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Do you have a proof that we don't hold ourselves to higher standards? There's actually a rather interesting little corner of mathematics called "proof theory." It deals with the question of what a proof is and how can we use them. It starts to look like philosophy from time to time. I think the real difference is that mathematics typically starts with a ...


18

If I'm understanding your question correctly, then you're basically asking "why doesn't philosophy have the same level of rigor as mathematical proof?" I think there's two parts involved in answering this. First, one aspect of philosophy for many philosophers (arguably all) is that philosophy is actually a form of history, meaning we are studying ideas ...


14

Philosophical theories are more like scientific theories than mathematical theories, in that they have empirical content. As such, there aren't any (universally agreed upon) "first principles" that must be respected. Any potential first principles might get discarded if the reasons for doing so are compelling enough. And even if there are some such ...


10

A proof is only as strong as the axioms it is built upon. Mathematics works over a very limited number of strong axioms to work with, which gives it a limited number* of things that can be proven, but the proofs are very strong thanks to the axioms they work with (and prior proofs relying on the same axioms). Philosophy works with much broader field of ...


9

Because it would then cease to be philosophy. Philosophy sees itself as the progenitor of all the sciences, as its questions lead to the paradigm shifts upon which branches of science are founded. To limit itself to a predetermined set of rules would be to strip itself of the flexibility needed to come up with the next new thing. In other words, it is ...


9

Non sequitur I'll go off of the example in the comments, namely “One dollar” = “money” : “Nickel” = “money.” Therefore, “one dollar” = “nickel.” This is non sequitur - there's no logical reason to assume that Therefore. Or, alternatively, this could be ambiguity fallacy as this seems to be caused by (intentional?) misapplication of the symbol "=" with ...


8

When something appears so obvious that it is uninteresting and yet one knows that others do not find it obvious at all, what one may be missing is understanding what is at stake for them. Why do they not agree with what is obvious? The OP provides some examples from David Hume's Dissertation on Passions that appeared particularly uninteresting and obvious, ...


6

This is a question in philosophy that deals with the metaphysics of identity. A classic problem in philosophy is the Ship of Theseus and goes back to the pre-Socratics, particularly Heraclitus and his proposition that one cannot stand in the same river twice. In logic, one often draws a distinction between a name (symbol) and the thing it represents (...


6

To approach this from a slightly different angle, this concept is important in computer programming. In a lot of languages, the programmer can decide what attributes make an object "equal to" another object. For example, if you have two "People" objects represented by "first name", "last name" and "address"; you could choose to say that if the first and ...


5

Another thing I would add is that proofs are built on strong axioms, but also on precise definitions. It's hard to find a precise and universally accepted definition for any complex concept in philosophy. What is life? Soul? What is a cause, an action? What is truth? Those are a much harder to define than a point, a circle or a function (not that they're ...


5

What is stopping the philosophical community from holding themselves to the same standard? The impression that the philosophers' "standards" are not sufficiently high, I think, is due to (1) the apparent lack of progress in solving philosophical puzzles in conjunction with (2) the deceiving simplicity of these puzzles. In fact, nothing stops the ...


4

I do believe you've missed the point of 'duplicate' here. 'Sameness' in this context is a fairly loose and utilitarian construct. Consider: if the temple priestess says she needs a statue of Zeus for entryway, and everyone in the village steps up to sculpt a statue of Zeus, well... the priestess still only needs (and will only use) one of those statues. The ...


3

I think your summary of Hume's points are shortchanging Hume. Let's take a look at just the first one to make this point. Most of our feelings about things are somewhere between joy and grief. Where they land along this spectrum depends on the probability of something happening and the amount of joy/grief it would cause if it did happen. No, the aspect ...


3

Just like now, in Hume's time there was a tendency to dismiss emotions as our animal nature, and essentially meaningless, vs our logical reasoning side as the arbiter of all meaning and virtue. This is deeply suspect, and we should be curious about why it is such a persistent bias. Probably Hume's most significant contributions to moral philosophy, are the ...


3

Nice question. I feel you're right about this, that we teach logic and then tend to leave it behind. The toolkit contains more than just logic but it is the main tool. The goal is truth but metaphysics is a theoretical discipline and as in physics the interim goal is the 'best' theory, not the 'true' one. We might have a theory that the marmalade is in ...


3

This is one of the most difficult issues for all of us because of the connection between opinion and knowledge or certainty. Much less attention has been given to the question of what opinions are, and much more to how to ascend from them to knowledge. In our own time the problem is largely neglected because of the assumption that the authority of the ...


3

Absolute time and space Relativity theory radically re-conceptualised space and time, a concept of both philosophical and scientific interest. Newton held an 'absolute' theory of time: 'Absolute, true and mathematical time, of itself, and from its own nature, flows equably without relation to anything external'. Most 18th and 19th century philosophers who ...


3

Probably quite a bit of Ryle's philosophy has to be brought into play before his position on philosophy and proof is fully clear - if indeed it is fully clear. The following extract may, however, clear a few spots of ground: IN "Proofs in Philosophy ", Professor Ryle points out that " Philosophical arguments can be or fail to be logically powerful ...


2

The essential distinction is this: Mysticism focuses on our subjective experience of the world. Metaphysics focuses on our objective ontological understanding of the world. The core idea in mysticism is that no expression of language can ever fully capture our subjective experience of the world. The richness and detail of subjective experience transcends ...


2

Do you need to know what philosophy is to study it? I think it perfectly possible to be exercised by questions, to be involved in topics, which are (or are generally classified as) philosophical without knowing that they are philosophical. For instance, a real one in my own case, when I was studying history many years ago I started to wonder how one could ...


2

In general, there are three main reasons philosophers make seemingly obvious statements: It wasn't obvious at the time - It might be a commonplace now, but it was controversial and/or groundbreaking at the time. It's a trap - You're being set up to be forced to accept something controversial or groundbreaking that is implied or entailed by the seemingly ...


2

'A Dissertation on the Passions' is a minor work compared with A Treatise of Human Nature, Enquiry concerning Human Understanding, and Enquiry concerning the Principles of Morals. These are works in which Hume sets out his principal philosophical positions. The passions matter to Hume because they, and not reason in his view, provide the foundations of ...


2

If you were to study, or example Psychology, you will notice from the history of Psychology that particular philosophical stances fosters particular psychological approaches. Remember the old adage: We don't know where we are going if we don't know where we come from? It comes into play here in two ways. Firstly, there is deepening your understanding of the ...


2

The argument generally carries a time limit - a pregnant woman would not be allowed to abort a eight month foetus, for example; which shows that the argument is not universally valid; it's a point of compromise between two views, between the right of a woman to her own body, and that of the newly to be born. The Aztecs were known to sacrifice their sons ...


2

It is hard to correlate Kant and Popper, at least I find it so, since their enterprises were so different. Kant's major epistemological concern was with what might be termed psychological epistemology. The forms of intuition (our sense of space and time) and the categories of the understanding (causality, quantity, quality, plurality, limitation, ...


2

Contrary to your hope, I don't think this will inspire a large number of divergent answers (I suppose for researchers on the topic of explanation there is a lot of room to disagree about the nitty-gritty, but for most philosophers they haven't put that much thought into what "account" means -- we just use the term). "account" is a term of art in contemporary ...


2

The mathematical community has proofs Please note that some of the best practitioners of mathematics disparage proofs. Lefzchetz, for example, told his students not to just present pretty new proofs (they probably already knew that they ought not to present ugly ones!). He wanted new substantiatial new ideas. Poincare was similarly disparaging in his book ...


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