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98

Neither Harris nor Hitchens dismiss or ridicule non-empirical philosophy itself. Harris, in particular, calls himself a philosopher and studies Eastern religions and similar traditions. What they ridicule, and rightly so, are the many attempts by philosophy and religion to make pronouncements about the physical world based on their non-empirical philosophy. ...


55

"p is false" implies "p is not true", but not vice verse because p can also be nonsense. "2 + 2 = 5" is both false and not true. "2 + 2 > red" is neither true nor false because it is nonsense. If it were false, its negation "2 + 2 ≤ red" would be true, which is not the case. Source An Inquiry Into Meaning and Truth


27

Any effectively axiomatized formal system that extends a very basic theory of formal arithmetic called Robinson Arithmetic (Q) will contain an undecidable sentence. In full generality, you can state the syntactic version of the First Incompleteness Theorem as follows: (G1T) For any effectively axiomatized theory T that extends Q there exists a T-sentence ...


24

How to think about "P ⊃ Q" in plain English In propositional logic, P ⊃ Q is what is called a material implication. It doesn't mean that P and Q mean the same thing (they might not have the same truth value); all that it is, is a claim that if P is true, then Q is also true — without making any more claims than this. An alternative ...


22

This is a very huge question spanning multiple fields in philosophy. I do not have the expertise to cover all of these, so I'll focus on my personal favourite, the Philosophy of Mind aspect. As it stands there are no universally agreed upon answers to whether humans are different from computers in how they think. There are people on both sides of the ...


19

The quote about facts gets it pretty right. A fact is, for many philosophers, a part of reality (Russel, for example). So as there are people and tables and chairs in our world, there is also the fact that I am sitting on the chair. It is as real as the chair itself. You often see some kind of brackets when someone speaks about fact, so for example: < I ...


17

I agree with the comment of @Philip Klöcking concerning the success story of empiricism in science. Apparently philosophy is not based on experience, in particular it is not based on observation. But the great benefit of the scientific method is the possibility to check its results. It is possible to derive consequences from scientific theories and to test ...


17

It is not just that empiricism works, and in 300 years has brought us from semaphore lines to global high speed interconnects, or that non-empiricism is a fervent breeding ground for falsehoods and mysticism; those are true and more than justify aversion to the magical, but they don't explain why that should be the case. Rather, it is that in the modern day ...


16

There isn't anything wrong with justifying a claim that Peano Arithmetic is either inconsistent or incomplete by reference to Gödel's Incompleteness Theorems; the claim is a direct application of the first Incompleteness Theorem. Gödel showed that any formal system of adequate expressive power for doing formal arithmetic was either inconsistent or ...


16

Quantifiers in connection to AND and OR In the most common forms of predicate logic, ∀ and ∃ act like a sort of logical conjunction (AND) across all objects, and logical disjunction (OR) across all objects, respectively. Connection between ∀ and 'AND' Consider an argument in which the only 'objects' are Scottish people, and let EPP(x) =...


14

In the classical logic something is neither true nor false if it is grammatically malformed to have a truth value, so 2+5 or "x is blue" are not "true", but not "false" either, they are not truth-apt. The classical assumption was that all truth-apt expressions can be distinguished by syntax alone, i.e. there is a clear way to tell from how they are formed ...


13

This is why people invented words like "probably": if a man habitually has yoghurt every morning then tomorrow morning I expect him to have yoghurt at breakfast though of course there is a small chance that he might not. That small chance is where the attention of scepticism directs itself; scepticism by itself - pure sceptism otherwise known classically ...


12

Your (1) and (2) are not enough. Here is an example: suppose I have excellent reasons to believe that the earth is round (I've seen photos, listened to lectures, etc.), and that it is in fact true that the earth is round, but nevertheless I do not believe it (because I'm irrational). Clearly this is not a case of knowledge. There is a recent view, however, ...


11

"Knowledge" is the primary subject of Epistemology, one of the major branches of philosophy. Its importance cannot be overstated. I suggest that you look at some basic encyclopedia articles on the subject, such as the one from Stanford, the IEP, or Wikipedia.


11

It is a natural idea, but unfortunately the answer is no, it is not feasible. The root of incompleteness is not numbers, but the possibility of (implicit) self-reference, arithmetic is just the simplest structure that already realizes that possibility. In fact, one does not even need the Peano arithmetic, but a much weaker Robinson arithmetic without even ...


10

As Michael points out, the notion of knowledge in philosophy is of great importance. The entire field of epistemology (which is essentially one of the top five fields of philosophy) focuses almost exclusively on knowledge: what it is, where it comes from and what it's limits are, for example. The primary difference between knowledge and truth in a nutshell ...


10

The answer you get will depend on who you ask. There is no consensus within philosophy, so depending on which philosopher you ask the answer may be either yes or no or maybe or it's-impossible-to-tell. However, within the natural sciences there is pretty good consensus that we are just (analog, noisy, non-deterministic (due to quantum mechanics)) computers....


10

There are a few things to unpick, here. First, there's a difference between provability in a formal system, and "truth", which is a question of the relationship between language acts and facts. The statement "Juh mapple Neele" is neither true nor false, but nonsense, unless it is recognised as a poorly pronounced version of the French phrase Je m'appele ...


10

One group of thinkers who thinks along those lines are Bayesians. For Bayesians, it's not so much that they think everything is an opinion, or that there is no truth, rather it's that their framework around learning the truth does not allow for certainty in the truth. There is a practical reason for this: every piece of data you receive should be able to ...


10

In classical logic these are the same by definition. But in very tentative logics like Constructivism or Intuitionism, things are only said to be true or false if they meet quite stringent conditions. People using criteria like this require a truth to be proved in a given way, or captured by a certain kind of generalization, and a falsehood to proceed from ...


10

Timm Lampert, cited by the OP, quotes Wittgenstein (§8 of Remarks on the Foundations of Mathematics, Appendix 3): ‘True in Russell’s system’ means, as was said: proved in Russell’s system; and ‘false in Russell’s system’ means: the opposite has been proved in Russell’s system. Lampert claims Wittgenstein is assuming what needs to be proven: Whether P =...


9

You've stumbled upon an old problem in philosophy, The Paradox of Inquiry, first formulated in Plato's Meno. The problem can be reformulated as follows: Either you know the answer to a question, or you don't. If you do, then there is no point searching for it. If you don't, then you will not know what to search for. The short answer is that you can ...


8

Heidegger famously argued for precisely this. He points out that the Greek word for truth, ἀλήθεια (Aletheia), grammatically relies upon the use of a privative; it literally means unconcealedness (with the privative use of "un-".)


8

No. Lying implies an intent to deceive. To speak a falsehood is not necessarily to lie. As for the truth-status of the statement, it's not at all paradoxical; it's just temporally bound.


8

Tarski's Convention T is not strictly speaking a definition principle for truth - it is an evaluation condition on whether a given axiomatically theorised predicate is a "Materially Adequate" definition to count as a Truth predicate. The work that Tarski did in showing how a truth predicate could be defined was not in presenting the T-Schema. That "snow ...


8

Bivalence and supertruth Yes, clearly a supervaluationist makes a distinction between the truth of a particular precisification and the supertruth of a statement true for all possible precisifications, which on the face of it could imply multiple truth values rather than the pure true/false dichotomy of bivalence. If we take for example the statement "...


8

According to Eric Schwitzgebel, Contemporary analytic philosophers of mind generally use the term “belief” to refer to the attitude we have, roughly, whenever we take something to be the case or regard it as true. To believe something, in this sense, needn't involve actively reflecting on it: Of the vast number of things ordinary adults believe, only a ...


8

Welcome to this SE, Daniel. I think the problem with the argument is what you are trying to prove: how can I disprove that there exists an inherent privilege (an entitlement) to believe whatever you want? Even Patrick Stokes agrees that people are entitled to their opinions. He writes: If “Everyone’s entitled to their opinion” just means no-one has ...


7

I think that we have to turn to the great philosopher Rumsfeld, who famously opined about "known knowns", "known unknowns", and "unknown unknowns." The size of what we don't know about the universe is an unknown unknown; we necessarily have no way of knowing how much (or how little) there is we don't know. So: all the more reason to examine rigorously ...


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