Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

New answers tagged

1

The famous 1964 paper of John Stewart Bell, in which "Bell's inequality" is established, begins by assuming two things. (The paper can be found here: https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf) One of them is "locality", which means (non-mathematically) that distant objects cannot affect one another instantaneously. Mathematically, Bell ...


0

Probability is the connection between the mathematical apparatus of quantum mechanics and experimental observation, data in the real world (it's what gives quantum mechanics the status of a scientific theory). A more appropriate question (for the philosophy section ) is related to the multitude of interpretations of quantum mechanics, but there is not ...


1

The thought experiment is to build a simulated universe that is ruled by a given mathematical model (that we completely know), including entities able to perform experiments, and try to discuss to which extent they are able, by means of experiment, to discover the rules. One might imagine that the results of their experiments will lead right back to the ...


1

I do not think that these questions have a straightforward answer. "approach" might be more appropriate than "answer". Let's say your universe's "entities" comprise a "collection" (set or whatever) E. And let's say your model also describes a "configuration space" accompanying E that we'll call its "state space", S(E). Then we could typically represent/...


0

Probabilities in quantum mechanics always respect the calculus of probabilities by definition. The square amplitudes of a set of orthogonal states, which are the quantities used to compute probabilities in quantum mechanics, don't always respect the calculus of probability, see: https://arxiv.org/abs/math/9911150


0

You will discover when you fill in the details of your question to model the world, that the question makes no sense. "round" or "square" in this question sounds like a name-of-the-thing problem; that is, they really see the same thing and are calling it something else. Non-universal reality is divergent. If we could throw a switch to allow two beings to ...


-1

Well, nobody here has challenged my belief/assertion/bit of philosophy about justification and truth: I think that truth is irrelevant to justification. It seems clear that historical (Pre-Kantian) methods have failed to produce a current consensus that any justification is adequate in theory or in practice to produce objective certainty about anybody's ...


0

In physics and the philosophy of physics, quantum Bayesianism (abbreviated QBism, pronounced "cubism") is an interpretation of quantum mechanics that takes an agent's actions and experiences as the central concerns of the theory. This interpretation is distinguished by its use of a subjective Bayesian account of probabilities to understand the quantum ...


0

‘There might be nothing’ is false when read epistemically. (Roughly, a proposition is epistemically possible if it is consistent with everything that is known.) For we know that something actually exists and knowledge of actuality precludes all rival epistemic possibilities. But when read metaphysically, ‘There might be nothing’ seems true. So ‘Why ...


0

Despite Logical Positivists and others who will tell you that some questions are not fit to ask, I hold it as a personal truth that all questions that can be framed can be asked, and even from nonsense we can sometimes learn something, such as where we are personally mistaken in our understanding. Given that, I say this looks like "what Martin Heidegger has ...


1

To answer this, we have to know what "knowledge" means. One answer is to take the radical skeptic's approach to say that we can know nothing, but that doesn't quite fit with the line of questioning you're after, so let's narrow the definition to assume that knowledge is something that can indeed be obtained. The most common criteria for knowledge in ...


0

Hmmmm. First I've heard of it and I've been studying the various forms of idealism for quite some time. Thanks. I'll add that to my collection. Things exist -- at least in our own experience -- according to the language we use to describe them? I'll take a shot. It's pretty clear, I think, that the world as we experience it is entirely a construction of our ...


0

There's a video of former President George W. Bush declaring in an interview (while he was President): "It's true because I believe it." I forget what exactly it was that Bush was so certain was true. But that particular rationale has always stuck in my head. At any rate, I don't know of any contemporary philosopher who would likely lay claim to absolute ...


1

Just to illustrate the quotation from Hadamard: The exponential function exp(z) satisfies for complex arguments z, w the addition theorem exp(z+w) = exp z * exp w The theorem follows from the definition of the exponential function as a power series and the binomial formula. To derive an addition theorem for trigonometric functions like sinus and cosinus ...


3

The so-called Demarcation Problem is a little bit later, emerging with Vienna Circle and Popper. But its origins are in the Tractatus : 4.03 A proposition communicates a situation to us, and so it must be essentially connected with the situation. Thus, a true proposition is the picture of a fact. 4.05 Reality is compared with propositions. 4.06 ...


0

To my mind, any kind of "scientific realism" is completely bogus. As several posters have pointed out, reality as we experience it is entirely a construction of our minds based on synthesizing our sensory input and then, in a sense, "projecting" this construction back out onto the world (so to speak) and experiencing it as the world. Given this obvious fact, ...


0

Abstract The article looks at the structure of impossible worlds, and their deployment in the analysis of some intentional notions. In particular, it is argued that one can, in fact, conceive anything, whether or not it is impossible. Thus a semantics of conceivability requires impossible worlds. [...] I now want to turn to the notion of conceiving....


