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Descartes was the modern founder of what is called foundationalism about knowledge, the idea that we must find a secure self-evident ground from which all the rest of our knowledge can be justified. Many classical philosophers (e.g. Plato, Kant, Frege, Husserl) shared this belief, and some continue to share it. The alternative, they believe, is universal ...


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Circular argument We know it's a trilemma because the argument is founded on logic and proofs, and all proofs will end in either circular logic, infinite regression, or a foundational assumption. Infinite regress You can always break a proof into parts. Those parts get simpler and simpler. Keep breaking them up long enough, and all parts will eventually ...


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I will make several suggestions, although I am not certain that I interpret the question as intended. The strongest case (arguably) for philosophical foundations to epistemology in modern times, including the idea that positive sciences require such an inquiry into their foundations to function properly, was emphatically made by Husserl throughout his life. ...


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You have misunderstood the point of the Munchausen Trilemma. It plays a key role in the process of philosophy showing that none of our beliefs are justified knowledge, per the standards of "reasoning". Most people hold that they have knowledge and beliefs based on justified reasons, and that beliefs SHOULD be justified, and knowledge isn't knowledge unless ...


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The fundamental disagreement between coherentism (to which Bonjour is but one — quite influential — contributor) and foundationalism is, at its root, the justification for knowledge. Bonjour's disagreement, much the same as most coherentists, lies in the foundationalist belief (in the general sense, as there are different types of foundationalism) that all ...


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Euclid was mocked for demonstrating existence of triangles, and Peano for proving that 1 is a number (by Poincaré, no less), but both contributed to clarifying foundations of mathematics. Considering that skeptics dispute Moore's conclusion "the thing" may not be as trivial as it seems (as is often the case in mathematics and philosophy). Even some non-...


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The trilemma is about justification of a given proposition. Any justification, so the story goes, takes ultimately one of these forms if faced with skepticism. Therefore, the third option is about people who answer to the question "But how do you know that x really is true" dogmatically, e.g. with "Because it is", "Because I say so", etc. Ultimately, the ...


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St. Thomas follows Aristotle in his solution of the regress problem: There must be an indemonstrable first principle because if everything were demonstrable, there would be an infinite regress; cf. his Expositio Posteriorum lib. 1 l. 7. Also, St. Thomas discusses in ibid. l.8 that circular demonstration ultimately leads to saying "if A is, A must be—a simple ...


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You need to be careful with the use of quotation marks here. A word in quotation marks is being mentioned, not used. The sentence "'French' is not French" is true. Because there I am mentioning the name of a language, and noting correctly that that is not the name of the french language in the french language. But the sentence, "French is not French" is a ...


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Rota himself hints at methods able to complement the axiomatic method in his article: historical analysis psychological explanations reversal considerations Rota blames mathematics for developments of analytical philosophy to become ahistorical and separate from psychology. Which is unfair, since mathematics was never ahistorical. The reversal ...


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The process of mathematics has evolved. We have good records of pre-axiomatic mathematics, and each of these was rigorous in its time. Mathematics started as an experimental science. The Egyptians contrived formulas out of intuitive notions of geometry, and they measured to determine the accuracy of their guesses. We have manuscripts containing formulas ...


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The non-axiomatic method is common in the work of applied mathematicians. At the turn of the 20th century leading mathematicians like Felix Klein, while acknowledging the importance of axiomatisations, warned that they may be a second fiddle to other fruitful developments where such axiomatisations are not that relevant. Klein engaged a team of top-level ...


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Whereas the facts of mathematics once discovered will never change Whilst true, the relative importance of these facts at the frontier of mathematics will change; for example, group theory was once called 'gruppenpest' whereas now it's generally recognised and known as the mathematics of symmetry, though symmetry is a wider concept than this, proof: look ...


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Should we keep on questioning until nothing is left to question or is there a point on which we need to stand (which we often tend to do). Descartes used 'I think' as this fixed point, there may be others. But what is a rational way to find one, if any? How is this question addressed in modern philosophy? Your first sentence ought to end with a question ...


