79 ideas
| 21405 | Cicero sees wisdom in terms of knowledge, but earlier Stoics saw it as moral [Cicero, by Long] |
| 20871 | Unfortunately we choose a way of life before we are old enough to think clearly [Cicero] |
| 5893 | A wise man has integrity, firmness of will, nobility, consistency, sobriety, patience [Cicero] |
| 5891 | Philosophy is the collection of rational arguments [Cicero] |
| 2661 | Dialectic is speech cast in the form of logical argument [Cicero] |
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 2653 | If the parts of the universe are subject to the law of nature, the whole universe must also be subject to it [Cicero] |
| 2673 | There cannot be more than one truth [Cicero] |
| 10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
| 10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
| 21677 | How can the not-true fail to be false, or the not-false fail to be true? [Cicero] |
| 2669 | Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| 10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
| 10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
| 10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
| 2664 | If we have complete healthy senses, what more could the gods give us? [Cicero] |
| 2665 | How can there be a memory of what is false? [Cicero] |
| 20800 | Every true presentation can have a false one of the same quality [Cicero] |
| 5879 | The soul is the heart, or blood in the heart, or part of the brain, of something living in heart or brain, or breath [Cicero] |
| 5884 | How can one mind perceive so many dissimilar sensations? [Cicero] |
| 5887 | The soul has a single nature, so it cannot be divided, and hence it cannot perish [Cicero] |
| 5886 | Like the eye, the soul has no power to see itself, but sees other things [Cicero] |
| 6029 | Whoever knows future causes knows everything that will be [Cicero] |
| 2628 | Why would mind mix with matter if it didn't need it? [Cicero] |
| 5885 | Souls contain no properties of elements, and elements contain no properties of souls [Cicero] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 21667 | Oratory and philosophy are closely allied; orators borrow from philosophy, and ornament it [Cicero] |
| 20814 | Eloquence educates, exhorts, comforts, distracts and unites us, and raises us from savagery [Cicero] |
| 21678 | If desire is not in our power then neither are choices, so we should not be praised or punished [Cicero] |
| 2672 | Virtues must be very detached, to avoid being motivated by pleasure [Cicero] |
| 5890 | We should not share the distress of others, but simply try to relieve it [Cicero] |
| 5894 | All men except philosophers fear poverty [Cicero] |
| 6031 | The essence of propriety is consistency [Cicero] |
| 5895 | If one despises illiterate mechanics individually, they are not worth more collectively [Cicero] |
| 2640 | We have the death penalty, but still have thousands of robbers [Cicero] |
| 2652 | Some regard nature simply as an irrational force that imparts movement [Cicero] |
| 2645 | Why shouldn't the gods fear their own destruction? [Cicero] |
| 2627 | I wonder whether loss of reverence for the gods would mean the end of all virtue [Cicero] |
| 2651 | God doesn't obey the laws of nature; they are subject to the law of God [Cicero] |
| 2634 | It seems clear to me that we have an innate idea of the divine [Cicero] |
| 2636 | Many primitive people know nothing of the gods [Cicero] |
| 2647 | It is obvious from order that someone is in charge, as when we visit a gymnasium [Cicero] |
| 2650 | If a person cannot feel the power of God when looking at the stars, they are probably incapable of feeling [Cicero] |
| 2655 | If the barbarians of Britain saw a complex machine, they would be baffled, but would know it was designed [Cicero] |
| 2656 | Chance is no more likely to create the world than spilling lots of letters is likely to create a famous poem [Cicero] |
| 2657 | If everything with regular movement and order is divine, then recurrent illnesses must be divine [Cicero] |
| 2638 | Either the gods are identical, or one is more beautiful than another [Cicero] |
| 2635 | The gods are happy, so virtuous, so rational, so must have human shape [Cicero] |
| 2641 | Why believe in gods if you have never seen them? [Cicero] |
| 2659 | The lists of good men who have suffered and bad men who have prospered are endless [Cicero] |
| 2658 | The gods blame men for having vices, but they could have given us enough reason to avoid them [Cicero] |