115 ideas
| 3722 | Metaphysics goes beyond the empirical, so doesn't need examples [Kant] |
| 3738 | The hallmark of rationality is setting itself an end [Kant] |
| 9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
| 9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
| 9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
| 9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
| 13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
| 9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
| 9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
| 9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
| 9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
| 13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
| 13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
| 13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
| 13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
| 9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
| 13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
| 13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
| 13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
| 13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
| 9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
| 13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
| 9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
| 9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
| 13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
| 13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
| 3726 | The categorical imperative is a practical synthetic a priori proposition [Kant] |
| 3739 | Free will is a kind of causality which works independently of other causes [Kant] |
| 3741 | We shall never be able to comprehend how freedom is possible [Kant] |
| 3740 | We cannot conceive of reason as being externally controlled [Kant] |
| 5296 | Kant made the political will into a pure self-determined "free" will [Kant, by Marx/Engels] |
| 24011 | Kant thought emotions are too random and passive to be part of morality [Kant, by Williams,B] |
| 5074 | Kant united religion and philosophy, by basing obedience to law on reason instead of faith [Taylor,R on Kant] |
| 8024 | The categorical imperative says nothing about what our activities and ends should be [MacIntyre on Kant] |
| 22390 | Kant thought human nature was pure hedonism, so virtue is only possible via the categorical imperative [Foot on Kant] |
| 9750 | We must only value what others find acceptable [Kant, by Korsgaard] |
| 20160 | Kant focuses exclusively on human values, and neglects cultural and personal values [Kekes on Kant] |
| 9749 | Our rational choices confer value, arising from the sense that we ourselves are important [Kant, by Korsgaard] |
| 7671 | Values are created by human choices, and are not some intrinsic quality, out there [Kant, by Berlin] |
| 16764 | The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus] |
| 3720 | We may claim noble motives, but we cannot penetrate our secret impulses [Kant] |
| 3717 | Reverence is awareness of a value which demolishes my self-love [Kant] |
| 3712 | A good will is not good because of what it achieves [Kant] |
| 3725 | The good of an action is in the mind of the doer, not the consequences [Kant] |
| 3733 | The 'golden rule' cannot be a universal law as it implies no duties [Kant] |
| 3736 | Virtue lets a rational being make universal law, and share in the kingdom of ends [Kant] |
| 3544 | Kant thinks virtue becomes passive, and hence morally unaccountable [Kant, by Annas] |
| 7674 | Generosity and pity are vices, because they falsely imply one person's superiority to another [Kant, by Berlin] |
| 21029 | Kantian respect is for humanity and reason (not from love or sympathy or solidarity) [Kant, by Sandel] |
| 7105 | If 'maxims' are deeper underlying intentions, Kant can be read as a virtue theorist [Kant, by Statman] |
| 7625 | We can ask how rational goodness is, but also why is rationality good [Putnam on Kant] |
| 3715 | Other causes can produce nice results, so morality must consist in the law, found only in rational beings [Kant] |
| 20715 | It is basic that moral actions must be done from duty [Kant] |
| 3710 | The only purely good thing is a good will [Kant] |
| 3737 | The will is good if its universalised maxim is never in conflict with itself [Kant] |
| 4024 | Kant follows Rousseau in defining freedom and morality in terms of each other [Taylor,C on Kant] |
| 3735 | Men are subject to laws which are both self-made and universal [Kant] |
| 3724 | A categorical imperative sees an action as necessary purely for its own sake [Kant] |
| 3718 | Telling the truth from duty is quite different from doing so to avoid inconvenience [Kant] |
| 3723 | There are no imperatives for a holy will, as the will is in harmony with moral law [Kant] |
| 3714 | Dutiful actions are judged not by purpose, but by the maxim followed [Kant] |
| 5295 | Kant was happy with 'good will', even if it had no result [Kant, by Marx/Engels] |
| 6695 | Kant has to attribute high moral worth to some deeply unattractive human lives [Kant, by Graham] |
| 8028 | Kantian duty seems to imply conformism with authority [MacIntyre on Kant] |
| 8026 | Almost any precept can be consistently universalized [MacIntyre on Kant] |
| 15673 | The intuition behind the categorical imperative is that one ought not to make an exception of oneself [Kant, by Finlayson] |
| 8068 | Universalising a maxim needs to first stipulate the right description for the action [Anscombe on Kant] |
| 8025 | The categorical imperative will not suggest maxims suitable for testing [MacIntyre on Kant] |
| 8027 | I can universalize a selfish maxim, if it is expressed in a way that only applies to me [MacIntyre on Kant] |
| 3728 | Suicide, false promises, neglected talent, and lack of charity all involve contradictions of principle [Kant, by PG] |
| 22008 | Always treat yourself and others as an end, and never simply as a means [Kant] |
| 3719 | If lying were the universal law it would make promises impossible [Kant] |
| 3762 | Why couldn't all rational beings accept outrageously immoral rules of conduct? [Mill on Kant] |
| 22009 | Morality is the creation of the laws that enable a Kingdom of Ends [Kant] |
| 4413 | The categorical imperative smells of cruelty [Nietzsche on Kant] |
| 3716 | Act according to a maxim you can will as a universal law [Kant] |
| 3727 | Act as if your maxim were to become a universal law of nature [Kant] |
| 22050 | The maxim of an action is chosen, and not externally imposed [Kant, by Bowie] |
| 6694 | Always treat humanity as an end and never as a means only [Kant] |
| 3731 | Rational beings necessarily conceive their own existence as an end in itself [Kant] |
| 4345 | For Kant, even a person who lacks all sympathy for others still has a motive for benevolence [Kant, by Hursthouse] |
| 4251 | If we are required to give moral thought the highest priority, this gives morality no content [Williams,B on Kant] |
| 16004 | If Kant lives by self-administered laws, this is as feeble as self-administered punishments [Kierkegaard on Kant] |
| 3711 | Only a good will makes us worthy of happiness [Kant] |
| 3713 | The function of reason is to produce a good will [Kant] |
| 3729 | Our inclinations are not innately desirable; in fact most rational beings would like to be rid of them [Kant] |
| 4344 | Actions where people spread happiness because they enjoy it have no genuine moral worth [Kant] |
| 3732 | Rational beings have a right to share in the end of an action, not just be part of the means [Kant] |
| 7670 | Kant is the father of the notion of exploitation as an evil [Kant, by Berlin] |
| 7591 | Kant completed Grotius's project of a non-religious basis for natural law [Scruton on Kant] |
| 7673 | Retributive punishment is better than being sent to hospital for your crimes [Kant, by Berlin] |
| 3730 | Non-rational beings only have a relative value, as means rather than as ends [Kant] |
| 3721 | We judge God to be good by a priori standards of moral perfection [Kant] |
| 8046 | We can only know we should obey God if we already have moral standards for judging God [Kant, by MacIntyre] |
| 20714 | God is not proved by reason, but is a postulate of moral thinking [Kant, by Davies,B] |