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I had read someone claim he was against foundationalism, or specifically psychologism. Does he agree to use a limited amount or am I wrong about this being an experience? Although it may sound like Descarte relied on the 'seeming' (i.e: subjective experience) of there being an 'I'; his argument does not rely on it, in fact, it is build on something that ...


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You might be interested in three attempt to reconcile foundationalism and coherentism : Sven Ove Hansson, 'The False Dichotomy between Coherentism and Foundationalism', The Journal of Philosophy, Vol. 104, No. 6 (Jun., 2007), pp. 290-300. This is a response to and commentary on : Ernest Sosa, 'The Raft and the Pyramid: Coherence versus Foundations in ...


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Let's get Moore's text up on screen : I can prove now, for instance, that two human hands exist. How? By holding up my two hands, and saying, as I make a certain gesture with the right hand, 'Here is one hand, and adding, as I make a certain gesture with the left, 'and here is another'. And if, by doing this, I have proved ipso facto the existence of ...


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The first and main point to understand about the trilemma is that it is an argument. As such, its function is to convince other human beings, at least to the extent that they are rational. The trilemma is an argument about knowledge and for this reason is often misunderstood as proving the impossibility of any knowledge. This, however, is a logical ...


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You're using the word 'foundationalism' quite imprecisely, which is why you see Hegel as a foundationalist. Foundationalism is an epistemological doctrine about the structure of justification. They hold that all inferences must end in some non-inferential knowledge or justified belief. Nowhere in Hegel does anything like this structure of justification occur....


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Infinite regress problems are a result of a misunderstanding of epistemology. Epistemology is about how knowledge is created, how you can distinguish what ideas you should adopt and act on, and similar problems. Philosophers have commonly tried to solve this problem by saying there is a process called 'justification': a process that can make conclusions true ...


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Philosophy is traditionally considered as the "mother" of all other disciplines. It is also true that when you get deeply into the foundations of nearly any discipline, it begins to overlap with philosophy, which is why the doctorate for most disciplines is called the Doctorate of Philosophy (PhD). The foundation of philosophy is the question "Why?"


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Eleonore Stump tries to extricate Aquinas from the Cartesian problematic of foundationalism in this article, "Aquinas on the foundations of knowledge". https://philpapers.org/rec/STUAOT-3 One author who cites Stump wrote an article called "Is Aquinas a Foundationalist?" https://philpapers.org/rec/WILIAA-11 I think the way you phrase what foundationalism ...


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Yes, we should question everything. Just not all at once. That, according to a central strand in modern philosophy, for which Descartes himself has been a guiding example. Descartes's so called fixed point was a point that he reached through the questioning process. It's not as if he decided on a fixed point before he started questioning. On the contrary, he ...


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This question is quite vague (esoteric?), so the answer will not be very precise, too. First, I agree that "oneness" and "twoness" are fundamental because the former gives us the basic unit, the latter binary opposition and connection. As you noticed, a relation r: X → Y is about "twoness". After all, it is formally defined as a subset of the Cartesian ...


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So the Cartesian project of complete foundationalist certainty has been abandoned my contemporary epistemologists. Nevertheless there are still foundationalists, and they tend to really stress the defeasibility of their knowledge. Foundationalists hold that relative certainty of the truth is achievable through some starting point. A domain-non-specific ...


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I don't have an answer to your first question; but an observation that may help bring forward more helpful answers by focusing on a particular discipline where formal arguments are made as a kind of case study. Take physics, here simplicity is often put forward as a key criteria and thus also a kind of mantra to characterise useful ideas and theories and ...


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Your first observation sounds like the principle of parsimony, stated cynically, if you are looking for a name. The principle is that the most compact theory is preferred over any more complicated theory that explains the same data. And yours, among other, more aesthetic, considerations is the basic argument supporting the principle. But the connection ...


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Please excuse the double-post, but this is a completely separate stream of thought. I am a programmer, so deal with logic all day. So I thought about this question in those terms. For those with no coding background, a boolean variable is either true or false. No other value is possible, it's a binary value. So, referring to a boolean variable x: 1 ...


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