# Tag Info

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As far as I understand the notion of knowledge in Kantian philosophy, we cannot speak of knowing something unless there is a relation between its concept and some object of intuition in experience.< This is WRONG : knowledge requires the union of concept and intuition, but not necessarily "in experience". Kant denies that all intuition is empirical. ...

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My understanding of the use-mention distinction is that the former refers to a disposition (behavior) or proposition (meaning bearer) while the latter is merely a reference (syntactical expression such as a string). In this way, dispositions correspond to correspondent truths (combining two individual cookies in results in a state of affairs that a box has a ...

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1+1=2 is a formula (an expression of mathematical language that express a statement) and "1+1=2" is the way to refer to the expression: correct. 1+1 is a term, i.e. an expression that denotes a number. Thus, it is not a formula. The principle of the Indiscernibility of Identicals (the converse of the Identity of Indiscernibles) in its predicate logic ...

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We have a very brief introduction How does Frege's definition of number solve the Julius Caesar problem? here on SE. Zalta's review of it for SEP is a good place to start more scholarly research. Dummett's book Frege: Philosophy of Mathematics is a comprehensive classical commentary. In 2005 Dialectica devoted a whole issue to the Julius Caesar problem, with ...

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Reference : Russell, Introduction to Mathematical Philosophy. As to what belongs to "logic" : See Alonzo Church's article " logic , formal - " in Rune's Dictionary Of Philosophy . ( at Archive.org). You will see that the algebra of classes ( set algebra) , the algebra of relations, and even " set theory" is considered as a part of logic. Brief answer : ...

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Frege considered the notion of functions to be logically primitive and so to be undefinable. He tried to give some elucidations of his idea of functions by saying that functions comprise all and only the unsaturated or incomplete things. So Frege's logicism simply takes functions for granted as it does regarding objects (the complement of functions). As a ...

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In essence, your question is like this SE post which asks "how science is related to philosophy". Other closely related question are "is science just a more refined and effective method of philosophy?", "how does one know whether a discipline is a science of philosophy?", and "How should we characterize the relationship between mathematics and philosophy of ...

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Let's separate out two aspects of philosophy. First, there is a broad sense in which philosophy is the study of the application of higher reasoning. This goes straight back to the ancient Greek philosophers in the West (and to other ancient thinkers in other regions of the world): to the Socratic method, or Aristotles system of categorization. Note that for ...

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Both discipline use low level logic. But they have a different goal : Science answer the question : How the world ? Philosophy answer the question : Why the world ? So, based on these statements, I think we can't say that maths or physics are a branch of philosophy.

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This is a knotty problem and there are many different perspectives on it but I would recommend looking at the details. You might need a mind to discover the laws of physics and program a computer to simulate them. But when it's running it just carries on by itself and does not require any mental intervention. So there's nothing here to imply that the ...

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I feel like I repeat this point a lot, but so be it... The mind makes models of the universe in order to explain its own perceptions. Mathematics is one of those models. If we go down right to the root of mathematics — the concept of 'number' — we can see that 'number' is intimately tied to the concept of 'object'. 'Objects' are things that we count and ...

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Karl Popper is wrong. Falsifiability is not synonymous with testability or verifiability. Consider the following diagram: In this very simple table, we see that the true state of a claim is verifiable if the true state matches a condition which is determinable. It does not matter if a true claim has a proof that is unfalsifiable; a "false" outcome is ...

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On a logical level, (unlike J D's practical answer), let's suppose that neither side knows any factual property, (and for the sake of the question they don't get to find out), about policy change P, nor the qualities of group X, its polled subset Y, nor Y's two pro & larger con divisions or X-Y; other than the fact that Y_con outnumbers Y_pro say ten-to-...

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I must point out that, even if one starts with a biased coin (in the sense that the probability of tossing heads is always P, tails always 1-P, but these are not necessarily equal), it is always possible to synthesize a toss for which heads and tails have equal probability. The procedure is simple: Toss the coin twice in succession; if the two tosses show ...

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(Welcome to SE Philosophy, and thanks for contributing with a question/response! If you haven't done so, please take a quick moment to take the tour. More specifics can be found in the help center.) SHORT ANSWER Depends. The question you ask is one regarding statistics and sampling of population, and is a branch of study of it's own. Opinion polling is a ...

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Since Theorems in Mathematics are those formulas that are proved and every proved formula is true (Completeness of 1st order logic), the falsifiability can not be applied to Theorems in Mathematics.

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Great question, I have been studying this for some years. Here are a few short thoughts: There are alot of issues when dealing with infinity and ironically it can get chaotic as we are dealing with fundamentally questions in measurement that are not just roots in counting and mathematics but also how we qualify phenomenon rooted in a very basic platonic ...

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