17 ideas
| 14600 | Analysis aims at secure necessary and sufficient conditions [Schaffer,J] |
| Full Idea: An analysis is an attempt at providing finite, non-circular, and intuitively adequate necessary and sufficient conditions. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], 3) | |
| A reaction: Specifying the 'conditions' for something doesn't seem to quite add up to telling you what the thing is. A trivial side-effect might qualify as a sufficient condition for something, if it always happens. |
| 14603 | 'Reification' occurs if we mistake a concept for a thing [Schaffer,J] |
| Full Idea: 'Reification' occurs when a mere concept is mistaken for a thing. We seem generally prone to this sort of error. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], 3.1) | |
| A reaction: Personally I think we should face up to the fact that this is the only way we can think about generalised or abstract entities, and stop thinking of it as an 'error'. We have evolved to think well about objects, so we translate everything that way. |
| 14607 | T adds □p→p for reflexivity, and is ideal for modeling lawhood [Schaffer,J] |
| Full Idea: System T is a normal modal system augmented with the reflexivity-generating axiom □p→p, and is, I think, the best modal logic for modeling lawhood. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], n46) | |
| A reaction: Schaffer shows in the article why transitivity would not be appropriate for lawhood. |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
| From: George Boolos (On Second-Order Logic [1975], p.45) | |
| A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
| A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
| From: George Boolos (On Second-Order Logic [1975], p.44) | |
| A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
| From: George Boolos (On Second-Order Logic [1975], p.46) | |
| A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
| From: George Boolos (On Second-Order Logic [1975], p.52) | |
| A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity. | |
| From: George Boolos (On Second-Order Logic [1975], p.48) |
| 14604 | If a notion is ontologically basic, it should be needed in our best attempt at science [Schaffer,J] |
| Full Idea: Science represents our best systematic understanding of the world, and if a certain notion proves unneeded in our best attempt at that, this provides strong evidence that what this notion concerns is not ontologically basic. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], 3.2) | |
| A reaction: But is the objective of science to find out what is 'ontologically basic'? If scientists can't get a purchase on a question, they have no interest in it. What are electrons made of? |
| 14599 | Three types of reduction: Theoretical (of terms), Definitional (of concepts), Ontological (of reality) [Schaffer,J] |
| Full Idea: Theoretical reduction concerns terms found in a theory; Definitional reduction concerns concepts found in the mind; Ontological reduction is independent of how we conceptualize entities, or theorize about them, and is about reality. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], 1) | |
| A reaction: An Aristotelian definition refers to reality, rather than to our words or concepts. |
| 14605 | Tropes are the same as events [Schaffer,J] |
| Full Idea: Tropes can be identified with events. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], n17) | |
| A reaction: This is presumably on the view of events, associated with Kim, as instantiations of properties. This idea is a new angle on tropes and events which had never occurred to me. |
| 14601 | Individuation aims to count entities, by saying when there is one [Schaffer,J] |
| Full Idea: Individuation principles are attempts to describe how to count entities in a given domain, by saying when there is one. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], 3) | |
| A reaction: At last, someone tells me what they mean by 'individuation'! So it is just saying what your units are prior to counting, followed (presumably) by successful counting. It seems to aim more at kinds than at particulars. |
| 14606 | Only ideal conceivability could indicate what is possible [Schaffer,J] |
| Full Idea: The only plausible link from conceivability to possibility is via ideal conceivability. | |
| From: Jonathan Schaffer (Causation and Laws of Nature [2008], n22) | |
| A reaction: [He cites Chalmers 2002] I'm not sure what 'via' could mean here. Since I don't know any other way than attempted conceivability for assessing a possibility, I am a bit baffled by this idea. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |