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6855
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Interesting philosophers hardly every give you explicitly valid arguments [Martin,M]
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Full Idea:
Notice that very few philosophers - certainly almost none of the ones who are interesting to read - give you explicitly valid arguments.
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From:
Michael Martin (Interview with Baggini and Stangroom [2001], p.134)
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A reaction:
I never thought that was going to happen in philosophy. What I do get is, firstly, lots of interesting reasons for holding beliefs, and a conviction that good beliefs need good reasons, and, secondly, a really coherent view of the world.
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6856
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Valid arguments can be rejected by challenging the premises or presuppositions [Martin,M]
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Full Idea:
Putting forward a valid argument isn't necessarily going to succeed in getting someone to see things your way, because if they don't accept the conclusion, they ask which premises they should reject, or whether an illegitimate assumption is being made.
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From:
Michael Martin (Interview with Baggini and Stangroom [2001], p.136)
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A reaction:
Valid arguments are still vital. It is just that good philosophers realise the problem noted here, and spend huge stretches of discussion on establishing acceptance of premises, and showing that there are no dodgy presuppositions.
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6408
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Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling]
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Full Idea:
In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility.
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From:
A.C. Grayling (Russell [1996], Ch.2)
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A reaction:
The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom.
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