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 ...


36

Reductio ad absurdum is not a fallacy. Rather, RAA is correct reasoning that exposes a fallacy. From the Logically Fallacious page for it: [RAA is a] mode of argumentation or a form of argument in which a proposition is disproven by following its implications logically to an absurd conclusion.... The fallacy is in the argument that could be reduced ...


35

Your example is not a valid case of Reductio ad Absurdum. It's just an example of an absurd argument. A real example would be: Miles: "Copying a DVD is stealing" Frank: "Why?" Miles: "If someone created a piece of art, they have full rights to allow or prohibit its reproduction" Frank: "Oh, so when I take a selfie in the city, I need to ...


21

Frank’s argument is not a reductio. It is an argument from analogy, which is not deductive reasoning and needs to be evaluated differently (Mark’s answer adequately covers the fact that reductio is a valid form of reasoning.)


11

There's two general answers I perceive to this. One is that the Flew argument targets a god with no fixed traits (that is hence infinitely mutable). In other words, the argument starts from the assumption that the god being defended does not exist. No believer actually believes in such a god, almost by definition. Every actual theist believes in a God ...


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 ...


10

This sounds like the identity of indiscernibles, (not to be confused with the indiscernibility of identicals) first formulated by Leibniz. If two objects have all their properties in common, then those two objects must in fact be identical. Slightly more formally, for every x and every y: if, for every property P, x is P if and only if y is P, then x = y. ...


8

No, and we should not want it to be falsifiable, nor expect it to be on its own terms. Philosophers of science generally — though not universally — dispute the idea that there is a scientific method, as opposed to many scientific methods. But leaving that point aside, if there were a single scientific method ... How could a scientific method be falsifiable,...


8

This argument is based on an assumption that science deals in eternal absolutes. That luxury is generally the preserve of, well, philosophy. Science deals with hypotheses and experiments. I can test the hypothesis that there exists black swans. And, by luck, I can confirm it readily (as I did last weekend). Now, if I try to confirm the hypothesis that ...


8

tl;dr– This is a pretty basic observation that appears in a lot of ancient works. I'd guess that you might be thinking of Heraclitus, who was big into how "no man may step into the same river twice" – because neither the man nor the river could change. This is an ancient concept, almost certainly predating recorded history, so it's hard to guess ...


7

Can a non-falsifiable belief be useful? Picture this thought experiment: You have a "lucky" friend. When people are around him, things seem to go better. One person wins the lottery, another one meets his future wife, etc. For the purposes of the example, let's assume the effect IS real, but unpredictable. This belief isn't falsifiable, because it ...


7

Reductio ad adsurbum requires that there be a valid chain of reasoning that leads from the initial premise to an impossible or unacceptable conclusion. Your example is not RAA because Frank's response does not describe an actual consequence of the Miles's statement. There may be some similarity between the two situations in Frank's mind, but Miles argues ...


6

The best way to understand Popper is to read Popper. There are a few commentators who have correctly understood his ideas, but the vast bulk of commentary on Popper is not even able to state his ideas correctly. Lakatos, Feyerabend and Kuhn are especially bad and should be avoided. To understand falsification properly, you need to understand Popper's theory ...


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 ...


5

Goodman's new riddle of induction is old wine in new bottles. The substance behind the problem of induction is the following. People imagine that they arrive at theories by looking at evidence and drawing conclusions from it. But a collection of observations doesn't imply anything at all about the future. So conclusions reached by current evidence may not ...


5

Usually Karl Popper is credited with having contributed to the death of logical positivism, so no, I wouldn't say Karl Popper is a logical positivist. That being said, many analytic philosophers after logical positivism still kept much of the attitude of positivism, such as logical analysis, defining ones terms, skepticism towards "grand" metaphysical ...


4

The reason some empiricists (most notably Popper) have denied that we can verify an empirical hypothesis is that they were thinking of universally quantified statements such as All ravens are black This statement, the argument would go, cannot be verified: regardless of how many ravens one observes, there is always the possibility that the next raven ...


4

Here is Popper's famous quote from 1976 that caused the controversy:"I have always been extremely interested in the theory of evolution and very ready to accept evolution as a fact... I have come to the conclusion that Darwinism is not a testable scientific theory, but a metaphysical research programme — a possible framework for testable scientific theories"....


4

Here is my understanding of Karl Popper and Nelson Goodman. Both talk about whether and when observations may corroborate a given hypothesis. Popper concludes that observations may falsify, but never affirmatively prove, a statement. Goodman’s New Riddle says nothing about falsification directly, but creates a hypothetical where corroboration and ...


4

In many epistemologies, unfalsifiable beliefs are going to have great value. In large part, this is because of the following: universal skepticism fails. A good way to grasp this is to think about Descartes' project (or perhaps better stated his supposed project). A common claim is that Descartes is this radical skeptic bent on doubting everything, but ...


4

I understand the value of falsifiable beliefs. Often they make predictions, and are classified as scientific ideas, useful in churning out predictions. But do unfalsifiable beliefs have any value? Philosophically or mathematically or otherwise? I know value is a little vague, but consider for example the concept of eternal return. If true it would have ...


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 closest quote I can think of from ancient authors is Seneca's:"One thing must be separate from another if they are to be two" (Ep CXIII 4-5). But he allows merely numerical, not necessarily qualitative (intrinsic) difference, so this is closer to a tautology. With the qualitative difference in mind, the principle is non-trivial, as it states that two ...


3

What you are looking for is the difference between scientific realism and scientific anti-realism. Scientific realism is the position that scientific entities (such as electrons, atoms, genes, etc...) have an objective real existence independent of (human) observers and that scientific theories are at least approximately true. Scientific anti-realism is ...


3

Why are you postulating that medicines might "have a bad day" as it were? The whole point of statistics is to avoid being fooled by chance circumstances. (You might still be fooled by unexpected correlations.) Anyway, yes, medicine is falsifiable. It's hard, because it's difficult to adequately control conditions, and it is tempting to use statistics ...


3

Popper proposed falsifiability as a demarcation criterion for science, not all knowledge. In his work he never declared that all truth claims needed to be falsifiable. Thus there is no issue since the principle of falsifiability is not a scientific claim, it is a claim about science. He referred to these non-scientific, but coherent, claims as "...


3

The problem described in that paper is about calculating the limiting behavior of a lattice as its size goes to infinity. Because the uncomputability only comes in when considering the limit, it is not possible based on the results in that paper to construct a real physical experiment with an uncomputable outcome. If someone did find a real finite (time, ...


3

An interpretation of a theory, in particular quantum theory, is said to be an account of what that theory is saying about the world that can be cleanly separated from the theory's predictions. People who accept this idea claim that different interpretations of quantum theory can't be tested, and the question of which interpretation is true is not solvable. ...


3

Aside from minimal interpretations, which simply relate theoretical abstractions to empirical/practical procedures, interpretations are typically treated as philosophy/metaphysics. As such they can be used as vague blueprints for extending/modifying the theory, this was Popper's own view, he called them "metaphysical research programs". On more ...


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