| 21267 | Supposing many principles is superfluous if a few will do it [Aquinas] |
| Full Idea: It is superfluous to suppose that what can be accounted for by a few principles has been produced by many. | |
| From: Thomas Aquinas (Summa Theologicae [1265], Ia,Q02,Art3,Ob2) | |
| A reaction: Notice that this is 'superfluous' rather than 'wrong'. But ten people can lift a piano which could have been lifted by eight. Note that this is 150 years before Ockham. |
| 16676 | Why use more things when fewer will do? [William of Ockham] |
| Full Idea: It is pointless to do through more things something that can be done through fewer. | |
| From: William of Ockham (Tractatus de corpore Christi [1323], Ch. 29), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 14.3 | |
| A reaction: The more famous formulation isn't found in his works, so I'm delighted to find an authentic quotation from the man. |
| 6806 | Do not multiply entities beyond necessity [William of Ockham] |
| Full Idea: Do not multiply entities beyond necessity. | |
| From: William of Ockham (works [1335]) | |
| A reaction: This is the classic statement of Ockham's Razor, though it is not found in his printed works. It appears to be mainly aimed at Plato's Theory of Forms. It is taken to refer to types of entities, not numbers. One seraph is as bad as a hundred. |
| 19342 | Reason avoids multiplying hypotheses or principles [Leibniz] |
| Full Idea: Reason requires that we avoid multiplying hypotheses or principles, in somewhat the same way that the simplest system is always preferred in astronomy. | |
| From: Gottfried Leibniz (Discourse on Metaphysics [1686], 5) | |
| A reaction: He offers this principle without mentioning Ockham, as if it were self-evident. |
| 4541 | Everything simple is merely imaginary [Nietzsche] |
| Full Idea: Everything simple is merely imaginary. | |
| From: Friedrich Nietzsche (The Will to Power (notebooks) [1888], §536) | |
| A reaction: A wonderful aphorism. This is one's worst fear, which is why it is suggested that ontological O's R is bad, though epistemological O's R ('be cautious') is fine. I have to admit that I have no idea whether reality is simple. |
| 22644 | Our greatest pleasure is the economy of reducing chaotic facts to one single fact [James] |
| Full Idea: Our pleasure at finding that a chaos of facts is the expression of single underlying fact is like a musician's relief at discovering harmony. …The passion for economy of means in thought is the philosophic passion par excellence. | |
| From: William James (The Sentiment of Rationality [1882], p.21) | |
| A reaction: We do, though, possess an inner klaxon warning against stupid simplistic reductions. Reducing all the miseries of life to the workings of the Devil is not satisfactory, even it it is economical. Simplicities are dangerously tempting. |
| 6106 | Reducing entities and premisses makes error less likely [Russell] |
| Full Idea: You diminish the risk of error with every diminution of entities and premisses. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §VIII) | |
| A reaction: If there are actually lots of entities, you would increase error if you reduced them too much. Ockham's Razor seems more to do with the limited capacity of the human mind than with the simplicity or complexity of reality. See Idea 4456. |
| 2939 | If a sign is useless it is meaningless; that is the point of Ockham's maxim [Wittgenstein] |
| Full Idea: If a sign is useless it is meaningless. That is the point of Occam's maxim. | |
| From: Ludwig Wittgenstein (Tractatus Logico-Philosophicus [1921], 3.328) |
| 22431 | Good algorithms and theories need many occurrences of just a few elements [Quine] |
| Full Idea: The power and simplicity of an algorithm, or indeed of any theory, depend on there being many occurrences of few elements rather than few occurrences of many. | |
| From: Willard Quine (Mr Strawson on Logical Theory [1953], III) | |
| A reaction: Not sure how this applies to a software function. One which produces a good result from a large number of input variables sounds particularly impressive to me. Many occurrences of a single variable sounds rather inefficient. |
| 8207 | The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine] |
| Full Idea: It is the quest for system and simplicity that has kept driving the scientist to posit further entities as values of his variables. By positing molecules, Boyles' law of gases could be assimilated into a general theory of bodies in motion. | |
| From: Willard Quine (On Multiplying Entities [1974], p.262) | |
