Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Alexander Paseau"'
What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight
Autor:
Alexander Paseau
Publikováno v:
Synthese. 199:9161-9184
Number theory abounds with conjectures asserting that every natural number has some arithmetic property. An example is Goldbach’s Conjecture, which states that every even number greater than 2 is the sum of two primes. Enumerative inductive evidenc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fafc09f063c677cb7a139d55379d3d43
https://doi.org/10.1007/s11229-021-03198-1
https://doi.org/10.1007/s11229-021-03198-1
Autor:
Alexander Paseau, Owen Griffiths
Publikováno v:
Thought: A Journal of Philosophy. 10:188-198
By mimicking the standard definition for a formal language, we define what it is for a natural language to be compact. We set out a valid English argument none of whose finite subarguments is valid. We consider one by one objections to the argument's
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f1a03a076f84779178db7621aa656c41
https://doi.org/10.1002/tht3.492
https://doi.org/10.1002/tht3.492
Autor:
Alexander Paseau
Publikováno v:
Erkenntnis. 87:2307-2328
The idea that sentences can be closer or further apart in meaning is highly intuitive. Not only that, it is also a pillar of logic, semantic theory and the philosophy of science, and follows from other commitments about similarity. The present paper
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4877452984e07aa65e1dc7226fa377a6
https://doi.org/10.1007/s10670-020-00303-7
https://doi.org/10.1007/s10670-020-00303-7
Autor:
Alexander Paseau
Publikováno v:
The Mathematical Gazette. 100:442-449
Metamathematics is the mathematical study of mathematics itself. Two of its most famous theorems were proved by Kurt Gödel in 1931. In a simplified form, Gödel's first incompleteness theorem states that no reasonable mathematical system can prove a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b499a04cbd99b4efbb046da10df1a7b2
https://doi.org/10.1017/mag.2016.109
https://doi.org/10.1017/mag.2016.109
Autor:
Alexander Paseau
Publikováno v:
Mind. 125:177-207
Complete inferential rigour is achieved by breaking down arguments into steps that are as small as possible: inferential ‘atoms’. For example, a mathematical or philosophical argument may be made completely inferentially rigorous (‘atomized’)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::71a8802461805744e56f76a2c6c825f4
https://doi.org/10.1093/mind/fzv140
https://doi.org/10.1093/mind/fzv140
Autor:
Alexander Paseau
There are three types of naturalism in the philosophy of mathematics: metaphysical, epistemological and methodological. Metaphysical naturalists maintain that all entities are natural. One reading of this claim is that mathematical ontology is the on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ce1e9b3ea7f5baea1db94587fed969d9
https://doi.org/10.4324/9780415249126-y094-1
https://doi.org/10.4324/9780415249126-y094-1
Autor:
Alexander Paseau
Publikováno v:
The British Journal for the Philosophy of Science. 66:775-799
Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support (f...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cf8aa7cccda97f802022bce34772df3d
https://doi.org/10.1093/bjps/axu012
https://doi.org/10.1093/bjps/axu012
Autor:
Alexander Paseau
Publikováno v:
Analysis. 75:379-386
Frege’s Basic Law V is inconsistent. The reason often given is that it posits the existence of an injection (one-one mapping) from the larger collection of first-order concepts to the smaller collection of objects. This article explains what is rig
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6397afd388363110835b08cf8079600e
https://doi.org/10.1093/analys/anv046
https://doi.org/10.1093/analys/anv046
Autor:
Alexander Paseau
Publikováno v:
Synthese. 196:2621-2642
The point of formalisation is to model various aspects of natural language. Perhaps the main use to which formalisation is put is to model and explain inferential relations between different sentences. Judged solely by this objective, a formalisation
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::25d1faaa3b7bf57d3689db666e9ecaec
https://doi.org/10.1007/s11229-015-0705-5
https://doi.org/10.1007/s11229-015-0705-5