That really depends on the definition of the term "objective". If the degree of objectivity of a shared belief increases with the number of believers,...
The theory (Q) is justified by its experimental test reports (P). Therefore, P => Q. The universal claim is not justified by visiting all cases in the...
Yes, I was only dealing with standard, objective methods for knowledge justification. It may be possible that knowledge is subjective. A belief may be...
I remember French fighter jets bombing Khadaffi's troops in order to make sure that the rebellion would succeed. It is not that I particularly liked K...
Hardy already admitted exactly that, in 1940, in "A Mathematician's Apology". It is not a secret: Hardy preferred his work to be considered pure mathe...
Concerning the coherence theory of truth, I agree with Bertrand Russell's objections: Perhaps the best-known objection to a coherence theory of truth ...
Numbers are still language. Diagrams are not. Bourbaki sought to ensure the purity of mathematics by axiomatizing and algebraizing. Bourbaki does not ...
Statements of reason, pure or not, will have to be expressed in language. Otherwise, they cannot be communicated. The term "purity" in Critique of Pur...
The real, physical world is something that will always be systematically eliminated from mathematics: Abstraction in mathematics is the process of ext...
Axiomatic thinking is meant to be used for abstract, Platonic worlds. It is not a tool for justifying statements about the real world, which are suppo...
Science is a growing collection of theories that can be justified by the scientific method. At any point in time it is a set, but over time it is a ch...
I think that Kant is the greatest epistemologist ever to have set foot on this earth. I also consider him to be the first epistemologist to have made ...
Dum Diversas (English: Until different) is a papal bull issued on 18 June 1452 by Pope Nicholas V. It authorized Afonso V of Portugal to conquer Sarac...
Islamic law has stiff maximum penalties for serious misbehaviour. Criminal justice is governed by sentencing guidelines. A maximum penalty of electroc...
Islam emerged out of Messianistic Judaism, i.e. Ebionite Christianity. That is why Hans Joachim Schoeps wrote: Thus we have a paradox of world-histori...
We do not have these basic universal axioms. We have no access to the Theory of Everything (ToE), also called, the Preserved Tablet of Wisdom. If we d...
Secular law is a concoction by the ruling elite at whose core core you can find a bunch of corrupt banksters. Of course, it suits the ruling elite abs...
There is also a merely mechanical reason why it does not work: Gödel incompleteness theorems. I am actually not against the use of meaning, i.e. infor...
V.I. Arnold is a constructivist heretic. I had to cringe when reading his article. Applied mathematics is the application of mathematical methods by d...
The term "mathematical science" is an oxymoron. A theorem is either mathematics or science but can never be both simultaneously. The two epistemic met...
"Applied math" is not math. If the object of mathematical language is the real world, it is not math. It is something else that merely uses mathematic...
The term "mathematical truth", with the term "true" being defined by the correspondence theory (CT) of truth, is actually an oxymoron. A mathematical ...
Yes, agreed. This problem is ignored and considered unimportant until our perception -- being an abstract model itself -- suffers from a serious abstr...
Physics does not use the axiomatic "method". Physics uses mathematical formalisms to maintain consistency in its theories, but has actually nothing to...
The lambda calculus was first described by Alonzo Church: Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician w...
"Philosophy" is exactly the type of term that layman dictionaries tend to get completely wrong. The person who wrote the definition, simply did not un...
No. The first thing will be to pick a subject for your degree, while the very concept of subject as some kind of subdivision of the world of knowledge...
A number is an abstraction that always emerges in a Turing-complete axiomatic system. For example, in the core axiomatization of functions, i.e. the l...
Mathematics, science, and history are not subject matters. They are epistemic domains, i.e. the sets of knowledge statements -- with knowledge a justi...
Number theory is no longer the dominant axiomatization in mathematics, and has not been for over a century (Dedekind-Peano). Nowadays, it is set theor...
Muslims believe that the divine destiny is when God wrote down in the Preserved Tablet ("al-lawh al-mahfooz") (several other spellings are used for th...
What we see, i.e. the input signals we receive, create some kind of model in our heads, i.e. an abstraction of the physical world. With all complex ab...
Say that L is the set of all possible expressions in language, then Lr is a subset of L in which the language expressions seek to be isomorphic with t...
I assume that the book is copyrighted, but I have still found a summary. Gödel's procedure is actually just a special case, i.e. merely an example, of...
The terminology is confusing in this regard, because metamathematics is defined as a subdivision of mathematics, while metaphysics is defined as non-p...
Ok, understood. I can only say that it is not the dominant view in mathematics, which is staunchly Platonic. There is a fringe philosophy, called cons...
I can only disagree. What about Game of Thrones? Doesn't the television series bathe in language? Does it even pretend to be about the real world? It ...
In fact, the term "Platonic" is just a figure of speech to refer to an abstraction, i.e. a mere language expression. I just use it to distinguish them...
Logic does not operate on real-world observables. It operates on statements, which are not real-world, but language objects that live in their own abs...
Proof is context-sensitive. It is only valid in the abstract, Platonic world in which it necessarily follows from its construction logic. For example,...
The real problem is that the proof is in violation of proof theory. Proving a theorem amounts to demonstrating that it necessarily follows from the ex...
It was probably quite predictable that a bout of scientific and technological progress would make some people, and even cultures, much more arrogant t...
You have (at least) two possible starting points. You can start from Euclid's classical axiomatic basis in geometry, or else axiomatize from number th...
I suspect that Socrates himself would have rejected the view: "Everything Socrates ever said, must be considered philosophical, because it was Socrate...
Yes, I agree. Furthermore, we do not really need to solve the problem. We would only need to show some progress, and give them impression that the app...
Yeah, that is why a highly simplified strategy is easier to implement. Check if the theorem is already known to be provable, and then it is not intere...
In my impression, we would need a function F that returns the a priori likelihood that any arbitrary theorem s is provable from theory T. From there o...
In the viewpoint that math is about symbol manipulation formalisms, we may not even be interested in the concept "meaning" as some kind of corresponde...
His argument is surprisingly closer to the examples Gettier gave, than it looks like. Gettier manually concocts what physicists call an entanglement, ...
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