Combining Philosophers

All the ideas for William W. Tait, James Rachels and Erik J. Olsson

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18 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 / B. Internal Justification / 5. Coherentism / a. Coherence as justification

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.

13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique

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.

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

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?

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.

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?