19 ideas
18901 | Truthmakers are facts 'of' a domain, not something 'in' the domain [Sommers] |
Full Idea: A fact is an existential characteristic 'of' the domain; it is not something 'in' the domain. To search for truth-making facts in the world is indeed futile. | |
From: Fred Sommers (Intellectual Autobiography [2005], 'Existence') | |
A reaction: Attacking Austin on truth. Helpful. It is hard to see how a physical object has a mysterious power to 'make' a truth. No energy-transfer seems involved in the making. Animals think true thoughts; I suspect that concerns their mental maps of the world. |
18904 | 'Predicable' terms come in charged pairs, with one the negation of the other [Sommers, by Engelbretsen] |
Full Idea: Sommers took the 'predicable' terms of any language to come in logically charged pairs. Examples might be red/nonred, massive/massless, tied/untied, in the house/not in the house. The idea that terms can be negated was essential for such pairing. | |
From: report of Fred Sommers (Intellectual Autobiography [2005]) by George Engelbretsen - Trees, Terms and Truth 2 | |
A reaction: If, as Rumfitt says, we learn affirmation and negation as a single linguistic operation, this would fit well with it, though Rumfitt doubtless (as a fan of classical logic) prefers to negation sentences. |
18895 | Logic which maps ordinary reasoning must be transparent, and free of variables [Sommers] |
Full Idea: What would a 'laws of thought' logic that cast light on natural language deductive thinking be like? Such a logic must be variable-free, conforming to normal syntax, and its modes of reasoning must be transparent, to make them virtually instantaneous. | |
From: Fred Sommers (Intellectual Autobiography [2005], 'How We') | |
A reaction: This is the main motivation for Fred Sommers's creation of modern term logic. Even if you are up to your neck in modern symbolic logic (which I'm not), you have to find this idea appealing. You can't leave it to the psychologists. |
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. |
18897 | Predicate logic has to spell out that its identity relation '=' is an equivalent relation [Sommers] |
Full Idea: Because predicate logic contrues identities dyadically, its account of inferences involving identity propositions needs laws or axioms of identity, explicitly asserting that the dyadic realtion in 'x=y' possesses symmetry, reflexivity and transitivity. | |
From: Fred Sommers (Intellectual Autobiography [2005], 'Syllogistic') |
18893 | Translating into quantificational idiom offers no clues as to how ordinary thinkers reason [Sommers] |
Full Idea: Modern predicate logic's methods of justification, which involve translation into an artificial quantificational idiom, offer no clues to how the average person, knowing no logic and adhering to the vernacular, is so logically adept. | |
From: Fred Sommers (Intellectual Autobiography [2005], Intro) | |
A reaction: Of course, people are very logically adept when the argument is simple (because, I guess, they can test it against the world), but not at all good when the reasoning becomes more complex. We do, though, reason in ordinary natural language. |
18903 | Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen] |
Full Idea: If there is one idea that is the keystone of the edifice that constitutes Sommers's united philosophy it is that terms are the linguistic entities subject to negation in the most basic sense. It is a very old idea, tending to be rejected in modern times. | |
From: report of Fred Sommers (Intellectual Autobiography [2005]) by George Engelbretsen - Trees, Terms and Truth 2 | |
A reaction: Negation in modern logic is an operator applied to sentences, typically writing '¬Fa', which denies that F is predicated of a, with Fa being an atomic sentence. Do we say 'not(Stan is happy)', or 'not-Stan is happy', or 'Stan is not-happy'? Third one? |
18894 | Predicates form a hierarchy, from the most general, down to names at the bottom [Sommers] |
Full Idea: We organise our concepts of predicability on a hierarchical tree. At the top are terms like 'interesting', 'exists', 'talked about', which are predicable of anything. At the bottom are names, and in between are predicables of some things and not others. | |
From: Fred Sommers (Intellectual Autobiography [2005], 'Category') | |
A reaction: The heirarchy seem be arranged simply by the scope of the predicate. 'Tallest' is predicable of anything in principle, but only of a few things in practice. Is 'John Doe' a name? What is 'cosmic' predicable of? Challenging! |
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. |
18900 | Unfortunately for realists, modern logic cannot say that some fact exists [Sommers] |
Full Idea: Unfortunately for the fate of realist philosophy, modern logic's treatment of 'exists' is resolutely inhospitable to facts as referents of phrases of the form 'the existence or non-existence of φ'. | |
From: Fred Sommers (Intellectual Autobiography [2005], 'Realism') | |
A reaction: Predicate logic has to talk about objects, and then attribute predicates to them. It tends to treat a fact as 'Fa' - this object has this predicate, but that's not really how we understand facts. |
13127 | Categories can't overlap; they are either disjoint, or inclusive [Sommers, by Westerhoff] |
Full Idea: Fred Sommers, in his treatment of types, says that two ontological categories cannot overlap; they are either disjoint, or one properly includes the other. This is sometimes referred to as Sommers' Law. | |
From: report of Fred Sommers (Types and Ontology [1963], p.355) by Jan Westerhoff - Ontological Categories §24 | |
A reaction: The 'types', of course, go back to Bertrand Russell's theory of types, which is important in discussions of ontological categories. Carnap pursued it, trying to derive ontological categories from grammatical categories. 85% agree with Sommers. |
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. |
18898 | In standard logic, names are the only way to refer [Sommers] |
Full Idea: In modern predicate logic, definite reference by proper names is the primary and sole form of reference. | |
From: Fred Sommers (Intellectual Autobiography [2005], 'Reference') | |
A reaction: Hence we have to translate definite descriptions into (logical) names, or else paraphrase them out of existence. The domain only contains 'objects', so only names can uniquely pick them out. |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |