27 ideas
10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
Full Idea: The If-thenist view seems to apply straightforwardly only to the axiomatised portions of mathematics. | |
From: Alan Musgrave (Logicism Revisited [1977], §5) | |
A reaction: He cites Lakatos to show that cutting-edge mathematics is never axiomatised. One might reply that if the new mathematics is any good then it ought to be axiomatis-able (barring Gödelian problems). |
10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
Full Idea: If we identify logic with first-order logic, and mathematics with the collection of first-order theories, then maybe we can continue to maintain the If-thenist position. | |
From: Alan Musgrave (Logicism Revisited [1977], §5) | |
A reaction: The problem is that If-thenism must rely on rules of inference. That seems to mean that what is needed is Soundness, rather than Completeness. That is, inference by the rules must work properly. |
10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
Full Idea: Containing only logical notions is not a necessary condition for being a logical truth, since a logical truth such as 'all men are men' may contain non-logical notions such as 'men'. | |
From: Alan Musgrave (Logicism Revisited [1977], §3) | |
A reaction: [He attributes this point to Russell] Maybe it is only a logical truth in its general form, as ∀x(x=x). Of course not all 'banks' are banks. |
10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
Full Idea: The standard modern view of logical truth is that a statement is logically true if it comes out true in all interpretations in all (non-empty) domains. | |
From: Alan Musgrave (Logicism Revisited [1977], §3) |
10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
Full Idea: The axiom of Peano which states that no two numbers have the same successor requires the Axiom of Infinity for its proof. | |
From: Alan Musgrave (Logicism Revisited [1977], §4 n) | |
A reaction: [He refers to Russell 1919:131-2] The Axiom of Infinity is controversial and non-logical. |
10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
Full Idea: Formalism seems to exclude from consideration all creative, growing mathematics. | |
From: Alan Musgrave (Logicism Revisited [1977], §5) | |
A reaction: [He cites Lakatos in support] I am not immediately clear why spotting the remote implications of a formal system should be uncreative. The greatest chess players are considered to be highly creative and imaginative. |
10063 | Formalism is a bulwark of logical positivism [Musgrave] |
Full Idea: Formalism is a bulwark of logical positivist philosophy. | |
From: Alan Musgrave (Logicism Revisited [1977], §5) | |
A reaction: Presumably if you drain all the empirical content out of arithmetic and geometry, you are only left with the bare formal syntax, of symbols and rules. That seems to be as analytic as you can get. |
14193 | 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA] |
Full Idea: Some deep essentialists resist the need to explain the structure under de re modal properties, taking them as primitive. One version (which we can call 'substance theory') takes them to fall under a sortal concept, with no further explanation. | |
From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
A reaction: A very helpful identification of what Wiggins stands for, and why I disagree with him. The whole point of essences is to provide a notion that fits in with sciences, which means they must have an explanatory role, which needs structures. |
14195 | If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA] |
Full Idea: If the substance essentialist holds that the sort an object belongs to determines its de re modal properties (rather than the other way round), then he needs to give an (ontological, not conceptual) explanation of what determines an object's sort. | |
From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
A reaction: See Idea 14193 for 'substance essentialism'. I find it quite incredible that anyone could think that a thing's sort could determine its properties, rather than the other way round. Even if sortals are conventional, they are not arbitrary. |
14196 | Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA] |
Full Idea: The explanation of material constitution given by substance essentialism is that there are multiple objects. A person is essentially human-shaped (falling under the human sort), while their hunk of tissue is accidentally human-shaped (as tissue). | |
From: L.A. Paul (In Defense of Essentialism [2006], §1) | |
A reaction: At this point sortal essentialism begins to look crazy. Persons are dubious examples (with sneaky dualism involved). A bronze statue is essentially harder to dent than a clay one, because of its bronze. If you remake it of clay, it isn't the same statue. |
