Mastodawn

Mathematics is either inconsistent or incomplete.

What is your philosophical interpretation of Gödel’s incompleteness theorems?

#math #mathematics #maths #logic #MathematicalLogic #gödel #kurtgödel #godel #KurtGodel #Philosophy #PhilosophyOfMathematics #PhilosophicalLogic #philosophyoflogic #logic

Intro to Gödel’s Incompleteness Theorem

YouTube

Wilhelm_Grafe Oct 6

#HistoryOfLogic #logic #PhilosophyOfLogic

I'd like to share here the announcement of an upcoming event organized by folks at the University Federico II, Naples

https://sites.google.com/view/hol-workshop/home

HoL Workshop

Welcome to the website of the 1st Naples Workshop on the History of Logic. The Workshop will take place on 28-29 October 2025 at the Department of Humanities of the "Federico II" University of Naples. See the Venue page for more. The Workshop is meant as the opening of the second cycle (2025-2026)

Friedrich Wilhelm Grafe Oct 7, 2024

#philsci
#philmath
#epistemology
#PhilosophyOfLogic

happy to have my most current research paper now approved as a fixed preprint at Cambridge Open Engage

https://www.cambridge.org/engage/coe/article-details/67063c69cec5d6c142aac4e0

objects are (not) ...

... try to explore, what properties objects are presupposed to have, in order to enter the universe of discourse of an interpreted formalized language. First I review Frege′s analysis of the logical structure of truth value definite sentences of scientific colloquial language, to draw suggestions from his saturated vs. unsaturated sentence components paradigm. Next try investigate, in how far reference to non pure math objects might allow for a role as argument of a truth value function. Object kinds to be considered are: common sense objects, technical objects, humanities object kinds (social, psychical, ...), objects of art, ... , be they abstract, concrete, or in this respect mixed objects. Then have a comment on the just referenced label abstract objects. Next try to get an idea wrt the ontological significance of the fact, that pure math objects and functions in some important classical cases can be uniquely defined by means of categorical theories. Here, in the course of my argument, I have a little corollary wrt the standard model of first order Peano arithmetic, reducing the epistemological significance of the existence of the non standard models. Next, wrt a special concept of a formalized empirical theory, I care for whether the impure math objects and mixed objects described here, and complying best with truth value function mapping, are also reliable candidates for the ontological commitment of such theories; and discuss an alternative, which reduces the ontological significance of the universe of discourse of the theories intended models. -finis

Cambridge Open Engage

Friedrich Wilhelm Grafe Jun 23, 2024

#PhilosophyOfMathematics
#PhilosophyOfLogic

occasional sunday finding wrt the applicability of logic, worth noting and worth discussion.

... It serves little purpose to argue that logic exists outside mathematics. Whatever,
outside mathematics, is reducible to pure logic is invariably found, on close inspection, to be nothing but a strictly mathematical scheme (mostly combinatorial), so devised as to apply to some concrete situation; one need
only think e.g. of the classical syllogism (every man is mortal, Socrates is a man, etc.) to convince oneself of the truth of this statement. Outside mathematics, even in the physical sciences, there is no statement that does not have to be qualified by the knowledge, common to the speaker and to his audience, of some physical or mental context. ...
[FOUNDATIONS OF MATHEMATICS FOR THE WORKING MATHEMATICIAN,
N. BOURBAKI, JSL 1949]

Friedrich Wilhelm Grafe Apr 21, 2024

@philosophy
@philosophie

@philpapers_bot
brought to my attention this nice piece in the #PhilosophyOfLogic

it's open access and imop truly worth a read

https://philpapers.org/rec/REIASN

Andrea Reichenberger, A Short Note on the Early History of the Spectrum Problem and Finite Model Theory - PhilPapers

Finite model theory is currently not one of the hot topics in the philosophy and history of mathematics, not even in the philosophy and history of mathematical logic. The philosophy of ...

Friedrich Wilhelm Grafe Mar 4, 2024

my current (still draft) paper is about

object references in purportedly truth value definite sentences

think there's something good in it ...
😅 #nontology

#PhilosophyOfLogic
#AppliedLogic
#PhilMath
#PhilSci
#PhilosophyOfMathematics
#PhilosophyOfScience

https://philarchive.org/rec/GRAOAN

Friedrich Wilhelm Grafe, Objects are (not) ... - PhilArchive

My goal in this paper is, to tentatively sketch and try defend some observations regarding the ontological dignity of object references, as they may be used from within in a formalized ...

Friedrich Wilhelm Grafe Dec 27, 2023

@philosophy
@philosophie

#logic

#PhilosophyOfLogic

#WorldLogicDay2024

these days found two events announced:

https://sites.google.com/view/wld-gil-2024/

https://sites.google.com/view/wldzurich2024

the general #wld24 event list may be found at:

http://wld.cipsh.international/wld2024.html