9 ideas
| 8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
| Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §1) | |
| A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to. |
| 8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
| Full Idea: The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §3) | |
| A reaction: Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others. |
| 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. |
| 19739 | The maxim for suicide is committed to the value of life, and is thus contradictory [Kant] |
| Full Idea: If my maxim is to shorten my life if its continuance threatens more evil than pleasure ...it is seen that a system of nature by whose law the feeling intended to further life should actually destroy life would contradict itself, and could not subsist. | |
| From: Immanuel Kant (Lectures on Ethics [1780], 422:53) | |
| A reaction: [compressed] I take it this means that a potential suicide is assessing what is best for life, and is therefore implicitly committed to life. Not persuasive! Should we not terminate the life of a mass murderer in mid-crime? |