14198 | Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA] |
Full Idea: Absolutely unrestricted qualitative composition would imply that objects with incompatible properties and objects such as winged pigs or golden mountains were actual. | |
From: L.A. Paul (In Defense of Essentialism [2006], §5) | |
A reaction: Note that this is 'qualitative' composition, and not composition of parts. The objection seems to rule out unrestricted qualitative composition, since you could hardly combine squareness with roundness. |
14190 | Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA] |
Full Idea: Essentialism says that objects have their properties essentially. 'Deep' essentialists take the (nontrivial) essential properties of an object to determine its nature. 'Shallow' essentialists substitute context-dependent truths for the independent ones. | |
From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
A reaction: If the deep essence determines a things nature, we should not need to say 'nontrivial'. This is my bete noire, the confusion of essential properties with necessary ones, where necessary properties (or predicates, at least) can indeed be trivial. |
14191 | Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA] |
Full Idea: The deep essentialist holds that most objects have essential properties such that there are many ways they could not be, or many changes through which they could not persist. Objects' modal profiles characterize their natures. | |
From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
A reaction: This is the view I like, especially the last bit. If your modal profile doesn't determine your nature, then what does? Think of how you sum up a person at a funeral. Your modal profile is determined by dispositions and powers. |
14192 | Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA] |
Full Idea: Two objections to deep essentialism are that it falters when faced with a skeptical objection concerning arbitrariness, and the need for a reductive account of de re modality. | |
From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
A reaction: An immediate response to the second objection might be to say that modal facts about things are not reducible. The charge of arbitrariness (i.e. total arbitrariness, not just a bit of uncertainty) is the main thing a theory of essences must deal with. |
14197 | An object's modal properties don't determine its possibilities [Paul,LA] |
Full Idea: I reject the view that an object's de re modal properties determine its relations to possibilia. | |
From: L.A. Paul (In Defense of Essentialism [2006], §3) | |
A reaction: You'll have to read Paul to see why, but I flat disagree with her on this. The whole point of accepting such properties is to determine the modal profile of the thing, and hence see how it can fit into and behave in the world. |
14189 | 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA] |
Full Idea: A 'modal realist' believes that there are many concrete worlds, while the 'actualist' believes in only one concrete world, the actual world. The 'ersatzist' is an actualist who takes nonactual possible worlds and their contents to be abstracta. | |
From: L.A. Paul (In Defense of Essentialism [2006], Intro) | |
A reaction: My view is something like that modal realism is wrong, and actualism is right, and possible worlds (if they really are that useful) are convenient abstract fictions, constructed (if we have any sense) out of the real possibilities in the actual world. |
19682 | Internalists are much more interested in evidence than externalists are [McGrew] |
Full Idea: The notion of evidence generally plays a much more significant role in internalist epistemologies than it does in various forms of externalism. | |
From: Timothy McGrew (Evidence [2011], 'Prop..') | |
A reaction: I'm guessing that this is because evidence needs a certain amount of interpretation, whereas raw facts (which externalists seem to rely on) may never even enter a mind. |
19684 | Does spotting a new possibility count as evidence? [McGrew] |
Full Idea: Does the sudden realization of a heretofore unrecognized possibility count as evidence? | |
From: Timothy McGrew (Evidence [2011], 'Evid..') | |
A reaction: [Nice use of 'heretofore'! Why say 'previously' when you can keep these wonderful old English words alive?] This means that we can imagine new evidence ('maybe the murderer was a snake'!). Wrong. The evidence is what suggests the possibility. |
19687 | Absence of evidence proves nothing, and weird claims need special evidence [McGrew] |
Full Idea: Two well know slogans (popularised by Carl Sagan) are 'absence of evidence is not evidence of absence', ...and 'extraordinary claims require extraordinary evidence'. | |
From: Timothy McGrew (Evidence [2011], 'Absence') | |
A reaction: [Sagan was a popular science writer and broadcaster] The second one is something like Hume's argument against miracles. The old problem of the 'missing link' for human evolution embodied the first idea. |
19688 | Every event is highly unlikely (in detail), but may be perfectly plausible [McGrew] |
Full Idea: At a certain level of detail, almost any claim is unprecedented. How likely is 'Matilda won at Scrabble on Thursday with a score of 438 while drinking mint tea'? But there is nothing particularly unbelievable about the claim. | |
From: Timothy McGrew (Evidence [2011], 'Extraordinary') | |
A reaction: A striking idea, which rules out the simplistic idea that we can just assess evidence by its isolated likelihood. Context is crucial. How good is 438? What if she smoked opium? What if there is no Scrabble set on her island? |
19686 | Criminal law needs two separate witnesses, but historians will accept one witness [McGrew] |
Full Idea: An ancient rule in law is that a criminal conviction needs evidence of two independent witnesses, but in history it is assumed that a document deserves the benefit of the doubt if it cannot be independently verified. | |
From: Timothy McGrew (Evidence [2011], 'Interp..') | |
A reaction: [compressed; McGrew's full account qualifies it a bit] A nice observation. One might even be suspicious of the two 'independent' witnesses, if there were lots of other reasons to doubt someon's guilt. A single weird document is also dubious. |
19680 | Maybe all evidence consists of beliefs, rather than of facts [McGrew] |
Full Idea: Some philosophers have been attracted to the view that, strictly speaking, what counts as evidence is not a set of physical objects or even experiences, but rather a set of believed propositions. | |
From: Timothy McGrew (Evidence [2011], 'Prop..') | |
A reaction: This may be right. However, as always, I think animals are a key test. Do animals respond to evidence? Even if they did, they might need to 'make sense' of what they experienced, and even formulate a non-linguistic proposition. |
19681 | If all evidence is propositional, what is the evidence for the proposition? Do we face a regress? [McGrew] |
Full Idea: Taking evidence as propositional may trade one problem for another. If the bloodstain isn't evidence, but 'this is a bloodstain' is evidence, then what serves as evidence for the belief about the bloodstain? Is there an infinite regress? | |
From: Timothy McGrew (Evidence [2011], 'Prop..') | |
A reaction: [compressed] I quite like evidence being propositional, but then find this. I'll retreat to my beloved coherence. I do not endorse Sellars's 'only a belief can justify a belief', because raw experience has to be part of what is coherent. |
19689 | Several unreliable witnesses can give good support, if they all say the same thing [McGrew] |
Full Idea: The testimony of a number of independent witnesses, none of them particularly reliable, who give substantially the same account of some event, may provide a strong argument in its favor. | |
From: Timothy McGrew (Evidence [2011], 'Testimonial') | |
A reaction: A striking point. It obviously works well for panicking people in a crowd during an incident. Does it also apply to independent scientists who are known to cheat? They may not collaborate, but may all want the same result. |
19683 | Narrow evidentialism relies wholly on propositions; the wider form includes other items [McGrew] |
Full Idea: Evidentialism comes in both narrow and wide forms depending on whether evidence is taken to consist only of propositions or of a wider range of items. | |
From: Timothy McGrew (Evidence [2011], 'Evid..') | |
A reaction: [He cites Conee and Feldman for the wide view, which is not restricted to beliefs] You can hardly rely on occurrent beliefs as evidence, so we often have good knowledge with forgotten justification. But such knowledge has been 'weakened'. |
19685 | Falsificationism would be naive if even a slight discrepancy in evidence killed a theory [McGrew] |
Full Idea: Data do not quite speak for themselves, which speaks against a naive form of falsificationism according to which even the slightest mismatch between theory and evidence suffices to overturn a theory. | |
From: Timothy McGrew (Evidence [2011], 'Interp..') | |
A reaction: [He cites Robert Boyle wisely ignoring some data to get a good fit for his graph] |
10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
Full Idea: Logical positivists did not adopt old-style logicism, but rather logicism spiced with varying doses of If-thenism. | |
From: Alan Musgrave (Logicism Revisited [1977], §4) | |
A reaction: This refers to their account of mathematics as a set of purely logical truths, rather than being either empirical, or a priori synthetic. |