16 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). |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 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) |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 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? |
| 1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
| Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone. | |
| From: Plato (Clitophon [c.372 BCE], 410b) | |
| A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus. |
| 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) |