19 ideas
| 21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
| Full Idea: Metaphysics is the most general attempt to make sense of things. | |
| From: A.W. Moore (The Evolution of Modern Metaphysics [2012], Intro) | |
| A reaction: This is the first sentence of Moore's book, and a touchstone idea all the way through. It stands up well, because it says enough without committing to too much. I have to agree with it. It implies explanation as the key. I like generality too. |
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| Full Idea: It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], Intro) | |
| A reaction: [He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut']. |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| Full Idea: Whenever we have to do a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §4) | |
| A reaction: Fine quotes this to show that the Dedekind Cut creates the irrational numbers, rather than hitting them. A consequence is that the irrational numbers depend on the rational numbers, and so can never be identical with any of them. See Idea 10573. |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| Full Idea: I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], §1) | |
| A reaction: Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting? |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| Full Idea: If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value. | |
| From: Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7 | |
| A reaction: [Kitcher says he 'showed' this, rather than just stating it] |
| 21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
| Full Idea: Appearances in general are nothing outside our representations, which is just what we mean by transcendental ideality. | |
| From: A.W. Moore (The Evolution of Modern Metaphysics [2012], B535/A507) |
| 3926 | The human heart has a natural concern for public good [Hume] |
| Full Idea: While the human heart is compounded of the same elements as at present, it will never be wholly indifferent to public good. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], IX.I.222) | |
| A reaction: Even criminals can be patriotic. Why do people dump rubbish in beauty spots? |
| 3929 | No moral theory is of any use if it doesn't serve the interests of the individual concerned [Hume] |
| Full Idea: What theory of morals can ever serve any useful purpose, unless it can show, by a particular detail, that all the duties which it recommends, are also the true interest of each individual? | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], IX.II.228) | |
| A reaction: It is hard to disagree, even if occasional cases of extreme altruism can occur. |
| 3925 | Personal Merit is the possession of useful or agreeable mental qualities [Hume] |
| Full Idea: Personal Merit consists altogether in the possession of mental qualities, useful or agreeable to the person himself or to others. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], IX.I.217) | |
| A reaction: If pleasure and utility can be intrinsically valuable, why can't virtue be as well? |
| 3922 | Justice only exists to support society [Hume] |
| Full Idea: The necessity of justice to the support of society is the sole foundation of that virtue. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], III.II.163) | |
| A reaction: A sense of fairness precedes the building of a society, rather than arising out of it. |
| 23560 | If we all naturally had everything we could ever desire, the virtue of justice would be irrelevant [Hume] |
| Full Idea: Suppose nature has bestowed on humans such abundance of external conveniences that every individual is fully provided with whatever his appetites can want. …Justice, in that case, would be totally useless, and have no place in the catalogue of virtues. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], I.III.145) | |
| A reaction: [compressed] This seems to emphasise possessions and satisfaction of appetites, but presumably it would also need total security from other humans, which nature might struggle to provide. No sharing in this imagined world. |
| 3918 | Moral philosophy aims to show us our duty [Hume] |
| Full Idea: The end of all moral speculations is to teach us our duty. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], I.136) | |
| A reaction: A surprising view from someone who thinks morals are basically sentiment. |
| 3919 | Conclusions of reason do not affect our emotions or decisions to act [Hume] |
| Full Idea: Inference and conclusions of the understanding have no hold of the affections nor set in motion the active powers of man. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], I.136) | |
| A reaction: I disagree. This is a typical empiricist separation of ideas from experience, of inner from outer, of analytic from synthetic. |
| 3928 | Virtue just requires careful calculation and a preference for the greater happiness [Hume] |
| Full Idea: The sole trouble which virtue demands is that of just calculation, and a steady preference for the greater happiness. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], IX.II.228) | |
| A reaction: Hume was the parent of utilitarianism. Can one person exhibit virtue on a desert island? |
| 3923 | No one would cause pain to a complete stranger who happened to be passing [Hume] |
| Full Idea: Would any man, who is walking along, tread as willingly on another's gouty toes, whom he has no quarrel with, as on the hard flint and pavement? | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], V.II.183) | |
| A reaction: He is right that we empathise with the pain of others, and this is presumably one of the bases of morality. Animals lack sympathy for other animals. |
| 3924 | Nature makes private affections come first, because public concerns are spread too thinly [Hume] |
| Full Idea: It is wisely ordained by nature, that private connexions should commonly prevail over universal views and considerations; otherwise our affections and actions would be dissipated and lost, for want of a proper limited object. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], V.II.186n) | |
| A reaction: A very good objection to the excessively altruistic demands of utilitarianism. |
| 3921 | The safety of the people is the supreme law [Hume] |
| Full Idea: The safety of the people is the supreme law. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], III.II.157) | |
| A reaction: No political system ever seems able to disagree with this. |
| 3927 | Society prefers helpful lies to harmful truth [Hume] |
| Full Idea: Truths which are pernicious to society, if any such there be, will yield to errors which are salutary and advantageous. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], IX.II.228) | |
| A reaction: Hume probably meant religion. Two centuries later we have a greater appetite for uncomfortable truth. |
| 3920 | If you equalise possessions, people's talents will make them unequal again [Hume] |
| Full Idea: Render possessions ever so equal, men's different degrees of art, care, and industry will immediately break that equality. | |
| From: David Hume (Enquiry concerning Principles of Morals [1751], III.II.155) | |
| A reaction: This might not be so if there is a totalitarian restriction of economic freedom. |