31 ideas
| 12124 | Metaphysics is the best knowledge, because it is the simplest [Bacon] |
| Full Idea: That knowledge is worthiest which is charged with least multiplicity, which appeareth to be metaphysic | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.6) | |
| A reaction: A surprising view, coming from the father of modern science, but essentially correct. Obviously metaphysics aspires to avoid multiplicity, but it is riddled not only with complexity in its researches, but massive uncertainties. |
| 12123 | Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon] |
| Full Idea: Knowledges are as pyramides, whereof history is the basis. So of natural philosophy, the basis is natural history, the stage next the basis is physic; the stage next the vertical point is metaphysic. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.6) | |
| A reaction: The father of modern science keeps a place for metaphysics, as the most abstract level above the physical sciences. I would say he is right. It leads to my own slogan: science is the servant of philosophy. |
| 12119 | Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon] |
| Full Idea: Physic should contemplate that which is inherent in matter, and therefore transitory; and metaphysic that which is abstracted and fixed | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.3) | |
| A reaction: He cites the ancients for this view, with which he agrees. One could do worse than hang onto metaphysics as the study of necessities, but must then face the attacks of the Quineans - that knowledge of necessities is beyond us. |
| 12120 | Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon] |
| Full Idea: Physic inquireth and handleth the material and efficient causes; and metaphysic handleth the formal and final causes. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.3) | |
| A reaction: Compare Idea 12119. This divides up Aristotle's famous Four Causes (or Explanations), outlined in 'Physics' II.3. The concept of 'matter', and the nature of 'cause' seem to me to fall with the purview of metaphysics. Interesting, though. |
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| Full Idea: Late nineteenth century mathematicians said that, although plus, minus and 0 could not be precisely defined, they could be partially 'implicitly defined' as a group. This nonsense was rejected by Frege and others, as expressed in Russell 1903. | |
| From: Wilfrid Hodges (Model Theory [2005], 2) | |
| A reaction: [compressed] This is helpful in understanding what is going on in Frege's 'Grundlagen'. I won't challenge Hodges's claim that such definitions are nonsense, but there is a case for understanding groups of concepts together. |
| 10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
| Full Idea: In first-order languages the completeness theorem tells us that T |= φ holds if and only if there is a proof of φ from T (T |- φ). Since the two symbols express the same relationship, theorist often just use |- (but only for first-order!). | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: [actually no spaces in the symbols] If you are going to study this kind of theory of logic, the first thing you need to do is sort out these symbols, which isn't easy! |
| 10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
| Full Idea: If every structure which is a model of a set of sentences T is also a model of one of its sentences φ, then this is known as the model-theoretic consequence relation, and is written T |= φ. Not to be confused with |= meaning 'satisfies'. | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: See also Idea 10474, which gives the other meaning of |=, as 'satisfies'. The symbol is ALSO used in propositional logical, to mean 'tautologically implies'! Sort your act out, logicians. |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| Full Idea: The symbol in 'I |= S' reads that if the interpretation I (about word meaning) happens to make the sentence S state something true, then I 'is a model for' S, or I 'satisfies' S. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: Unfortunately this is not the only reading of the symbol |= [no space between | and =!], so care and familiarity are needed, but this is how to read it when dealing with models. See also Idea 10477. |
| 10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
| Full Idea: Model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures, with Tarski's truth definition as a paradigm. | |
| From: Wilfrid Hodges (Model Theory [2005], Intro) | |
| A reaction: My attention is caught by the fact that natural languages are included. Might we say that science is model theory for English? That sounds like Quine's persistent message. |
| 10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
| Full Idea: A 'structure' in model theory is an interpretation which explains what objects some expressions refer to, and what classes some quantifiers range over. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: He cites as examples 'first-order structures' used in mathematical model theory, and 'Kripke structures' used in model theory for modal logic. A structure is also called a 'universe'. |
| 10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
| Full Idea: The models in model-theory are structures, but there is also a common use of 'model' to mean a formal theory which describes and explains a phenomenon, or plans to build it. | |
| From: Wilfrid Hodges (Model Theory [2005], 5) | |
| A reaction: Hodges is not at all clear here, but the idea seems to be that model-theory offers a set of objects and rules, where the common usage offers a set of descriptions. Model-theory needs homomorphisms to connect models to things, |
| 10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
| Full Idea: First-order logic is hopeless for discriminating between one infinite cardinal and another. | |
| From: Wilfrid Hodges (Model Theory [2005], 4) | |
| A reaction: This seems rather significant, since mathematics largely relies on first-order logic for its metatheory. Personally I'm tempted to Ockham's Razor out all these super-infinities, but mathematicians seem to make use of them. |
| 12121 | We don't assume there is no land, because we can only see sea [Bacon] |
| Full Idea: They are ill discoverers that think there is no land, when they can see nothing but sea. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.5) | |
| A reaction: Just the sort of pithy remark for which Bacon is famous. It is an obvious point, but a nice corrective to anyone who wants to apply empirical principles in a rather gormless way. |
| 12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
| Full Idea: All true and fruitful natural philosophy hath a double scale or ladder, ascendent and descendent, ascending from experiments to the invention of causes, and descending from causes to the invention of new experiments. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.1) | |
| A reaction: After several hundred years, I doubt whether anyone can come up with a better account of scientific method than Bacon's. |
| 12127 | Many different theories will fit the observed facts [Bacon] |
| Full Idea: The ordinary face and view of experience is many times satisfied by several theories and philosophies. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VIII.5) | |
| A reaction: He gives as his example that the Copernican system and the Ptolemaic system both seem to satisfy all the facts. He wrote in 1605, just before Galileo's telescope. His point is regularly made in modern discussions. In this case, he was wrong! |
| 12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
| Full Idea: It is the nature of the mind of man (to the extreme prejudice of knowledge) to delight in the spacious liberty of generalities, as in a champaign region, and not in the inclosures of particularity. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VIII.1) | |
| A reaction: I have to plead guilty to this myself. He may have pinpointed the key motivation behind philosophy. We all want to know things, as Aristotle said, but some of us want the broad brush, and others want the fine detail. |
| 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. |
| 12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
| Full Idea: To say 'leaves are for protecting of fruit', or that 'clouds are for watering the earth', is well inquired and collected in metaphysic, but in physic they are impertinent. They are hindrances, and the search of the physical causes hath been neglected. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.7) | |
| A reaction: This is the standard rebellion against Aristotle which gave rise to the birth of modern science. The story has been complicated by natural selection, which bestows a sort of purpose on living things. Nowadays we pursue both paths. |
| 12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |
| Full Idea: I assign to summary philosophy the operation of essences (as quantity, similitude, diversity, possibility), with this distinction - that they be handled as they have efficacy in nature, and not logically. | |
| From: Francis Bacon (The Advancement of Learning [1605], II.VII.3) | |
| A reaction: I take this to be a splendid motto for scientific essentialism, in a climate where modal logicians appear to have taken over the driving seat in our understanding of essences. |