RodolfoAP
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Stating that "statistics don't cause" is a misinterpretation of his message, in the form of a false dilemma (statistics don't cause X, then, he's wrong) then, a red herring (you introduced an irrelevant fact to the conversation, distracting the goal). He tries to get back the proper conversation ("it is logical...!"). After you compare "certainty" vs "probability", you must follow your own argument, but yours it is more probabilistic than his: that's a contradiction and a non sequitur. Then, he tries again to roll back to logic, that's his only possibility against such fallacies.

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The content of countable sets is subjective. Normally, countable sets are made of parts sharing some properties, but if you strictly follow such rule, you will count a different number of apples than me in border conditions, whatever the rule (if an apple requires 70g to be considered as such, you might measure 69.999999994 and I might measure 70.0000000002: two empirical measures will always differ at certain point on infinitesimal values). For now, we can't even agree if viruses belong to the set of living species.

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Although your question is too broad, the Wikipedia article about knowledge probably answers your questions.

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See math.stackexchange.com/a/49/952649

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Logic is the set of rules we have simultaneously discovered and proposed to describe nature. So, if you are asking if the set of rules exist: yes, find it in any book. If you ask if they apply to reality: yes, at least, that's the idea, we're not interested in rules that don't apply to reality. If you ask if logic applies to everything, we can't know, there a lot we don't know, and there's a lot of illogical facts, for example, Kant's antinomies (contradictory facts about things, time, space, etc.).

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Only interpretations can be said to be biases. Codes, customs, rules, screwdrivers or transistors are not biases.

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This is not a rule external to morals (applicable to all moral schools). It is internal. That is, it depends on each school. Most religious forms consider mandatory to obey their leaders. Other schools don't care and just focus on the goals. For example, if the moral rule has the goal of survival of the group, and you might save a life doing something immoral (e.g. impersonating someone), then perhaps you should.

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Following Aristotle's law of identity, a set with an apple is the same ten seconds after. But physically that's false. You are not the same person that you were one second ago. Your doubt is about physical objects, but as said, sets are rational concepts. A bag of apples is an static ideal, although physically, all apples are permanently changing and are never the same in two instants of time.

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Depends on what truth (absolute truth does not exist). Who believes in religious truth is perhaps a religious, etc.

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It depends on the axioms, but in general, yes. A set is a rational concept. You can put an apple and a circle in a set (e.g. the set of entities that are easy to draw), and that doesn't break any rule. But evidently, a set of geometrical figures cannot include apples.

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Strictly, if the system makes its parts, its SUB-systems cannot make its SUB-parts (either it is the system that makes them or either we tell it how to divide in parts). Maturana et.al. are criticized mainly due to such subjectivities. To follow Maturana and his school of thought, one must accept that things exhibit human features, and that the limits of a system (the frontier between what "is aotopoietically produced", and what is not) are absolute (they exist without need of humans), not subjective (they exist as assessed by human reason). An idea that is mostly unacceptable in philosophy.

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a) Yes, the impression in the mind of the observer. b) Precisely: I've wrote "almost independent of time". A state implies no change (hence the form "static"), and that implies no time involved. If you describe something as in a "changing state", the state is independent of time, while the change itself is dependent on time. That is equivalent to take a (static) picture of a switch in the "change" position, what you call "dynamic state".

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