23 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. |
| 8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
| Full Idea: Euclid gives proofs of many things which anyone would concede to him without question. ...The aim of proof is not merely to place the truth of a proposition beyond doubt, but also to afford us insight into the dependence of truths upon one another. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §02 | |
| A reaction: This connects nicely with Shoemaker's view of analysis (Idea 8559), which I will adopt as my general view. I've always thought of philosophy as the aspiration to wisdom through the cartography of concepts. |
| 13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
| Full Idea: Euclid begins proofs about all triangles with 'let ABC be a triangle', but ABC is not a proper name. It names an arbitrarily selected triangle, and if that has a property, then we can conclude that all triangles have the property. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by E.J. Lemmon - Beginning Logic 3.2 | |
| A reaction: Lemmon adds the proviso that there must be no hidden assumptions about the triangle we have selected. You must generalise the properties too. Pick a triangle, any triangle, say one with three angles of 60 degrees; now generalise from it. |
| 6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
| Full Idea: Euclid's geometry is a synthetic geometry; Descartes supplied an analytic version of Euclid's geometry, and we now have analytic versions of the early non-Euclidean geometries. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michael D. Resnik - Maths as a Science of Patterns One.4 | |
| A reaction: I take it that the original Euclidean axioms were observations about the nature of space, but Descartes turned them into a set of pure interlocking definitions which could still function if space ceased to exist. |
| 9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
| Full Idea: Assume a largest prime, then multiply the primes together and add one. The new number isn't prime, because we assumed a largest prime; but it can't be divided by a prime, because the remainder is one. So only a larger prime could divide it. Contradiction. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by James Robert Brown - Philosophy of Mathematics Ch.1 | |
| A reaction: Not only a very elegant mathematical argument, but a model for how much modern logic proceeds, by assuming that the proposition is false, and then deducing a contradiction from it. |
| 9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
| Full Idea: A unit is that according to which each existing thing is said to be one. | |
| From: Euclid (Elements of Geometry [c.290 BCE], 7 Def 1) | |
| A reaction: See Frege's 'Grundlagen' §29-44 for a sustained critique of this. Frege is good, but there must be something right about the Euclid idea. If I count stone, paper and scissors as three, each must first qualify to be counted as one. Psychology creeps in. |
| 8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
| Full Idea: Euclid's Postulate 2 says the geometer can 'produce a finite straight line continuously in a straight line'. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Thinking About Mathematics 4.2 | |
| A reaction: The point being that this takes infinity for granted, especially if you start counting how many points there are on the line. The Einstein idea that it might eventually come round and hit you on the back of the head would have charmed Euclid. |
| 22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
| Full Idea: Euclid's axioms were insufficient to derive all the theorems of geometry: at various points in his proofs he appealed to properties that are obvious from the diagrams but do not follow from the stated axioms. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'aim' | |
| A reaction: I suppose if the axioms of a system are based on self-evidence, this would licence an appeal to self-evidence elsewhere in the system. Only pedants insist on writing down what is obvious to everyone! |
| 8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
| Full Idea: Euclid's fifth 'parallel' postulate says if there is an infinite straight line and a point, then there is only one straight line through the point which won't intersect the first line. This axiom is independent of Euclid's first four (agreed) axioms. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 2.2 | |
| A reaction: This postulate was challenged in the nineteenth century, which was a major landmark in the development of modern relativist views of knowledge. |
| 10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
| Full Idea: Euclid gives no principle of continuity, which would sanction an inference that if a line goes from the outside of a circle to the inside of circle, then it must intersect the circle at some point. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Philosophy of Mathematics 6.1 n2 | |
| A reaction: Cantor and Dedekind began to contemplate discontinuous lines. |
| 10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
| Full Idea: Euclid postulates: One can join two points by a straight line; Hilbert states the axiom: Given any two points, there exists a straight line on which both are situated. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Paul Bernays - On Platonism in Mathematics p.259 |
| 14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
| Full Idea: In descriptive geometry the first 26 propositions of Euclid hold. In projective geometry the 1st, 7th, 16th and 17th require modification (as a straight line is not a closed series). Those after 26 depend on the postulate of parallels, so aren't assumed. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Bertrand Russell - The Principles of Mathematics §388 |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
| Full Idea: The best known example of Euclid's 'common notions' is "If equals are subtracted from equals the remainders are equal". These can be called axioms, and are what "the man who is to learn anything whatever must have". | |
| From: report of Euclid (Elements of Geometry [c.290 BCE], 72a17) by David Roochnik - The Tragedy of Reason p.149 |
| 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. |
| 18033 | The meaning of a representation is its role in thought, perception or decisions [Block] |
| Full Idea: According to conceptual role semantics, the meaning of a representation is the role of that representation in the cognitive life of the agent, for example, in perception, thought and decision-making. | |
| From: Ned Block (Semantics, Conceptual Role [1998]) | |
| A reaction: I never believe theories of this kind, because I always find myself asking 'what is the nature of this representation which enables it to play this role?'. |
| 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. |