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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 ...


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, ...


19

Welcome to the demarcation problem of science. What is this thing called science? In lower levels of education, one is often given the impression that 'science', whatever that may be, exists as a monolithic entity. There is no sufficiency and necessity definition of what science is. It's better to say 'sciences' or 'scientific' when speculating as to this ...


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 ...


12

Colloquial meanings of the two words are pretty close, accidental is "occurring unexpectedly or by chance", contingent is "subject to chance; occurring or existing only if (certain circumstances) are the case; dependent on". If there is a shade of difference, it is that contingent may well be expected as a possibility, albeit along other options, whereas ...


10

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 ...


8

What is Science? The Popperian view of science is that a claim is "scientific" if it can be falsified. Science cannot prove that a hypothesis is true, only that it is manifestly false. If economics can make falsifiable claims, then I think it is justified to say such claims are "scientific", at least on some level (the degree of repeatability is certainly ...


7

Darwin I should have thought that Darwin's theory of evolution does not recognise anything like an 'arc of history'; that evolution is not progressive, and that it moves with no purpose (cf. R.Dawkins, The Blind Watchmaker). Darwinian evolution, working causally through random variation and natural selection, is naturalistic, non-directional and non-...


7

The notion of evolution in the sense of different species descending from a common ancestor predates Hegel, Darwin's contribution was the theory of natural selection to explain how the process happens, along with lots of empirical evidence for common descent and local adaptive processes such as Darwin's finches. Darwin's own grandfather Erasmus Darwin (1731 -...


6

This is currently a major topic in academic philosophy of science. Among people who specialize in this topic — including myself — a strong majority now think that ethical values do and should play a role in evaluating scientific claims. One major argument for this claim is the argument from inductive risk. Inductive risk simply refers to the risk of ...


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. ...


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 ...


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

Mechanist (or mechanical) philosophy, in the original sense, meant the rejection of "substantial forms", i.e. forms with causal powers, such as souls, postulated by scholastics (who drew on some vague passages from Aristotle's De Anima). For a detailed discussion of substantial forms see How can the soul be a form in Aristotle's metaphysics? From the modern ...


5

This is a very common issue when dealing with science. Much of science's approaches to Truth (with a capital letter) is through abduction, an approach which assumes the most likely hypothesis is true. If you read the linked SEP article, this is fraught with nuances, as you suggest. Personally, I am a fan of radical skepticism, and the Aggripan Trilemma. ...


5

The evolutionary biologist (and student of the history of science), Stephen Jay Gould writes in his book Eight Little Piggies: Reflections in Natural History, chapter entitled Darwin and Paley Meet the Invisible Hand: Where did Darwin get such a radical version of evolution? Surely not from the birds and bees, the twigs and trees. Nature helped, but ...


4

There is a story, possibly apocryphal, of Faraday demonstrating an electromagnetic induction experiment at the Royal Institution in London. He was asked, what use is it? According to one version, he replied, "What use is a baby? It grows up." In another version, it was a politician who asked, "What use is it?" and Faraday replied, "Soon you will be able to ...


4

Today, this can have a significantly different answer than a few years ago. Let me explain why. Logically, an event would happen and you the observer would be irrelevant. Meaning, that tree would generate its sound and shockwave when falling no matter if you are there or not. This is physically valid and was practically demonstrated on numerous occasions. ...


4

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 ...


4

The quoted paragraph starts off with the wrong meaning of extraordinary by taking it to be synonymous with supernatural when it means remarkable or exceptional so everything that follows must be wrong. What that extraordinary quote means is simply that big claims need big evidence. For example if you saw a rainbow coloured car, I could be convinced to ...


4

If there are two distinct theories that are functionally equivalent — i.e. that make the same predictions, produce the same results, can be verified by the same empirical observations, etc — then why does it matter which we choose? The choice is aesthetic, not analytical. We might choose to use one theory in one case and the other theory in a different case, ...


4

The cited article references a paper by Sean M. Carroll which provides an overview of Boltzmann Brains (BB). Carroll views BBs not as a reality, but as a way to test whether a cosmological theory is plausible or not. The rule of thumb goes something like this: if the cosmological theory allows BBs then reject the cosmological theory. (page 23) We ...


4

Wikipedia says Natural science is concerned with the description, prediction, and understanding of natural phenomena based on empirical evidence from observation and experimentation. It can be divided into two main branches: life science (or biological science) and physical science. Social science is concerned with society and the relationships among ...


4

Interpreted narrowly, your question seems related to the problem of (data) fishing, where someone investigates hypothesis after hypothesis on the data until getting statistical significance on one (without correcting for the number of hypotheses considered), so that in all likelihood it was just a fluke. This is a well understood problem. Interpreted more ...


4

The concept of the colonization of knowledge (technically, the colonization of the lifeworld) comes out of Jurgen Habermas' 1992 "Faktizität und Geltung" ("Between Facts and Norms"). It's an interesting work, but heavy reading. The basic idea rests on a distinction between the kind of language and communication used in the 'lifeworld' — the rich, organic, ...


4

This is called Bertrand's box paradox. It's a "paradox" in the sense that the correct answer, P(other_coin_is_gold) = 2/3, is unintuitive to most people at first. To get a feel for the correct answer, break it down into cases. Let's call the box with 2 gold coins "G", the box with two silver coins "S", and the box with one of each "M" (for "mixed"). Further,...


3

Thanks for sharing. "The existence of your putative model describing the physical mechanism behind the quality collapse occurring in production lines (a, b, c, d...) cannot in and of itself disprove the existence of a completely different model That's correct, but Occam's razor deals with this that assigns root cause to a portion of the factory ...


3

Let's distinguish between the belief that a model is true and accepting it as effective for certain practical purposes. It's a safe guess that your model was incomplete — it left out some factors that you assumed to be less important and/or difficult to model. Your model also might have involved some simplifications — maybe using linear approximations, ...


3

Sven Ove Hansson summarizes attempts to create a demarcation between science and pseudo-science after Thomas Kuhn's (1974) use of normal science as a means for demarcation. Under "Criteria based on scientific progress" Hansson notes attempts to formulate a demarcation by Thagard (1978), Roshbart (1990) and Reisch (1998). Others, some after Kuhn, have ...


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