10 ideas
| 10190 | From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki] |
| Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures. | |
| From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79 | |
| A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s. |
| 18528 | The single imagined 'interval' between things only exists in the intellect [Auriol] |
| Full Idea: It appears that a single thing, which must be imagined as some sort of interval [intervallum] existing between two things, cannot exist in extramental reality, but only in the intellect. | |
| From: Peter Auriol (Sentences [1316], I fols318 v a-b), quoted by John Heil - The Universe as We Find It 7 | |
| A reaction: This is the standard medieval denial of the existence of real relations. It contrasts with post-Russell ontology, which seems to admit relations as entities. Heil and Auriol and right. |
| 21515 | Incoherence may be more important for enquiry than coherence [Olsson] |
| Full Idea: While coherence may lack the positive role many have assigned to it, ...incoherence plays an important negative role in our enquiries. | |
| From: Erik J. Olsson (Against Coherence [2005], 10.1) | |
| A reaction: [He cites Peirce as the main source for this idea] We can hardly by deeply impressed by incoherence if we have no sense of coherence. Incoherence is just one of many markers for theory failure. Missing the target, bad concepts... |
| 21514 | Coherence is the capacity to answer objections [Olsson] |
| Full Idea: According to Lehrer, coherence should be understood in terms of the capacity to answer objections. | |
| From: Erik J. Olsson (Against Coherence [2005], 9) | |
| A reaction: [Keith Lehrer 1990] We can connect this with the Greek requirement of being able to give an account [logos], which is the hallmark of understanding. I take coherence to be the best method of achieving understanding. Any understanding meets Lehrer's test. |
| 21496 | Mere agreement of testimonies is not enough to make truth very likely [Olsson] |
| Full Idea: Far from guaranteeing a high likelihood of truth by itself, testimonial agreement can apparently do so only if the circumstances are favourable as regards independence, prior probability, and individual credibility. | |
| From: Erik J. Olsson (Against Coherence [2005], 1) | |
| A reaction: This is Olson's main thesis. His targets are C.I.Lewis and Bonjour, who hoped that a mere consensus of evidence would increase verisimilitude. I don't see a problem for coherence in general, since his favourable circumstances are part of it. |
| 21499 | Coherence is only needed if the information sources are not fully reliable [Olsson] |
| Full Idea: An enquirer who is fortunate enough to have at his or her disposal fully reliable information sources has no use for coherence, the need for which arises only in the context of less than fully reliable informations sources. | |
| From: Erik J. Olsson (Against Coherence [2005], 2.6.2) | |
| A reaction: I take this to be entirely false. How do you assess reliability? 'I've seen it with my own eyes'. Why trust your eyes? In what visibility conditions do you begin to doubt your eyes? Why do rational people mistrust their intuitions? |
| 21502 | A purely coherent theory cannot be true of the world without some contact with the world [Olsson] |
| Full Idea: The Input Objection says a pure coherence theory would seem to allow that a system of beliefs be justified in spite of being utterly out of contact with the world it purports to describe, so long as it is, to a sufficient extent, coherent. | |
| From: Erik J. Olsson (Against Coherence [2005], 4.1) | |
| A reaction: Olson seems impressed by this objection, but I don't see how a system could be coherently about the world if it had no known contact with the world. Olson seems to ignore meta-coherence, which evaluates the status of the system being studied. |
| 21512 | Extending a system makes it less probable, so extending coherence can't make it more probable [Olsson] |
| Full Idea: Any non-trivial extension of a belief system is less probable than the original system, but there are extensions that are more coherent than the original system. Hence more coherence does not imply a higher probability. | |
| From: Erik J. Olsson (Against Coherence [2005], 6.4) | |
| A reaction: [Olson cites Klein and Warfield 1994; compressed] The example rightly says the extension could have high internal coherence, but not whether the extension is coherent with the system being extended. |
| 16589 | Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol] |
| Full Idea: Prime matter has no essence, nor a nature that is determinate, distinct, and actual. Instead, it is pure potential, and determinable, so that it is indeterminately and indistinctly a material thing. | |
| From: Peter Auriol (Sentences [1316], II.12.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1 | |
| A reaction: Pasnau thinks Auriol has the best shot at explaining the vague idea of 'prime matter', with the thought that it exists, but indeterminateness is what gives it a lesser mode of existence. It strikes me as best to treat 'exist' as univocal. |
| 16651 | God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol] |
| Full Idea: If someone says 'God could make straightness without a line, and roughness and lightness in weight without parts', …then show me the reason why God can do whatever does not imply a contradiction, yet cannot do these things. | |
| From: Peter Auriol (Sentences [1316], IV.12.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 11.4 | |
| A reaction: How engagingly bonkers. The key idea preceding this is that God can do all sorts of things that are beyond our understanding. He is then obliged to offer some examples. |