16 ideas
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 21506 | A coherence theory of justification can combine with a correspondence theory of truth [Bonjour] |
| Full Idea: There is no manifest absurdity in combining a coherence theory of justification with a correspondence theory of truth. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.1) | |
| A reaction: His point is to sharply (and correctly) distinguish coherent justification from a coherence theory of truth. Personally I would recommend talking of a 'robust' theory of truth, without tricky commitment to 'correspondence' between very dissimilar things. |
| 21509 | There will always be a vast number of equally coherent but rival systems [Bonjour] |
| Full Idea: On any plausible conception of coherence, there will always be many, probably infinitely many, different and incompatible systems of belief which are equally coherent. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.5) | |
| A reaction: If 'infinitely many' theories are allowed, that blocks the coherentist hope that widening and precisifying the system will narrow down the options and offer some verisimilitude. If we stick to current English expression, that should keep them finite. |
| 21503 | Empirical coherence must attribute reliability to spontaneous experience [Bonjour] |
| Full Idea: An empirical coherence theory needs, for the beliefs of a cognitive system to be even candidates for empirical justification, that the system must contain laws attributing a high degree of reliability to a variety of spontaneous cognitive beliefs. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 7.1) | |
| A reaction: Wanting such a 'law' seems optimistic, and not in the spirit of true coherentism, which can individually evaluate each experiential belief. I'm not sure Bonjour's Observation Requirement is needed, since it is incoherent to neglect observations. |
| 21511 | A well written novel cannot possibly match a real belief system for coherence [Bonjour] |
| Full Idea: It is not even minimally plausible that a well written novel ...would have the degree of coherence required to be a serious alternative to anyone's actual system of beliefs. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.5) | |
| A reaction: This seems correct. 'Bleak House' is wonderfully consistent, but its elements are entirely verbal, and nothing occupies the space between the facts that are described. And Lady Dedlock is not in Debrett. I think this kills a standard objection. |
| 21510 | The objection that a negated system is equally coherent assume that coherence is consistency [Bonjour] |
| Full Idea: Sometimes it is said that if one has an appropriately coherent system, an alternative system can be produced simply be negating all of the components of the first system. This would only be so if coherence amounted simply to consistency. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.5) | |
| A reaction: I associate Russell with this original objection to coherentism. I formerly took this to be a serious problem, and am now relieved to see that it clearly isn't. |
| 21505 | A coherent system can be justified with initial beliefs lacking all credibility [Bonjour] |
| Full Idea: It is simply not necessary in order for [the coherence] view to yield justification to suppose that cognitively spontaneous beliefs have some degree of initial or independent credibility. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 7.2) | |
| A reaction: This is thoroughly and rather persuasively criticised by Erik Olson. But he always focuses on the coherence of a 'system' with multiple beliefs. I take the credibility of each individual belief to need coherent assessment against a full background. |
| 21504 | The best explanation of coherent observations is they are caused by and correspond to reality [Bonjour] |
| Full Idea: The best explanation for a stable system of beliefs which rely on observation is that the beliefs are caused by what they depict, and the system roughly corresponds to the independent reality it describes. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 8.3) | |
| A reaction: [compressed] Anyone who links best explanation to coherence (and to induction) warms the cockles of my heart. Erik Olson offers a critique, but doesn't convince me. The alternative is to find a better explanation (than reality), or give up. |
| 21508 | Anomalies challenge the claim that the basic explanations are actually basic [Bonjour] |
| Full Idea: The distinctive significance of anomalies lies in the fact that they undermine the claim of the allegedly basic explanatory principles to be genuinely basic. | |
| From: Laurence Bonjour (The Structure of Empirical Knowledge [1985], 5.3) | |
| A reaction: This seems plausible, suggesting that (rather than an anomaly flatly 'falsifying' a theory) an anomaly may just demand a restructuring or reconceptualising of the theory. |
| 4988 | Folk psychology may not be reducible, but that doesn't make it false [Kirk,R on Churchland,PM] |
| Full Idea: It may well be that completed neuroscience will not include a reduction of folk psychology, but why should that be a reason to regard it as false? It would only be a reason if irreducibility entailed that they could not possibly both be true. | |
| From: comment on Paul M. Churchland (Eliminative Materialism and Prop. Attitudes [1981]) by Robert Kirk - Mind and Body §3.9 | |
| A reaction: If all our behaviour had been explained by a future neuro-science, this might not falsify folk psychology, but it would totally marginalise it. It is still possible that dewdrops are placed on leaves by fairies, but this is no longer a hot theory. |
| 4987 | Eliminative materialism says folk psychology will be replaced, not reduced [Churchland,PM] |
| Full Idea: Eliminative materialism says our common-sense conception of psychological phenomena is a radically false theory, so defective that both the principles and the ontology of that theory will eventually be displaced (rather than reduced). | |
| From: Paul M. Churchland (Eliminative Materialism and Prop. Attitudes [1981], Intro) | |
| A reaction: It is hard to see what you could replace the idea of a 'belief' with in ordinary conversation. We may reduce beliefs to neuronal phenomena, but we can't drop the vocabulary of the macro-phenomena. The physics of weather doesn't eliminate 'storms'. |