Combining Philosophers

All the ideas for Archimedes, Samir Okasha and Marcus Rossberg

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22 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10759 There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753 Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752 Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754 In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10761 Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755 A deductive system is only incomplete with respect to a formal semantics [Rossberg]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
7. Existence / C. Structure of Existence / 2. Reduction
22180 Multiple realisability is said to make reduction impossible [Okasha]
14. Science / A. Basis of Science / 3. Experiment
22172 Not all sciences are experimental; astronomy relies on careful observation [Okasha]
22177 Randomised Control Trials have a treatment and a control group, chosen at random [Okasha]
14. Science / A. Basis of Science / 6. Falsification
22174 The discoverers of Neptune didn't change their theory because of an anomaly [Okasha]
22175 Science mostly aims at confirming theories, rather than falsifying them [Okasha]
14. Science / B. Scientific Theories / 1. Scientific Theory
22182 Theories with unobservables are underdetermined by the evidence [Okasha]
14. Science / B. Scientific Theories / 5. Commensurability
22185 Two things can't be incompatible if they are incommensurable [Okasha]
14. Science / C. Induction / 1. Induction
22176 Induction is inferences from examined to unexamined instances of a given kind [Okasha]
14. Science / C. Induction / 6. Bayes's Theorem
22178 If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
22173 Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha]
27. Natural Reality / G. Biology / 5. Species
17366 Virtually all modern views of speciation rest on relational rather than intrinsic features [Okasha]