43 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
16756 | Substantial forms must exist, to explain the stability of metals like silver and tin [Albertus Magnus] |
20146 | 'Luck' is the unpredictable and inexplicable intersection of causal chains [Kekes] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
20169 | An action may be intended under one description, but not under another [Kekes] |
20149 | To control our actions better, make them result from our attitudes, not from circumstances [Kekes] |
19738 | Values are an attempt to achieve well-being by bringing contingencies under control [Kekes] |
20145 | Values help us to control life, by connecting it to what is stable and manageable [Kekes] |
20170 | Responsibility is unprovoked foreseeable harm, against society, arising from vicious character [Kekes] |
20165 | Reason and morality do not coincide; immorality can be reasonable, with an ideology [Kekes] |
20171 | Practical reason is not universal and impersonal, because it depends on what success is [Kekes] |
20175 | If morality has to be rational, then moral conflicts need us to be irrational and immoral [Kekes] |
20174 | Relativists say all values are relative; pluralists concede much of that, but not 'human' values [Kekes] |
20159 | Cultural values are interpretations of humanity, conduct, institutions, and evaluations [Kekes] |
20161 | The big value problems are evil (humanity), disenchantment (cultures), and boredom (individuals) [Kekes] |
20156 | We are bound to regret some values we never aspired to [Kekes] |
20150 | There are far more values than we can pursue, so they are optional possibilities [Kekes] |
20158 | Innumerable values arise for us, from our humanity, our culture, and our individuality [Kekes] |
20151 | Our attitudes include what possibilities we value, and also what is allowable, and unthinkable [Kekes] |
20152 | Unconditional commitments are our most basic convictions, saying what must never be done [Kekes] |
20153 | Doing the unthinkable damages ourselves, so it is more basic than any value [Kekes] |
20162 | Evil isn't explained by nature, by monsters, by uncharacteristic actions, or by society [Kekes] |
20157 | Well-being needs correct attitudes and well-ordered commitments to local values [Kekes] |
20154 | Control is the key to well-being [Kekes] |
20172 | Boredom destroys our ability to evaluate [Kekes] |
20173 | Boredom is apathy and restlessness, yearning for something interesting [Kekes] |
20155 | Society is alienating if it lacks our values, and its values repel us [Kekes] |
20164 | The ideal of an ideology is embodied in a text, a role model, a law of history, a dream of the past... [Kekes] |
20163 | Ideologies have beliefs about reality, ideals, a gap with actuality, and a program [Kekes] |
20148 | Equal distribution is no good in a shortage, because there might be no one satisfied [Kekes] |