71 ideas
1606 | You have to be a Platonist to debate about reality, so every philosopher is a Platonist [Roochnik] |
1595 | Philosophy aims to satisfy the chief human desire - the articulation of beauty itself [Roochnik] |
1571 | 'Logos' ranges from thought/reasoning, to words, to rational structures outside thought [Roochnik] |
1572 | In the seventeenth century the only acceptable form of logos was technical knowledge [Roochnik] |
1573 | The hallmark of a person with logos is that they give reasons why one opinion is superior to another [Roochnik] |
1592 | Logos cannot refute the relativist, and so must admit that it too is a matter of desire (for truth and agreement) [Roochnik] |
1593 | Human desire has an ordered structure, with logos at the pinnacle [Roochnik] |
1603 | Logos is not unconditionally good, but good if there is another person willing to engage with it [Roochnik] |
1598 | We prefer reason or poetry according to whether basics are intelligible or not [Roochnik] |
1584 | Modern science, by aiming for clarity about the external world, has abandoned rationality in the human world [Roochnik] |
1591 | Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik] |
1599 | Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik] |
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
22886 | The modern idea of 'limit' allows infinite quantities to have a finite sum [Bardon] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
22914 | An equally good question would be why there was nothing instead of something [Bardon] |
1605 | Reality can be viewed neutrally, or as an object of desire [Roochnik] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
1577 | Relativism is a disease which destroys the possibility of rational debate [Roochnik] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
1578 | If relativism is the correct account of human values, then rhetoric is more important than reasoning [Roochnik] |
1596 | Reasoning aims not at the understanding of objects, but at the desire to give beautiful speeches [Roochnik] |
22902 | Why does an effect require a prior event if the prior event isn't a cause? [Bardon] |
22905 | Becoming disordered is much easier for a system than becoming ordered [Bardon] |
22913 | The universe expands, so space-time is enlarging [Bardon] |
22889 | We should treat time as adverbial, so we don't experience time, we experience things temporally [Bardon, by Bardon] |
22900 | How can we question the passage of time, if the question takes time to ask? [Bardon] |
22898 | What is time's passage relative to, and how fast does it pass? [Bardon] |
22897 | The A-series says a past event is becoming more past, but how can it do that? [Bardon] |
22901 | The B-series needs a revised view of causes, laws and explanations [Bardon] |
22896 | The B-series is realist about time, but idealist about its passage [Bardon] |
22903 | The B-series adds directionality when it accepts 'earlier' and 'later' [Bardon] |
22910 | To define time's arrow by causation, we need a timeless definition of causation [Bardon] |
22909 | We judge memories to be of the past because the events cause the memories [Bardon] |
22904 | The psychological arrow of time is the direction from our memories to our anticipations [Bardon] |
22906 | The direction of entropy is probabilistic, not necessary, so cannot be identical to time's arrow [Bardon] |
22907 | It is arbitrary to reverse time in a more orderly universe, but not in a sub-system of it [Bardon] |
22883 | It seems hard to understand change without understanding time first [Bardon] |
22890 | We experience static states (while walking round a house) and observe change (ship leaving dock) [Bardon] |
22884 | The motion of a thing should be a fact in the present moment [Bardon] |
22892 | Experiences of motion may be overlapping, thus stretching out the experience [Bardon] |
22911 | At least eternal time gives time travellers a possible destination [Bardon] |
22912 | Time travel is not a paradox if we include it in the eternal continuum of events [Bardon] |
22882 | We use calendars for the order of events, and clocks for their passing [Bardon] |