29 ideas
| 1606 | You have to be a Platonist to debate about reality, so every philosopher is a Platonist [Roochnik] |
| Full Idea: Everyone who enters into a debate about reality automatically becomes a Platonist. Since such debates are the essence of philosophy, every philosopher is a Platonist. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.199) | |
| A reaction: This is correct |
| 1595 | Philosophy aims to satisfy the chief human desire - the articulation of beauty itself [Roochnik] |
| Full Idea: Philosophy, the attempt to articulate the vision of beauty itself, is the attempt to satisfy the highest human desire. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.120) | |
| A reaction: A million miles away from modern philosophy, but still an ideal to be taken seriously. |
| 1572 | In the seventeenth century the only acceptable form of logos was technical knowledge [Roochnik] |
| Full Idea: In the seventeenth century only a certain type of logos was deemed legitimate, namely that identified with technical knowledge (or 'techné'). | |
| From: David Roochnik (The Tragedy of Reason [1990], Intro. 15) |
| 1603 | Logos is not unconditionally good, but good if there is another person willing to engage with it [Roochnik] |
| Full Idea: Logos is not unconditionally good, but good contingent on there being some other person (out there) who is willing to talk with logos, to approach it even as an opponent. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.175) |
| 1573 | The hallmark of a person with logos is that they give reasons why one opinion is superior to another [Roochnik] |
| Full Idea: What is supposed to identify the person of logos from the one without is the commitment to giving reasons explaining why one opinion is superior to another. | |
| From: David Roochnik (The Tragedy of Reason [1990], Intro. 17) |
| 1593 | Human desire has an ordered structure, with logos at the pinnacle [Roochnik] |
| Full Idea: Human desire has an ordered structure, with logos at the pinnacle. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.109) |
| 1571 | 'Logos' ranges from thought/reasoning, to words, to rational structures outside thought [Roochnik] |
| Full Idea: Logos can mean i) a thought or reasoning, ii) the word which expresses a thought, iii) a rational structure outside human thought. These meanings give 'logos' an extraordinary range. | |
| From: David Roochnik (The Tragedy of Reason [1990], Intro. 12) |
| 1592 | Logos cannot refute the relativist, and so must admit that it too is a matter of desire (for truth and agreement) [Roochnik] |
| Full Idea: Logos cannot refute the radical, consistent and self-conscious relativist. Therefore it must admit that, like the relativist, it itself is essentially a matter of desire. It wants to say what is right and wrong, true and false, and for others to agree. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.108) |
| 1598 | We prefer reason or poetry according to whether basics are intelligible or not [Roochnik] |
| Full Idea: Is the arché (basis) intelligible, or is it chaos? Upon this question hinges all, for answering it determines whether poetry or logos is the form of human speech that best does justice to the world. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.139) |
| 1584 | Modern science, by aiming for clarity about the external world, has abandoned rationality in the human world [Roochnik] |
| Full Idea: The modern scientific world view, with all its hope for clarity and precision, has a flipside, …which is its abandonment of rationality in the world of human significance. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.74) |
| 1591 | Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik] |
| Full Idea: Unfortunately for the logos there is no argument that can, without begging the question, establish the goodness of argumentation. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.106) |
| 1599 | Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik] |
| Full Idea: To debate about suspending all our presuppositions requires a common ground which, upon being established, immediately renders the debate superfluous. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.144) |
| 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. |
| 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 |
| 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. |
| 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 |
| 1605 | Reality can be viewed neutrally, or as an object of desire [Roochnik] |
| Full Idea: There are two extremes: the Aristotelian views reality simply as reality, and the sophist or poet views reality only as an object of desire. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.199) | |
| A reaction: Not sure about the second one. Does this express an actual desire, or just a hope? Could there be a mind for which its reality was only an aspiration? |
| 1577 | Relativism is a disease which destroys the possibility of rational debate [Roochnik] |
| Full Idea: Relativism is disease, is pollution, for it negates the efficacy of logos. It destroys the possibility of a complete rational debate of fundamental questions. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.41) |
| 1596 | Reasoning aims not at the understanding of objects, but at the desire to give beautiful speeches [Roochnik] |
| Full Idea: Logos originates not in a cognitive capacity for the apprehension of objects, but in the desire to give birth to beautiful speeches. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.124) | |
| A reaction: It is hard for us to grasp this, but it might be quite life-enhancing if we could return to that old way of thought. |
| 1578 | If relativism is the correct account of human values, then rhetoric is more important than reasoning [Roochnik] |
| Full Idea: If relativism offers an accurate description of human values, then rhetoric replaces logos as the most fundamental human activity. | |
| From: David Roochnik (The Tragedy of Reason [1990], p.47) | |
| A reaction: Or putting it another way, logos (reason) becomes meaningless. I suppose, though, that a relativist can conduct conditional reasoning (but must belief in some rules of reason). |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
| From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
| A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |