64 ideas
18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
10455 | Free logic at least allows empty names, but struggles to express non-existence [Bach] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
10454 | In first-order we can't just assert existence, and it is very hard to deny something's existence [Bach] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
10453 | In logic constants play the role of proper names [Bach] |
10452 | Proper names can be non-referential - even predicate as well as attributive uses [Bach] |
10456 | Millian names struggle with existence, empty names, identities and attitude ascription [Bach] |
10440 | An object can be described without being referred to [Bach] |
10444 | Definite descriptions can be used to refer, but are not semantically referential [Bach] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
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] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
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] |
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] |
10446 | Fictional reference is different inside and outside the fiction [Bach] |
10447 | We can refer to fictional entities if they are abstract objects [Bach] |
10443 | You 'allude to', not 'refer to', an individual if you keep their identity vague [Bach] |
10439 | What refers: indefinite or definite or demonstrative descriptions, names, indexicals, demonstratives? [Bach] |
10441 | If we can refer to things which change, we can't be obliged to single out their properties [Bach] |
10442 | We can think of an individual without have a uniquely characterizing description [Bach] |
10445 | It can't be real reference if it could refer to some other thing that satisfies the description [Bach] |
10457 | Since most expressions can be used non-referentially, none of them are inherently referential [Bach] |
10463 | Just alluding to or describing an object is not the same as referring to it [Bach] |
10459 | Context does not create reference; it is just something speakers can exploit [Bach] |
10460 | 'That duck' may not refer to the most obvious one in the group [Bach] |
10461 | What a pronoun like 'he' refers back to is usually a matter of speaker's intentions [Bach] |
10462 | Information comes from knowing who is speaking, not just from interpretation of the utterance [Bach] |
10458 | People slide from contextual variability all the way to contextual determination [Bach] |