by Here’s a poser (of sorts): as recently as 1984[1], Derek Parfit (who I genuinely think is one of the most insightful philosophers of the current era), claimed was a profoundly difficult philosophical problem:
1 grain of wheat does not make a heap.
If 1 grain of wheat does not make a heap then 2 grains of wheat do not.
If 2 grains of wheat do not make a heap then 3 grains do not.
…
If 9,999 grains of wheat do not make a heap then 10,000 do not.
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10,000 grains of wheat do not make a heap.[2]
I’m not going to feign humility. The solution' to this 'puzzle' is clearly to either a) define a heap of wheat as something which includes (specify whatever number you like) of grains, or b) to avoid defining a heap in physical terms, and refer it to our intuition as something we just recognise on sight. If you think I’m overconfident, show it to a mathematician – I’ll give you better than 9 out of 10 odds that if you present it as a ‘challenging problem’ they’ll laugh in your face.
Anyway, option b) tells you nothing about the nature of heaps of wheat, though it’s often a more practically helpful definition for activities which allow for imprecision.
Option a) also tells you nothing about the nature of heaps. But it lets you talk more clearly about things which involve heaps. And it gives you a sense of the method you could use for learning more about their nature – or rather, which methods to avoid. Specifically, it saves you wasting time on semantic questions about heapness. Discussing how you’re going to use language can be very helpful for clarity. Discussing how – in any sense – you ‘should’ use it is utterly useless.
It’s tough to prove, but I believe that all supposedly philosophical questions are reducible by defining key terms to either questions of logical deduction or [scientific research]. I think this follows from assumptions we all share. This view is similar to logical positivism, but whereas I think logical positivism as it’s usually formulated was logically inconsistent, no-one’s yet pointed out to me any such inconsistency in a worldview that treats induction and deduction as part of the same category.
Even if it turns out not to, it’s usually helpful to approach philosophical questions that way, but it’s a depressingly rare approach.
[1] In Reasons and Persons - the book's index isn't substantial enough for me to find the exact quote. Maybe someone here can help?
[2] From the Stanford Encyclopedia of Philosophy's Sorites Paradox entry.
1 grain of wheat does not make a heap.
If 1 grain of wheat does not make a heap then 2 grains of wheat do not.
If 2 grains of wheat do not make a heap then 3 grains do not.
…
If 9,999 grains of wheat do not make a heap then 10,000 do not.
--------------------------------------------------------------------
10,000 grains of wheat do not make a heap.[2]
I’m not going to feign humility. The solution' to this 'puzzle' is clearly to either a) define a heap of wheat as something which includes (specify whatever number you like) of grains, or b) to avoid defining a heap in physical terms, and refer it to our intuition as something we just recognise on sight. If you think I’m overconfident, show it to a mathematician – I’ll give you better than 9 out of 10 odds that if you present it as a ‘challenging problem’ they’ll laugh in your face.
Anyway, option b) tells you nothing about the nature of heaps of wheat, though it’s often a more practically helpful definition for activities which allow for imprecision.
Option a) also tells you nothing about the nature of heaps. But it lets you talk more clearly about things which involve heaps. And it gives you a sense of the method you could use for learning more about their nature – or rather, which methods to avoid. Specifically, it saves you wasting time on semantic questions about heapness. Discussing how you’re going to use language can be very helpful for clarity. Discussing how – in any sense – you ‘should’ use it is utterly useless.
It’s tough to prove, but I believe that all supposedly philosophical questions are reducible by defining key terms to either questions of logical deduction or [scientific research]. I think this follows from assumptions we all share. This view is similar to logical positivism, but whereas I think logical positivism as it’s usually formulated was logically inconsistent, no-one’s yet pointed out to me any such inconsistency in a worldview that treats induction and deduction as part of the same category.
Even if it turns out not to, it’s usually helpful to approach philosophical questions that way, but it’s a depressingly rare approach.
[1] In Reasons and Persons - the book's index isn't substantial enough for me to find the exact quote. Maybe someone here can help?
[2] From the Stanford Encyclopedia of Philosophy's Sorites Paradox entry.
