102 ideas
3722 | Metaphysics goes beyond the empirical, so doesn't need examples [Kant] |
3738 | The hallmark of rationality is setting itself an end [Kant] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
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] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
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] |
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] |
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] |
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] |
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] |
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] |
3724 | A categorical imperative sees an action as necessary purely for its own sake [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] |
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] |
22009 | Morality is the creation of the laws that enable a Kingdom of Ends [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] |