52 ideas
| 19115 | You can 'rebut' an argument's conclusion, or 'undercut' its premises [Antonelli] |
| 19119 | We infer that other objects are like some exceptional object, if they share some of its properties [Antonelli] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 19111 | Reasoning may be defeated by new premises, or by finding out more about the given ones [Antonelli] |
| 19114 | Should we accept Floating Conclusions, derived from two arguments in conflict? [Antonelli] |
| 19113 | Weakest Link Principle: prefer the argument whose weakest link is the stronger [Antonelli] |
| 19116 | Non-monotonic core: Reflexivity, Cut, Cautious Monotonicity, Left Logical Equivalence, Right Weakening [Antonelli] |
| 19117 | We can rank a formula by the level of surprise if it were to hold [Antonelli] |
| 19118 | People don't actually use classical logic, but may actually use non-monotonic logic [Antonelli] |
| 12430 | Classical logic is our preconditions for assessing empirical evidence [Kitcher] |
| 12431 | I believe classical logic because I was taught it and use it, but it could be undermined [Kitcher] |
| 19110 | In classical logic the relation |= has Monotony built into its definition [Antonelli] |
| 19112 | Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved [Antonelli] |
| 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] |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [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] |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [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] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 12428 | Many necessities are inexpressible, and unknowable a priori [Kitcher] |
| 12429 | Knowing our own existence is a priori, but not necessary [Kitcher] |
| 19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
| 19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
| 19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
| 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] |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| 19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
| 19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |