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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 ...


21

In general, no, it is not inappropriate. Scientific research can take many forms, some of which could have negative effects on people. Pharmaceutical research, for example, follows a tightly controlled set of steps in researching a drug and getting it approved and marketed. You can't just brew something up in your garage and start dosing people with it. We'...


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 ...


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 ...


10

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 ...


7

This is an active topic of debate among professional philosophers of science today. Julian Reiss explains the problem nicely in his paper "The Explanation Paradox". His paper is focused on economics, but we can generalize the problem. Basically, the following statements are all highly plausible: Explanations must be true. Many fields of science make ...


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

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 rule that the article appears to be concerned with is Docket ID No. EPA-HQ-OA-2018-0259 and has this as part of the summary. This document proposes a regulation intended to strengthen the transparency of EPA regulatory science. The proposed regulation provides that when EPA develops regulations, including regulations for which the public is likely to ...


5

Fatima. 'Good' explanation is ambiguous between 'plausible' and 'true' explanation. An explanation may be both but a plausible explanation is not necessarily a true explanation. For instance, a plausible explanation might be this. I enter a room. A vase has fallen from a table. There are cat prints leading to the table; cat prints on the table, and cat ...


4

Thinking about who decides which experiments are conducted, to whose benefit those results might be, can be a starting point. The peer review process is not perfectly objective. Old scientists refuse to consider new theories (Max Planck said that "science advances one funeral at a time"). Plus you can look at scientific history, especially about racial ...


4

There is a very large difference between "making rules for science" and "People who are not scientists are telling us how scientific synthesis and analysis should be done." Do scientists need some form of regulation? Sure. The material covered in courses on medical ethics will let you know exactly how bad things can get when there is no oversight. There's ...


4

So far as I can see, Ockham's Razor is simply a methodological rule, a principle of parsimony, that tells us not to assume more than we absolutely have to in order to explain something - an object, an event, a state of affairs or whatever. Hence the old familiar, 'Ockham's razor shaved Plato's beard' - meaning that there was no need to assume the existence ...


4

I wrote my dissertation on this topic; you can read a paper based on that work here. I use the term "practices" or "communal practices," which emphasizes what communities do rather than what they "are"; but I'd suggest that the community for a practice is just the group of people who engage in that practice. So the scientific community is simply the ...


4

The author you quote seems to be oversimplifying, but it is possible to understand some work of the logical positivists as an attempt at a purely syntactic approach to expressing the relation between evidence and hypothesis. Rudolf Carnap, in particular, attempted to set out a formal logic of induction in which inductive probabilities can be derived from ...


4

The most comprehensive text that I have run into outlining precisely how the philosophy of positive science -- the study of purportedly rational theory choice -- was conquered by the history/sociology of science, a process which started with the concepts of holism and indeterminacy in the early/mid 20th Century and culminated in the so called Strong Program ...


4

1) Problem with the energy of causes Energy-neutral causation need not involve anything supernatural or extraordinary. A rock on the tracks may cause a train to derail, but it does not expend any energy to do so, it simply redirects it. So does a rail switch. Reflecting on these examples shows that there is a problem with associating energy with causes in ...


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

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 ...


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