12

It's actually misquoted. From: http://homepage.divms.uiowa.edu/~jorgen/hadamardquotesource.html A longer and more nuanced formulation appears (in English) in Hadamard's An Essay on the Psychology of Invention in the Mathematical Field (Princeton U. Press, 1945; Dover, 1954; Princeton U. Press, as The Mathematician's Mind, 1996), page 123: "It has been ...


6

I don't think there is much philosophical significance in what he said. Basically, he is saying that the complex field is a nice field to work with---and indeed it is. For example, every n degree polynomial in C[x] has exactly n roots in C, while R[x] does not enjoy this property. Of course, there any many reasons why C is nice. Another one is that the ...


6

Considering An important paper concerning the distribution of prime numbers was Riemann's 1859 memoir "On the Number of Primes Less Than a Given Magnitude", the only paper he ever wrote on the subject. Riemann introduced new ideas into the subject, the chief of them being that the distribution of prime numbers is intimately connected with the zeros of the ...


0

Basic statements are not justified by our immediate experiences ... but by an act, a free decision. A free decision does not mean an arbitrary acceptance of a hypothesis, an observation or a deduction. Popper is merely acknowledging here that man is free and free to make decisions.


-1

One answer could be that his is a conventionalism (as the SEP says), one that means that the decision is free and arbitrary (as the SEP says), but is free and arbitrary only for specific people, experts. Then accepting or rejecting a scientific theory need not really be irrational, even if doing so is not a valid deductive argument.


0

I completely disagree: strong skepticism isn't self refuting in an interesting way. The strong skeptic can say that they know one thing, or are they just engaged in the psychological gratification to 'everything'? Though I guess it may be "incoherent" in a less semantic sense. Your breakdown of different skepticisms is interesting, and makes intuitive (...


2

Before trying to ask 'How to measure', first you should confirm whether consciousness is a thing like light, waves, radiation etc. If you are quite sure about it, you may try to search a tool for measuring it. We don't even know whether consciousness is zero dimensional, infinite dimensional or something more than these. Those who could realize ...


1

Apart from any (a)theological or biblical references, non-interventionist evolution and young-earth creationism (YEC) are comparable. Both make claims about the physical world, present and past, that in principle can be tested. The challenges of testing claims about the distant past applies to both. Their key claims are comparable: (1) the evolutionary tree ...


0

You are correct that strong skepticism is self-refuting and thus invalid. Weak skepticism 1/2 also refute themselves since philosophers observe the world through their senses and thus any logical framework they build is contingent on their ability to perceive the world and to assume the world remains such after the philosopher looks away. Example: A = A has ...


0

@PeterJ, thank you for this excellent explanation (despite the self-deprecating conclusion which of course must be untrue!). Is certainty all-or-none, as truth is supposed to be? If so it’s theoretically unobtainable, but in practice only the wiser people realise this; the rest of us are busy arguing about who’s right or wrong about being in possession of ...


1

I believe this is one of the most important question in philosophy. It questions whether philosophy is worth doing. The solution to the problem lies in seeing that Kant and Popper deny the possibility of certain knowledge, as does their tradition of thought. Thus the question of truth for them is confusing. This denial of the possibility of knowledge ...


1

The discovery of gravitational waves in 2016 shows that spacetime is a physical object. The gravitational masses of two merging black holes act on spacetime. Since 100 years we know the bending of light by curved spacetime. Hence spacetime acts on other physical objects like light rays. Therefore, spacetime is accepted for membership in the ontology of ...


3

Indirect realism is the view that our contact with reality is mediated ("filtered") through our sense organs and/or cognitive faculties. We do not experience reality "as it is, out there". This isn't assumed by science per se, but it is probably supported by science. Colors for example, do not inhere in mind-independent objects, but in our perceptions of ...


2

It is hard to correlate Kant and Popper, at least I find it so, since their enterprises were so different. Kant's major epistemological concern was with what might be termed psychological epistemology. The forms of intuition (our sense of space and time) and the categories of the understanding (causality, quantity, quality, plurality, limitation, ...


0

Some epistemologists have taken fallibilism to imply skepticism, according to which none of those claims or views are ever well justified or knowledge. In fact, though, it is fallibilist epistemologists (which is to say, the majority of epistemologists) who tend not to be skeptics about the existence of knowledge or justified belief. Emphasis mine ...


1

Stephen Hetherington claims the following: Almost all contemporary epistemologists will say that they are fallibilists. Yet the vast majority of them also wish not to be skeptics. They would rather not be committed to embracing principles about the nature of knowledge and justification which commit them to denying that there can be any knowledge or ...


0

The basic formula of QM in its most simple form is Schrödinger's equation. That's a linear differential equation like other differential equations from classical Newtonian mechanics or Maxwell's electrodynamics. The distinctiveness of the Schrödinger equation: The equation describes in a deterministic way the time development of a probability. According ...


2

Two understand why this is so, you have to understand the distinction between "false" and "incorrect".nYour question is caused by conflation of the two. I must admit that my usage of the two terms is not universal, but the distinction is common even when people use other terms for it (confusingly enough, textbooks on formal logic tend to use "false" for what ...


4

Your example from mathematics shows: To assess a mathematical statement one should first fix the context, the domain of validity of the symbols. Because in the context of natural numbers the statement 1+1=0 is false. While in the context of Z/2Z the statement is correct. Except the rare case of undecidable questions, in mathematics one can prove or disprove ...


58

In math, we define stuff like numbers and operators, then we go on to prove other stuff from those premises. When you ask: "Is 1 + 1 = 0?", a mathematician will just ask back: "With what definition of +?" If you assume natural numbers and the common definition of +, then this statement is false. If you assume numbers modulo 2 and + meaning XOR, then this ...


6

1 + 1 = 0 is false. Meanwhile, (1_2) +_2 (1_2) = 0_2 is true. Here +_2 is a different operation than +, and 1_2 and 0_2 are different things than 1 and 0. So it's not surprising that one equation is true while the other is false. The problem is that we do not like to write "_2" everywhere, so we often write 1 + 1 = 0 when we mean 1_2 +_2 1_2 = 0_2. This ...


3

Hmmm. What about 1 + 1 = 10 ? Is that equation, expressed in binary arithmetic, "false in the domain of natural numbers"? My grounding in math and logic isn't very strong, but I understand the Wikipedia entry...I just don't think that the notions of truth and falsity can coherently apply to inductive inferences (abstract descriptions of unobservable ...


11

The hypothesis 1+1=0 is false in the domain of natural numbers. If the domain is the finite field of the integers mod 2, then one is no longer in the domain of the natural numbers and the statement 1+1=0 would be true in that domain. The question is why do we not consider these to be falsifications of each other? These are not contradictions or ...


3

Well, mavavilj, definitions are easy - dictionaries are teeming with them. None of them is right or wrong, they're only more or less agreeable to whomever interprets them! However, 'knowledge' isn't a scientific term, it's a philosophical issue. Science is more concerned with evidence, theory and statistical analysis. Are you keeping in mind the ...


0

There is an experimental approach to resolving the problem of induction via means of pattern recognition and prediction. There is this particular paper:-- Rathmanner, Samuel, and Marcus Hutter. "A philosophical treatise of universal induction." Entropy 13.6 (2011): 1076-1136. (https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_inductive_inference) ...


2

I am not familiar with formulations of the non-existence of objective reality, but here's my stab at the question anyway: Suppose you have the hypothesis "All apples are red", and you see a green apple. If objective reality exists, then the hypothesis has been falsified by the observation. If objective reality does not exist, then the hypothesis was false ...


1

That change in species occurs is evident from both paleontology and Darwin's theory. It also seems, if one looks at it from a high enough level, that a progress-like pattern from simpler to more complex life forms appears to characterize it. If there is real progress going on then an explanation for that would likely be some holistic cause effectively ...


1

Your link gives two definitions. The first is "Forward or onward movement towards a destination." Evolution is "movement", in the metaphorical sense, from earlier forms to later forms. If we take "forward" to mean "going from earlier to later", then evolution does indeed constitute progress. But the second definition is "Development towards an improved or ...


0

I was thinking about this last night when I was thinking of its possible to arrive at truth through philosophy as did the ancients (if I understand your question correctly). You see, we are currently coming full circle back to the gnosis of the past. Science was once purely about explaining the material realm of existence to the exclusion of any deity ...


2

The main skill of a philosopher, in my view, should be the ability to simplify. The complexity of most issues is an illusion caused by incomprehension. Comprehension requires simplification. KISS, or Keep it Simple Stupid, is the method. The philosopher has only a secondary interest in groupology or even particular instances. The first thing to do is ...


1

Depends on what you would define as progress. If you say that being fit for nature, the environment, and getting more and more adapted to it, then yes, I would argue evolution is a progress of process. However, part of evolution is selection, and that includes the death and extinction of those living organisms, which are unfortunate enough to not be well-...


6

Biological evolution is an undirected process driven by chance mutation. Many mutations have severe consequences, and even those that could be considered beneficial in certain contexts may have nasty side effects in different contexts. And of course even many of those changes which could be considered beneficial don't get passed on to the next generation. ...


0

Scientific realism is a thesis that is concerned with the relation between scientific representation and the external world. Linguistic idealism is concerned with the relation between linguistic representation and inner experience. Therefore the two thesis are not directly related. It's common nowadays to think that scientific representation is not ...


Top 50 recent answers are included