21 ideas
| 2546 | Philosophy is a magnificent failure in its attempt to overstep the limits of our knowledge [McGinn] |
| Full Idea: Philosophy marks the limits of human theoretical intelligence. Philosophy is an attempt to overstep our cognitive bounds, a kind of magnificent failure. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.209) | |
| A reaction: No one attempts to overstep boundaries once they are confirmed as such. The magnificent attempts persist because failure is impossible to demonstrate (except, perhaps, by Gödel's Theorem). |
| 17962 | The truth-maker principle is that every truth has a sufficient truth-maker [Forrest] |
| Full Idea: Item x is said to be a sufficient truth-maker for truth-bearer p just in case necessarily if x exists then p is true. ...Every truth has a sufficient truth-maker. Hence, I take it, the sum of all sufficient truth-makers is a universal truth-maker. | |
| From: Peter Forrest (General Facts,Phys Necessity, and Metaph of Time [2006], 1) | |
| A reaction: Note that it is not 'necessary', because something else might make p true instead. |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| Full Idea: The axiom of choice has a troubled history, but is now standard in mathematics. It could be replaced with a principle of comprehension for functions), or one could omit the variables ranging over functions. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], n 3) |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| Full Idea: Early study of first-order logic revealed a number of important features. Gödel showed that there is a complete, sound and effective deductive system. It follows that it is Compact, and there are also the downward and upward Löwenheim-Skolem Theorems. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| Full Idea: Some authors argue that second-order logic (with standard semantics) is not logic at all, but is a rather obscure form of mathematics. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| Full Idea: If the goal of logical study is to present a canon of inference, a calculus which codifies correct inference patterns, then second-order logic is a non-starter. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: This seems to be because it is not 'complete'. However, moves like plural quantification seem aimed at capturing ordinary language inferences, so the difficulty is only that there isn't a precise 'calculus'. |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| Full Idea: Informally, logical consequence is sometimes defined in terms of the meanings of a certain collection of terms, the so-called 'logical terminology'. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: This seems to be a compositional account, where we build a full account from an account of the atomic bits, perhaps presented as truth-tables. |
| 2544 | Thoughts have a dual aspect: as they seem to introspection, and their underlying logical reality [McGinn] |
| Full Idea: Our thoughts have a kind of duality, corresponding to their surface appearance to introspection and their underlying logical reality. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.147) |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| Full Idea: Second-order variables can range over properties, sets, or relations on the items in the domain-of-discourse, or over functions from the domain itself. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| Full Idea: Upward Löwenheim-Skolem: if a set of first-order formulas is satisfied by a domain of at least the natural numbers, then it is satisfied by a model of at least some infinite cardinal. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| Full Idea: Both of the Löwenheim-Skolem Theorems fail for second-order languages with a standard semantics | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.3.2) |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| Full Idea: The Löwenheim-Skolem theorem is usually taken as a sort of defect (often thought to be inevitable) of the first-order logic. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: [He is quoting Wang 1974 p.154] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| Full Idea: Downward Löwenheim-Skolem: a finite or denumerable set of first-order formulas that is satisfied by a model whose domain is infinite is satisfied in a model whose domain is the natural numbers | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| Full Idea: Full second-order logic has all the expressive power needed to do mathematics, but has an unworkable model theory. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) | |
| A reaction: [he credits Cowles for this remark] Having an unworkable model theory sounds pretty serious to me, as I'm not inclined to be interested in languages which don't produce models of some sort. Surely models are the whole point? |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| Full Idea: In studying second-order logic one can think of relations and functions as extensional or intensional, or one can leave it open. Little turns on this here, and so words like 'property', 'class', and 'set' are used interchangeably. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.2.1) | |
| A reaction: Important. Students of the metaphysics of properties, who arrive with limited experience of logic, are bewildered by this attitude. Note that the metaphysics is left wide open, so never let logicians hijack the metaphysical problem of properties. |
| 2539 | Mental modules for language, social, action, theory, space, emotion [McGinn] |
| Full Idea: The prevailing view in cognitive psychology is that the mind consists of separate faculties, each with a certain cognitive task: linguistic, social, practical, theoretical, abstract, spatial and emotional. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.40) | |
| A reaction: 'Faculties' are not quite the same as 'modules', and this list mostly involves more higher-order activities than a modules list (e.g. Idea 2495). The idea that emotion is a 'faculty' sounds old-fashioned. |
| 2545 | Free will is mental causation in action [McGinn] |
| Full Idea: Free will is mental causation in action. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.167) |
| 2543 | Brains aren't made of anything special, suggesting panpsychism [McGinn] |
| Full Idea: All matter must contain the potential to underlie consciousness, since there is nothing special about the matter that composes brain tissue. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.100) | |
| A reaction: This seems to me one of the most basic assumptions which we should all make about the mind. The mind is made of the brain, and the brain is made of food. However, there must be something 'special' about the brain. |
| 2540 | Examining mind sees no brain; examining brain sees no mind [McGinn] |
| Full Idea: You can look into your mind until you burst and not discover neurons and synapses, and you can stare at someone's brain from dawn till dusk and not perceive the consciousness that is so apparent to the person whose brain it is. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.47) | |
| A reaction: This is a striking symmetry of ignorance, though hardly enough to justify McGinn's pessimism about understanding the mind. 'When you are in the grass you can't see the whole of England; if you can see the whole of England, you won't see the grass'. |
| 2547 | There is information if there are symbols which refer, and which can combine into a truth or falsehood [McGinn] |
| Full Idea: There is information in a system if there are symbols in it that refer to things and that together form strings that can be true or false. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.225) | |
| A reaction: We can also directly apprehend information by perception. Are facts identical with correct information? Can a universal generalisation be information? |
| 2542 | Causation in the material world is energy-transfer, of motion, electricity or gravity [McGinn] |
| Full Idea: Causation in the material world works by energy transfer of some sort: transfer of motion, of electrical energy, of gravitational force. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.92) |