57

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 ...


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 ...


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 ...


5

Ed Feser's Scholastic Metaphysics: A Contemporary Introduction (2014) is a good defense of Aristotelian-Thomistic metaphysics and natural philosophy: Scholastic Metaphysics: A Contemporary Introduction provides an overview of Scholastic approaches to causation, substance, essence, modality, identity, persistence, teleology, and other issues in fundamental ...


5

On Aristotle's conception, yes. There is a subtle distinction between the potential and the possible, and the reality of the possible (as in possible worlds) is a controversial issue. Lewis is the chief proponent of modal realism, granting full reality to the possible worlds, the same reality as to our actual world, but this is even more exuberant than moral ...


5

A true random number is one that is unpredictable, even knowing the state of the Universe beforehand. In the special case of a random series of numbers, each number has to be generated with probability independent of all the previous numbers. It's not possible to do this with a mathematical formula or computer program, but it is possible to use principles ...


5

The infinitesimal instants are non-zero-it is infinitely small. Infinitesimals have a colorful history. In the later part of the 18th-century continuity of a function was taken to mean that infinitesimal changes in the value of the argument induced infinitesimal changes in the value of the function. With the abandonment of infinitesimals in the 19th ...


5

A compelling answer is given in Rynasiewicz, R. (1996). Absolute Versus Relational Space-Time: An Outmoded Debate? The Journal of Philosophy, 93(6), 279-306. doi:10.2307/2941076 Isaac Newton provided the locus classicus for substantivalism in the scholium to the opening definitions of the Principia, where he laid out and defended the distinction ...


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 ...


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. ...


4

What it means for a scientific theory to be "proven" is different from what it means for a mathematical theorem to be proven. Indeed, for any scientific theory, we can never be 100% sure that there aren't somehow some unusual conditions under which it is not accurate, and under which we have done no experiments yet. This was the case for Newtonian ...


4

Act (or actuality) and potency (or potentiality) are both real. For example, if the potentiality of an acorn grow into a oak were not real, how could it indeed grow into an oak? Something non-existent cannot give rise to something existing; something cannot give what it does not have.


4

Epistemology is the study of knowledge and justified belief. As the study of knowledge, epistemology is concerned with the following questions: What are the necessary and sufficient conditions of knowledge? What are its sources? What is its structure, and what are its limits? As the study of justified belief, epistemology aims to answer questions ...


4

Epistemology is the theory of knowledge (including belief and evidence) and not just of scientific knowledge : Naturalists seek continuity between epistemology and science so that epistemology may be conducted within science, as part of science. They propose creating such continuity by extending the epistemology of the sciences (e.g., their a ...


4

See SEP's entry The Incommensurability of Scientific Theories : 2.3 Kuhn’s subsequent development of incommensurability : 2.3.1 Taxonomic incommensurability for discussion. The relevant loci are from : Thomas Kuhn, The Road since Structure : Philosophical Essays 1970-1993, Chicago UP, mainly from Ch.2 : Commensurability, Comparability, Communicability, page ...


4

Essentialism is compatible with naturalism, Aristotle, the father of essentialism, is typically named as a precursor of naturalism (and even empiricism), and today we have scientific essentialism founded by Kripke and Putnam. Essentialism is simply the claim that objects have some properties "of necessity" while others are "accidental". It usually requires ...


4

If I am correct, you asked if, as humans, we can always find a new question for which we do not know the answer. This means that there will never be a human that knows the answer to any question he/she can ask. I think that the answer is yes. For example, you can always ask, what is the next prime number? If your question is about the number of question ...


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 ...


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