12 ideas
| 8956 | What is a singleton set, if a set is meant to be a collection of objects? [Szabó] |
| Full Idea: The relationship between an object and its singleton is puzzling. Our intuitive conception of a set is a collection of objects - what are we to make of a collection of a single object? | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 4.1) | |
| A reaction: The ontological problem seems to be the same as that of the empty set, and indeed the claim that a pair of entities is three things. For logicians the empty set is as real as a pet dog, but not for me. |
| 8953 | Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things [Szabó] |
| Full Idea: It is better not to include in the definition of abstract entities that they ontologically depend on their concrete correlates. Note: ..but they may depend on the totality of concreta; maybe 'the supervenience of the abstract' is part of ordinary thought. | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 2.2) | |
| A reaction: [the quoted phrase is from Gideon Rosen] It certainly seems unlikely that the concept of the perfect hexagon depends on a perfect hexagon having existed. Human minds have intervened between the concrete and the abstract. |
| 19544 | Closure says if you know P, and also know P implies Q, then you must know Q [Dretske] |
| Full Idea: Closure is the epistemological principle that if S knows that P is true and knows that P implies Q, then, evidentially speaking, this is enough for S to know that Q is true. Nothing more is needed. | |
| From: Fred Dretske (The Case against Closure (and reply) [2005], p.25) | |
| A reaction: [Dretske was the first to raise this issue] It is 'closure' because it applies to every case of Q, which is every implication of P that is known. The issue is whether we really do know all such Qs. Dretske doubts it. See his zebra case. |
| 19545 | We needn't regret the implications of our regrets; regretting drinking too much implies the past is real [Dretske] |
| Full Idea: One doesn't have to regret everything one knows to be implied by what one regrets. Tom regrets drinking three martinis, but doesn't regret what he knows to be implied by this - that he drank 'something', or that the past is real. | |
| From: Fred Dretske (The Case against Closure (and reply) [2005], p.28) | |
| A reaction: A nice case of analogy! He's right about regret. Perceptual and inferential knowledge have different grounds. To deny inferential knowledge seems to be a denial that modus ponens can be a justification. But MP gives truth, not knowledge. |
| 19547 | Reasons for believing P may not transmit to its implication, Q [Dretske] |
| Full Idea: Some reasons for believing P do not transmit to things, Q, known to be implied by P. | |
| From: Fred Dretske (The Case against Closure (and reply) [2005], p.29) | |
| A reaction: That seems true enough. I see someone limping, but infer that their leg is damaged. The only question is whether I should accept the inference. How can I accept that inference, but then back out of that knowledge? |
| 19546 | Knowing by visual perception is not the same as knowing by implication [Dretske] |
| Full Idea: A way of knowing there are cookies in the jar - visual perception - is not a way of knowing what one knows to be implied by this - that visual appearances are not misleading. | |
| From: Fred Dretske (The Case against Closure (and reply) [2005], p.29) | |
| A reaction: Why is the 'way of knowing' relevant? Isn't the only question that of whether implication of a truth is in infallible route to a truth (modus ponens)? If you know THAT it is true, then you must believe it, and implication is top quality justification. No? |
| 19548 | The only way to preserve our homely truths is to abandon closure [Dretske] |
| Full Idea: The only way to preserve knowledge of homely truths, the truths everyone takes themselves to know, is to abandon closure. | |
| From: Fred Dretske (The Case against Closure (and reply) [2005], p.32) | |
| A reaction: His point is that knowledge of homely truths seems to imply knowledge of the background facts needed to support them, which he takes to be an unreasonable requirement. I recommend pursuing contextualism, rather than abandoning closure. |
| 19549 | P may imply Q, but evidence for P doesn't imply evidence for Q, so closure fails [Dretske] |
| Full Idea: The evidence that gives me knowledge of P (there are cookies in the jar) can exist without evidence for knowing Q (they are not fake), despite my knowing that P implies Q. So closure fails. | |
| From: Fred Dretske (The Case against Closure (and reply) [2005], p.33) | |
| A reaction: His more famous example is the zebra. How can P imply Q if there is no evidence for Q? Maybe 'there are cookies in the jar' does not entail they are not fake, once you disambiguate what is being said? |
| 19550 | We know past events by memory, but we don't know the past is real (an implication) by memory [Dretske] |
| Full Idea: The reality of the past (a 'heavyweight implication') ...is something we know to be implied by things we remember, but it is not itself something we remember. | |
| From: Fred Dretske (The Case against Closure (and reply) [2005], p.35) | |
| A reaction: If I begin to doubt that the past is real, then I must necessarily begin to doubt my ordinary memories. This seems to be the modus tollens of knowledge closure. Doesn't that imply that the modus ponens was valid, and closure is correct? |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |
| 8954 | Geometrical circles cannot identify a circular paint patch, presumably because they lack something [Szabó] |
| Full Idea: The vocabulary of geometry is sufficient to identify the circle, but could not be used to identify any circular paint patch. The reason must be that the circle lacks certain properties that can distinguish paint patches from one another. | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 2.2) | |
| A reaction: I take this to be support for the traditional view, that abstractions are created by omitting some of the properties of physical objects. I take them to be fictional creations, reified by language, and not actual hidden entities that have been observed. |
| 8955 | Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others) [Szabó] |
| Full Idea: In current discussions, abstract entities are usually distinguished as 1) in principle imperceptible, 2) incapable of causal interaction, 3) not located in space-time. The first is often explained by the second, which is in turn explained by the third. | |
| From: Zoltán Gendler Szabó (Nominalism [2003], 2.2) | |
| A reaction: Szabó concludes by offering 3 as the sole criterion of abstraction. As Lewis points out, the Way of Negation for defining abstracta doesn't tell us very much. Courage may be non-spatiotemporal, but what about Alexander the Great's courage? |