| A reaction: Interesting that a desire for simplicity might lead to multiplications of entities. In fact, I presume molecules had been proposed elsewhere in science, and were adopted in gas-theory because they were thought to exist, not because simplicity is nice. |
| 8208 | In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine] |
| Full Idea: In classical arithmetic, ratios were posited to make division generally applicable, negative numbers to make subtraction generally applicable, and irrationals and finally imaginaries to make exponentiation generally applicable. | |
| From: Willard Quine (On Multiplying Entities [1974], p.263) | |
| A reaction: This is part of Quine's proposal (c.f. Idea 8207) that entities have to be multiplied in order to produce simplicity. He is speculating. Maybe they are proposed because they are just obvious, and the generality is a nice side-effect. |
| 4036 | What matters is not how many entities we postulate, but how many kinds of entities [Armstrong, by Mellor/Oliver] |
| Full Idea: Armstrong argues that what matters is not how few entities we postulate (quantitative economy), but how few kinds of entities (qualitative economy). | |
| From: report of David M. Armstrong (Properties [1992]) by DH Mellor / A Oliver - Introduction to 'Properties' §9 | |
| A reaction: Is this what Ockham meant? Armstrong is claiming that the notion of a 'property' is needed to identify kinds. See also Idea 7038. |
| 3426 | If one theory is reduced to another, we make fewer independent assumptions about the world [Kim] |
| Full Idea: If we reduce one theory to another, we reduce the number of independent assumptions about the world. | |
| From: Jaegwon Kim (Philosophy of Mind [1996], p.215) |
| 21021 | Keep premises as weak as possible, to avoid controversial difficulties [Nussbaum] |
| Full Idea: One should always choose the weakest premises from which one's conclusion follows, rather than saddling the theory with thicker or more controversial premises. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 8) | |
| A reaction: I like this because it connects the rather vague Ockham's Razor to the logical concept of Thinning. The key point is that a thinner set of premises that prove something will be more persuasive, because critics may reject premises instead of conclusion. |
| 15784 | The Razor seems irrelevant for Meinongians, who allow absolutely everything to exist [Lycan] |
| Full Idea: A Meinongian has already posited everything that could, or even could not, be; how, then, can any subsequent brandishing of Ockham's Razor be to the point? | |
| From: William Lycan (The Trouble with Possible Worlds [1979], 02) | |
| A reaction: See the ideas of Alexius Meinong. Presumably these crazy Meinongians must make some distinction between what actually exists in front of your nose, and the rest. So the Razor can use that distinction too. |
| 15787 | Maybe Ockham's Razor is a purely aesthetic principle [Lycan] |
| Full Idea: It might be said that Ockham's Razor is a purely aesthetic principle. | |
| From: William Lycan (The Trouble with Possible Worlds [1979], 02) | |
| A reaction: I don't buy this, if it meant to be dismissive of the relevance of the principle to truth. A deep question might be, what is so aesthetically attractive about simplicity? I'm inclined to think that application of the Razor has delivered terrific results. |
| 10471 | Ockham's Razor has more content if it says believe only in what is causal [Oliver] |
| Full Idea: One might give Ockham's Razor a bit more content by advising belief in only those entities which are causally efficacious. | |
| From: Alex Oliver (The Metaphysics of Properties [1996], §03) | |
| A reaction: He cites Armstrong as taking this line, but I immediately think of Shoemaker's account of properties. It seems to me to be the only account which will separate properties from predicates, and bring them under common sense control. |
| 7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
| Full Idea: A commitment to parsimony is not a commitment to a conception of the world as simple. The idea, rather, is that we should not complicate our theories about the world unnecessarily. | |
| From: John Heil (From an Ontological Point of View [2003], 13.6) | |
| A reaction: In other words, Ockham's Razor is about us, not about the world. It would be absurd to make the a priori assumption that the world has to be simple. Are we, though, creating bad theories by insisting that they should be simple? |
| 7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
