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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


35

Ill formed question. Mathematics (specifically, logics) define what truth is. You are trying to test the validity of the tool with the tool itself. The answer would be a plain "yes". Otherwise (if you discuss mathematics as an issue of perception) you fall into Rusi's answer. Yes, you can have i apples, if you define the domain of i (i is not just a ...


33

Various candidates would be: self-referential sentences such as "This sentence is false." opinion-based sentences such as "Chocolate is the most delicious ice cream flavor." sentences where the truth value depends on the referents: "I am awake right now." (indexical) "The team went on to win the cup." (context) sentences with metaphor / poetry / nonsense:...


26

The answer is a point of contention between realism and anti-realism. Truths that "do not have evidence" are termed verification-transcendent truths (coined by Dummett), and realists are committed to their existence. Anti-realists, on the other hand, hold that unverifiable in principle statements have no truth values. So if no trace of dinosaurs remains, ...


25

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 ...


21

I think it is a mistake to assume that there exists something like a context-independent notion of truth. Let me explain what I mean with the context dependence of truth. Consider the following simple question: Did Han shoot first? Now you can observe that in the real world, as far as we can tell, Han didn't exist at all. Obviously a person that doesn't ...


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

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) =...


16

Despite some claims, the Cartesian myth that math is independent of physical reality is arguably false. Mathematics is NOT independent of the physical systems which embody it. Physical systems are structured in such a way that mathematical statements supervene on them. An excellent introduction into how mathematical truths are functions of conceptual mapping ...


16

The OP asks the following: Can I write or utter any sentence which is neither false nor true? Yes. An example would be Tomorrow I will rise at precisely 6 am. That sentence today is neither true nor false. However, I will know tomorrow, but by then I will have a different sentence, perhaps: Today I rose at 6:30. That sentence could be viewed as either ...


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 ...


13

tl;dr: Yes to pragmatists; no to everybody else: For them, mathematics is about correctness, not about truth. While it is true that mathematics obviously was — and, perhaps less obviously, still is — inspired by our (perceived) reality, it is one of the essential traits of mathematics that it quickly and rigorously abstracts from that reality.3 ...


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, ...


12

Is every sentence we write or utter either true or false? NO. A sentence is "a textual unit consisting of one or more words that are grammatically linked. [... The] words [are] grouped meaningfully to express a statement, question, exclamation, request, command or suggestion. A question is neither true nor false.


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

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 =...


10

“You can’t have i apples” As @Conifold points out you cannot even have √2 apples. I'd go further. Can you have -2 apples ⅓ apples? I'd say (from a certain pov) no. All physics is based on measurements All measurements come from instruments Which can only ever deliver integral non-negative bounded multiples of least count Note: I added the “bounded” ...


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 ...


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