53 ideas
| 11051 | Frege's logical approach dominates the analytical tradition [Hanna] |
| 11054 | Scientism says most knowledge comes from the exact sciences [Hanna] |
| 11070 | 'Denying the antecedent' fallacy: φ→ψ, ¬φ, so ¬ψ [Hanna] |
| 11071 | 'Affirming the consequent' fallacy: φ→ψ, ψ, so φ [Hanna] |
| 11088 | We can list at least fourteen informal fallacies [Hanna] |
| 11059 | Circular arguments are formally valid, though informally inadmissible [Hanna] |
| 11089 | Formally, composition and division fallacies occur in mereology [Hanna] |
| 11058 | Logic is explanatorily and ontologically dependent on rational animals [Hanna] |
| 11072 | Logic is personal and variable, but it has a universal core [Hanna] |
| 11061 | Intensional consequence is based on the content of the concepts [Hanna] |
| 9912 | There are no such things as numbers [Benacerraf] |
| 9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
| 9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
| 13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
| 17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
| 17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
| 9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
| 17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
| 9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| 8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
| 8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
| 9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| 9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
| 9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
| 8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
| 9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
| 9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
| 9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
| 9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
| 11063 | Logicism struggles because there is no decent theory of analyticity [Hanna] |
| 11055 | Supervenience can add covariation, upward dependence, and nomological connection [Hanna] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 11083 | A sentence is necessary if it is true in a set of worlds, and nonfalse in the other worlds [Hanna] |
| 11086 | Metaphysical necessity can be 'weak' (same as logical) and 'strong' (based on essences) [Hanna] |
| 11084 | Logical necessity is truth in all logically possible worlds, because of laws and concepts [Hanna] |
| 11085 | Nomological necessity is truth in all logically possible worlds with our laws [Hanna] |
| 11077 | Intuition includes apriority, clarity, modality, authority, fallibility and no inferences [Hanna] |
| 11080 | Intuition is more like memory, imagination or understanding, than like perception [Hanna] |
| 11078 | Intuition is only outside the 'space of reasons' if all reasons are inferential [Hanna] |
| 11053 | Explanatory reduction is stronger than ontological reduction [Hanna] |
| 11081 | Imagination grasps abstracta, generates images, and has its own correctness conditions [Hanna] |
| 11082 | Should we take the 'depictivist' or the 'descriptivist/propositionalist' view of mental imagery? [Hanna] |
| 11067 | Rational animals have a normative concept of necessity [Hanna] |
| 11068 | One tradition says talking is the essence of rationality; the other says the essence is logic [Hanna] |
| 11047 | Hegelian holistic rationality is the capacity to seek coherence [Hanna] |
| 11048 | Humean Instrumental rationality is the capacity to seek contingent truths [Hanna] |
| 11046 | Kantian principled rationality is recognition of a priori universal truths [Hanna] |
| 11045 | Most psychologists are now cognitivists [Hanna] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |