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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 ...


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 ...


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,...


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

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 ...


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 ...


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

There are several points of confusion here. First, your examples are someone more complicated than they need to be because of the temporal aspect of the problem (immortality). We need to make a distinction between global statements that are falsifiable in practice (such as "All crows are black" which equals "No crows are white" which can be falsified by ...


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 ...


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

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

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

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 skeptical ...


3

This is a question about predicate denial. Certainly in Fregean logic, where predicate denial is taken as the unary "it is not the case that", for a predicate P, P¬x is logically equivalent to ¬Px. So the question becomes, is the Fregean notion of predicate denial the correct notion to apply to the predicate "is falsifiable". Here, one might argue ...


3

If you reduce your statement to the known facts, of course there is nothing wrong with the statement. "I saw something in the sky on three separate occasions." "The thing or things was alive / mechanistic / inert and personal / impersonal." "I did not know what the thing or things was / I did know what the thing or things was." "The thing behaved in a ...


3

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 ...


2

Popper said that to be a scientific a theory had to subject to experimental test. He explicitly said on many occasions, e.g. - "Realism and the Aim of Science" Chapter III, that non-testable theories could have value. So his position was not that an untestable idea is rubbish, just that it wasn't scientific. Popper also pointed out that methodology could ...


2

QM is already 'undecidable'; the measurement of state collapses it into an eigenstate; this collapse is usually described as indeterministic, that is one can't determine or decide what the eigenstate will be given knowledge of the state and the measurement to be made. This is usually considered part of the Copenhagen Interpretation - the mainstream ...


2

Your example assumes that "medicine" is making some absolute claim of doing something, but that is not what medicine claims. If "medicine" is the general population's understanding of medicine, then you may have a point. However, to medical researchers, medical practitioners, and other medical agencies (FDA, etc), "medicine" describes our knowledge of ...


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