| Full Idea: It could well turn out that a simpler theory - a theory with fewer fundamental principles - posits more entities than a more complex competitor. | |
| From: John Heil (From an Ontological Point of View [2003], 13.6) | |
| A reaction: See also Idea 4036. The point here is that you can't simply translate Ockham as 'keep it simple', as there are different types of simplicity. The best theory will negotiate a balance between entities and principles. |
| 8964 | Entities can be multiplied either by excessive categories, or excessive entities within a category [Hoffman/Rosenkrantz] |
| Full Idea: There are two ways that entities can be multiplied unnecessarily: by multiplying the number of explanatory categories, and by multiplying the number of entities within a category. | |
| From: J Hoffman/G Rosenkrantz (Platonistic Theories of Universals [2003], 4) | |
| A reaction: An important distinction. The orthodox view is that it is the excess of categories that is to be avoided (e.g. by nominalists). Possible worlds in metaphysics, and multiple worlds in physics, claim not to violate the first case. |
| 4037 | Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver] |
| Full Idea: Ockham's Razor is the principle that we need reasons to believe in entities. | |
| From: DH Mellor / A Oliver (Introduction to 'Properties' [1997], §9) | |
| A reaction: This presumably follows from an assumption that all beliefs need reasons, but is that the case? The Principle of Sufficient Reason precedes Ockham's Razor. |
| 4217 | It is more extravagant, in general, to revise one's logic than to augment one's ontology [Lowe] |
| Full Idea: It is more extravagant, in general, to revise one's logic than to augment one's ontology. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.219) | |
| A reaction: Meaning there are stronger principles of thought which can trump Ockham's Razor. A few more entities won't hurt. Sound right. |
| 4456 | Epistemological Ockham's Razor demands good reasons, but the ontological version says reality is simple [Moreland] |
| Full Idea: Ockham's Razor has an epistemological version, which says we should not multiply existences or explanations without adequate reason, and an ontological version, which says reality is simple, and so a simpler ontology represents it more accurately. | |
| From: J.P. Moreland (Universals [2001], Ch.2) | |
| A reaction: A nice distinction. Is it reality which is simple, or us? One shouldn't write off the ontological version. If one explanation is simpler than the others, there may be a reason in nature for that. |
| 16244 | If the universe is profligate, the Razor leads us astray [Maudlin] |
| Full Idea: If the universe has been profligate, then Ockham's Razor will lead us astray. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: That is, there may be a vast number of entities which exist beyond what seems to be 'necessary'. |
| 16255 | The Razor rightly prefers one cause of multiple events to coincidences of causes [Maudlin] |
| Full Idea: The Razor is good when it councils higher credence to explanations which posit a single cause to multiple events that occur in a striking pattern, over explanations involving coincidental multiple causes. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: This is in the context of Maudlin warning against embracing the Razor too strongly. Presumably inductive success suggests that the world supports this particular use of the Razor. |
| 13743 | We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J] |
| Full Idea: Occam's Razor should only be understood to concern substances: do not multiply basic entities without necessity. There is no problem with the multiplication of derivative entities - they are an 'ontological free lunch'. | |
| From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
| A reaction: The phrase 'ontological free lunch' comes from Armstrong. This is probably what Occam meant. A few extra specks of dust, or even a few more numbers (thank you, Cantor!) don't seem to challenge the principle. |
| 16677 | Anti-Razor: if you can't account for a truth, keep positing things until you can [Pasnau] |
| Full Idea: The Anti-Razor says 'whenever an affirmative proposition is truly stated, if one thing does not suffice to account for its truth, then one must posit things, and if two do not suffice then three, and so on to infinity'. | |
| From: Robert Pasnau (Metaphysical Themes 1274-1671 [2011], 14.3) | |
| A reaction: This is quoted from an anonymous logic text of 1325. Apparently Ockham himself articulated the idea more than once. |