Combining Philosophers

All the ideas for William W. Tait, James Rachels and Timothy McGrew

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22 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
9978 Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait]
     Full Idea: The tendency to attack forms of expression rather than attempting to appreciate what is actually being said is one of the more unfortunate habits that analytic philosophy inherited from Frege.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], IV)
     A reaction: The key to this, I say, is to acknowledge the existence of propositions (in brains). For example, this belief will make teachers more sympathetic to pupils who are struggling to express an idea, and verbal nit-picking becomes totally irrelevant.
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
9986 The null set was doubted, because numbering seemed to require 'units' [Tait]
     Full Idea: The conception that what can be numbered is some object (including flocks of sheep) relative to a partition - a choice of unit - survived even in the late nineteenth century in the form of the rejection of the null set (and difficulties with unit sets).
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], IX)
     A reaction: This old view can't be entirely wrong! Frege makes the point that if asked to count a pack of cards, you must decide whether to count cards, or suits, or pips. You may not need a 'unit', but you need a concept. 'Units' name concept-extensions nicely!
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
9984 We can have a series with identical members [Tait]
     Full Idea: Why can't we have a series (as opposed to a linearly ordered set) all of whose members are identical, such as (a, a, a...,a)?
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], VII)
     A reaction: The question is whether the items order themselves, which presumably the natural numbers are supposed to do, or whether we impose the order (and length) of the series. What decides how many a's there are? Do we order, or does nature?
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
13416 Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C]
     Full Idea: The axiomatic conception of mathematics is the only viable one. ...But they are true because they are axioms, in contrast to the view advanced by Frege (to Hilbert) that to be a candidate for axiomhood a statement must be true.
     From: report of William W. Tait (Intro to 'Provenance of Pure Reason' [2005], p.4) by Charles Parsons - Review of Tait 'Provenance of Pure Reason' §2
     A reaction: This looks like the classic twentieth century shift in the attitude to axioms. The Greek idea is that they must be self-evident truths, but the Tait-style view is that they are just the first steps in establishing a logical structure. I prefer the Greeks.
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
19682 Internalists are much more interested in evidence than externalists are [McGrew]
     Full Idea: The notion of evidence generally plays a much more significant role in internalist epistemologies than it does in various forms of externalism.
     From: Timothy McGrew (Evidence [2011], 'Prop..')
     A reaction: I'm guessing that this is because evidence needs a certain amount of interpretation, whereas raw facts (which externalists seem to rely on) may never even enter a mind.
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
19687 Absence of evidence proves nothing, and weird claims need special evidence [McGrew]
     Full Idea: Two well know slogans (popularised by Carl Sagan) are 'absence of evidence is not evidence of absence', ...and 'extraordinary claims require extraordinary evidence'.
     From: Timothy McGrew (Evidence [2011], 'Absence')
     A reaction: [Sagan was a popular science writer and broadcaster] The second one is something like Hume's argument against miracles. The old problem of the 'missing link' for human evolution embodied the first idea.
19684 Does spotting a new possibility count as evidence? [McGrew]
     Full Idea: Does the sudden realization of a heretofore unrecognized possibility count as evidence?
     From: Timothy McGrew (Evidence [2011], 'Evid..')
     A reaction: [Nice use of 'heretofore'! Why say 'previously' when you can keep these wonderful old English words alive?] This means that we can imagine new evidence ('maybe the murderer was a snake'!). Wrong. The evidence is what suggests the possibility.
19688 Every event is highly unlikely (in detail), but may be perfectly plausible [McGrew]
     Full Idea: At a certain level of detail, almost any claim is unprecedented. How likely is 'Matilda won at Scrabble on Thursday with a score of 438 while drinking mint tea'? But there is nothing particularly unbelievable about the claim.
     From: Timothy McGrew (Evidence [2011], 'Extraordinary')
     A reaction: A striking idea, which rules out the simplistic idea that we can just assess evidence by its isolated likelihood. Context is crucial. How good is 438? What if she smoked opium? What if there is no Scrabble set on her island?
19686 Criminal law needs two separate witnesses, but historians will accept one witness [McGrew]
     Full Idea: An ancient rule in law is that a criminal conviction needs evidence of two independent witnesses, but in history it is assumed that a document deserves the benefit of the doubt if it cannot be independently verified.
     From: Timothy McGrew (Evidence [2011], 'Interp..')
     A reaction: [compressed; McGrew's full account qualifies it a bit] A nice observation. One might even be suspicious of the two 'independent' witnesses, if there were lots of other reasons to doubt someon's guilt. A single weird document is also dubious.
19680 Maybe all evidence consists of beliefs, rather than of facts [McGrew]
     Full Idea: Some philosophers have been attracted to the view that, strictly speaking, what counts as evidence is not a set of physical objects or even experiences, but rather a set of believed propositions.
     From: Timothy McGrew (Evidence [2011], 'Prop..')
     A reaction: This may be right. However, as always, I think animals are a key test. Do animals respond to evidence? Even if they did, they might need to 'make sense' of what they experienced, and even formulate a non-linguistic proposition.
19681 If all evidence is propositional, what is the evidence for the proposition? Do we face a regress? [McGrew]
     Full Idea: Taking evidence as propositional may trade one problem for another. If the bloodstain isn't evidence, but 'this is a bloodstain' is evidence, then what serves as evidence for the belief about the bloodstain? Is there an infinite regress?
     From: Timothy McGrew (Evidence [2011], 'Prop..')
     A reaction: [compressed] I quite like evidence being propositional, but then find this. I'll retreat to my beloved coherence. I do not endorse Sellars's 'only a belief can justify a belief', because raw experience has to be part of what is coherent.
19689 Several unreliable witnesses can give good support, if they all say the same thing [McGrew]
     Full Idea: The testimony of a number of independent witnesses, none of them particularly reliable, who give substantially the same account of some event, may provide a strong argument in its favor.
     From: Timothy McGrew (Evidence [2011], 'Testimonial')
     A reaction: A striking point. It obviously works well for panicking people in a crowd during an incident. Does it also apply to independent scientists who are known to cheat? They may not collaborate, but may all want the same result.
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
19683 Narrow evidentialism relies wholly on propositions; the wider form includes other items [McGrew]
     Full Idea: Evidentialism comes in both narrow and wide forms depending on whether evidence is taken to consist only of propositions or of a wider range of items.
     From: Timothy McGrew (Evidence [2011], 'Evid..')
     A reaction: [He cites Conee and Feldman for the wide view, which is not restricted to beliefs] You can hardly rely on occurrent beliefs as evidence, so we often have good knowledge with forgotten justification. But such knowledge has been 'weakened'.
14. Science / A. Basis of Science / 6. Falsification
19685 Falsificationism would be naive if even a slight discrepancy in evidence killed a theory [McGrew]
     Full Idea: Data do not quite speak for themselves, which speaks against a naive form of falsificationism according to which even the slightest mismatch between theory and evidence suffices to overturn a theory.
     From: Timothy McGrew (Evidence [2011], 'Interp..')
     A reaction: [He cites Robert Boyle wisely ignoring some data to get a good fit for his graph]
18. Thought / E. Abstraction / 2. Abstracta by Selection
9981 Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait]
     Full Idea: If the sense of a proposition about the abstract domain is given in terms of the corresponding proposition about the (relatively) concrete domain, ..and the truth of the former is founded upon the truth of the latter, then this is 'logical abstraction'.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], V)
     A reaction: The 'relatively' in parentheses allows us to apply his idea to levels of abstraction, and not just to the simple jump up from the concrete. I think Tait's proposal is excellent, rather than purloining 'abstraction' for an internal concept within logic.
9982 Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
     Full Idea: Although (in Cantor and Dedekind) abstraction does not (as has often been observed) play any role in their proofs, but it does play a role, in that it fixes the grammar, the domain of meaningful propositions, and so determining the objects in the proofs.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], V)
     A reaction: [compressed] This is part of a defence of abstractionism in Cantor and Dedekind (see K.Fine also on the subject). To know the members of a set, or size of a domain, you need to know the process or function which created the set.
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
9985 Abstraction may concern the individuation of the set itself, not its elements [Tait]
     Full Idea: A different reading of abstraction is that it concerns, not the individuating properties of the elements relative to one another, but rather the individuating properties of the set itself, for example the concept of what is its extension.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], VIII)
     A reaction: If the set was 'objects in the room next door', we would not be able to abstract from the objects, but we might get to the idea of things being contain in things, or the concept of an object, or a room. Wrong. That's because they are objects... Hm.
18. Thought / E. Abstraction / 8. Abstractionism Critique
9972 Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait]
     Full Idea: Why should abstraction from two equipollent sets lead to the same set of 'pure units'?
     From: William W. Tait (Frege versus Cantor and Dedekind [1996])
     A reaction: [Tait is criticising Cantor] This expresses rather better than Frege or Dummett the central problem with the abstractionist view of how numbers are derived from matching groups of objects.
9980 If abstraction produces power sets, their identity should imply identity of the originals [Tait]
     Full Idea: If the power |A| is obtained by abstraction from set A, then if A is equipollent to set B, then |A| = |B|. But this does not imply that A = B. So |A| cannot just be A, taken in abstraction, unless that can identify distinct sets, ..or create new objects.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], V)
     A reaction: An elegant piece of argument, which shows rather crucial facts about abstraction. We are then obliged to ask how abstraction can create an object or a set, if the central activity of abstraction is just ignoring certain features.
25. Social Practice / F. Life Issues / 2. Euthanasia
4052 It has become normal to consider passive euthanasia while condemning active euthanasia [Rachels]
     Full Idea: It seems to have become accepted that passive euthanasia (by withholding treatment and allowing a patient to die) may be acceptable, whereas active euthanasia (direct action to kill the patient) is never acceptable.
     From: James Rachels (No Moral Difference [1975], p.97)
     A reaction: He goes on to attack the distinction. It is hard to distinguish the two cases, as well as being hard to judge them.
4053 If it is desirable that a given patient die, then moral objections to killing them do not apply [Rachels]
     Full Idea: The cause of death (injection or disease) is important from the legal point of view, but not morally. If euthanasia is desirable in a given case then the patient's death is not an evil, so the usual objections to killing do not apply.
     From: James Rachels (No Moral Difference [1975], p.102)
     A reaction: Seems reasonable, but a very consequentialist view. Is it good that small children should clean public toilets?
28. God / B. Proving God / 2. Proofs of Reason / c. Moral Argument
20713 God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B]
     Full Idea: Rachels argues 1) If any being is God, he must be a fitting object of worship, 2) No being could be a fitting object of worship, since worship requires the abandonment of one's role as an autonomous moral agent, so 3) There cannot be a being who is God.
     From: report of James Rachels (God and Human Attributes [1971], 7 p.334) by Brian Davies - Introduction to the Philosophy of Religion 9 'd morality'
     A reaction: Presumably Lionel Messi can be a fitting object of worship without being God. Since the problem is with being worshipful, rather than with being God, should I infer that Messi doesn't exist?