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The answer depends on whether you are interested in this topic from a philosophical point of view, or a physics point of view. In the case of the philosophical point of view, there is no right or wrong answer. Anyone is entitled to argue the point any way they wish, and you are free to select whichever argument you prefer. From the physics point of view, ...


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According to Leibniz's Principle of sufficient reason, space cannot be thought of as some absolute container or background platform in which all objects are created and evolved: Leibniz also used the principle of sufficient reason to refute the idea of absolute space: I say then, that if space is an absolute being, there would be something for which it ...


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Many fields that we now call "sciences" were originally thought of as branches of philosophy. For that reason, philosophy is often called the "mother of sciences." A good way of conceptualizing it is that philosophy deals with open questions --ones to which there is no universally acclaimed, uncontroversial answer. All disciplines pose ...


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What would be some problems if we would define them to be branches of philosophy? When we use the term -- 'branch', we must be able to distinguish one branch from other branches. In other words, we must be able to demark them. This is not possible in the case of some subjects. IMHO, it would be good for us to consider a thing that is subtler and that ...


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Extended from the original XKCD comic strip, which is in the frame.


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Logical modalities are usually expressed through relational semantics for modal logic developed by Saul Kripke and André Joyal in the late 1950s and early 1960s. In this semantics, formulas are assigned truth values relative to a possible world. A formula's truth value at one possible world can depend on the truth values of other formulas at other ...


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The split between Rationalism and Empiricism (note the capital letters) goes back to the 17th century. Basically, it is a dispute about the proper foundation of knowledge: Rationalism holds that knowledge is (in one of several ways) founded in our mind and in the human capacity to use reason. Empiricism holds that knowledge must (in one form or another) be ...


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This is a bit subtle. I'm guessing "case of knowledge justified through reason alone" is pointing to the Kantian conception of mathematics as synthetic a priori knowledge. Frege really wanted to be a Kantian and expressed great admiration for Kant, whom had come up with the distinction between synthetic a priori and analytic a priori knowledge. But ...


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Logical positivism may not be the perfect label, actually according to Hempel who's one of its major figures during its heyday in last century, it should be more properly called logical empiricism as described here: Hempel never embraced the term "logical positivism" as an accurate description of the Vienna Circle and Berlin Group, preferring to ...


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In projective geometry (specifically, in the projective plane with homogeneous coordinates) there are at least four significant ways to construct a circle. The first is as a smooth curve, which is one of the conic sections (the others being the ellipse, parabola, hyperbola and, degenerately, certain apparently straight lines). Another is as the set of points ...


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Science is specifically an empirical and data driven study. It has so far worked incredibly well when the goal is predicting future results. And in the process of predicting future results, modeling reality with math and scientific theories allows for incredibly precise predictions, like measuring down to 10^-17 cm's in quantum mechanical experiments. At ...


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You are correct that mathematics continues to have mysteries that the passage of the years has not erased. Chief among these is the fact that we come to know and understand mathematical concepts such as shape and number by their physical instantiations, yet there can never be a perfect correspondence between the physical world and the world of theoretical ...


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Hence, how could we truly claim that those old problems were actually being correctly solved up to our current dates? Any elaborate thinking requires representations (like words, or drawings) and all representations are approximations. Live with it.


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As Tetlock says, having skin in the game is facilitative: more specifically, it adds a sense of salience and urgency. If someone has to decide whether to take a business trip, they will be more focused, attentive, and judicious with the question if they have to pay for the trip themselves than if the company pays for it. But like anything else, perspective ...


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Within philosophy realm, knowledge is usually defined as "justified true belief" as here: For centuries upon centuries, philosophers accepted Plato's theory of knowledge, the view that knowledge is justified true belief. This view is also known as the JTB theory. It's not only a true belief, but also needs to be justified which is the key why ...


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Assuming your knowledge concerns things besides pure mathematics and logic, what you are looking for is empiricism or phenomenology depending on what you are focusing on. If you are interested in how knowledge is related to what we perceive, what you want is empiricism. If you are interested in how mental states, such as belief, is related to what we ...


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I think this SEP article does a decent job at that: Bonaventura (ca. 1217–1274), one of the most renowned theologians of the time, explicitly places emphasis on the sign's relation to the significate, claiming that … a sign has a twofold comparison: both to that which it signifies, and to that to which it signifies; and the first is essential and the ...


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