraction / 1. Abstract Thought
The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR]
'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR]
19. Language / B. Reference / 2. Denoting
Terms denote objects with properties, and statements denote the world with that property [Engelbretsen]
19. Language / D. Propositions / 1. Propositions
'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen]
19. Language / F. Communication / 3. Denial
Negating a predicate term and denying its unnegated version are quite different [Engelbretsen]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR]