16 ideas
| 12766 | Logical space is abstracted from the actual world [Stalnaker] |
| Full Idea: Logical space is not given independently of the individuals that occupy it, but is abstracted from the world as we find it. | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.85) | |
| A reaction: I very much like the second half of this idea, and am delighted to find Stalnaker endorsing it. I take the logical connectives to be descriptions of how things behave, at a high level of generality. |
| 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. |
| 12764 | For the bare particular view, properties must be features, not just groups of objects [Stalnaker] |
| Full Idea: If we are to make sense of the bare particular theory, a property must be not just a rule for grouping individuals, but a feature of individuals in virtue of which they may be grouped. | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.76) | |
| A reaction: He is offering an objection to the thoroughly extensional account of properties that is found in standard possible worlds semantics. Quite right too. We can't give up on the common sense notion of a property. |
| 12761 | An essential property is one had in all the possible worlds where a thing exists [Stalnaker] |
| Full Idea: If necessity is explained in terms of possible worlds, ...then an essential property is a property that a thing has in all possible worlds in which it exists. | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.71) | |
| A reaction: This seems to me to be a quite shocking confusion of necessary properties with essential properties. The point is that utterly trivial properties can be necessary, but in no way part of the real essence of something. |
| 12763 | Necessarily self-identical, or being what it is, or its world-indexed properties, aren't essential [Stalnaker] |
| Full Idea: We can remain anti-essentialist while allowing some necessary properties: those essential to everything (self-identity), relational properties (being what it is), and world-indexed properties (being snub-nosed-only-in-Kronos). | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.73) | |
| A reaction: [a summary] He defined essential properties as necessary properties (Idea 12761), and now backpeddles. World-indexed properties are an invention of Plantinga, as essential properties to don't limit individuals. But they are necessary, not essential! |
| 12762 | Bare particular anti-essentialism makes no sense within modal logic semantics [Stalnaker] |
| Full Idea: I argue that one cannot make semantical sense out of bare particular anti-essentialism within the framework of standard semantics for modal logic. | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.71) | |
| A reaction: Stalnaker characterises the bare particular view as ANTI-essentialist, because he has defined essence in terms of necessary properties. The bare particular seems to allow the possibility of Aristotle being a poached egg. |
| 12765 | Why imagine that Babe Ruth might be a billiard ball; nothing useful could be said about the ball [Stalnaker] |
| Full Idea: I cannot think of any point in making the counterfactual supposition that Babe Ruth is a billiard ball; there is nothing I can say about him in that imagined state that I could not just as well say about billiard balls that are not him. | |
| From: Robert C. Stalnaker (Anti-essentialism [1979], p.79) | |
| A reaction: A bizarrely circumspect semanticists way of saying that Ruth couldn't possibly be a billiard ball! Would he say the same about a group of old men in wheelchairs, one of whom IS Babe Ruth? |
| 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. |
| 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. |