20 ideas
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 16755 | The possible Aristotelian view that forms are real and active principles is clearly wrong [Fine,K, by Pasnau] |
| Full Idea: Aristotle seems to have a possible basis for the belief [in individual forms], namely that forms are real and active principles in the world, which is denied by any right-minded modern. | |
| From: report of Kit Fine (A Puzzle Concerning Matter and Form [1994], p.19) by Robert Pasnau - Metaphysical Themes 1274-1671 24.3 n8 | |
| A reaction: Pasnau says this is the view of forms promoted by the scholastics, whereas Aristotle's own view should be understood as 'metaphysical'. |
| 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. |