64 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] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| 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] |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| 6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik] |
| 12392 | Mathematical a priorism is conceptualist, constructivist or realist [Kitcher] |
| 18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher] |
| 12426 | The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher] |
| 12395 | Real numbers stand to measurement as natural numbers stand to counting [Kitcher] |
| 12425 | Complex numbers were only accepted when a geometrical model for them was found [Kitcher] |
| 18071 | A one-operation is the segregation of a single object [Kitcher] |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| 12387 | Mathematical knowledge arises from basic perception [Kitcher] |
| 12412 | My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher] |
| 18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher] |
| 18077 | The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher] |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| 11063 | Logicism struggles because there is no decent theory of analyticity [Hanna] |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| 11055 | Supervenience can add covariation, upward dependence, and nomological connection [Hanna] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 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] |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| 11078 | Intuition is only outside the 'space of reasons' if all reasons are inferential [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] |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| 11053 | Explanatory reduction is stronger than ontological reduction [Hanna] |
| 11081 | Imagination grasps abstracta, generates images, and has its own correctness conditions [Hanna] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 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] |
| 11048 | Humean Instrumental rationality is the capacity to seek contingent truths [Hanna] |
| 11047 | Hegelian holistic rationality is the capacity to seek coherence [Hanna] |
| 11046 | Kantian principled rationality is recognition of a priori universal truths [Hanna] |
| 11045 | Most psychologists are now cognitivists [Hanna] |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |