Equally, you can never have a heap of stones. For a single stone is not a heap and adding one stone to a non- heap will not make a heap. So no stone collection can constitute a heap.
Baldness and heaps of stones have now been worrying philosophers for nearly 2,000 years. The latest reference I have found is The Hidden Logic of Slippery Slope Arguments by Dale Jacquette (Philosophy and Rhetoric, vol 22, 1989, 59-70). Baldly stating that Eubulides's inferences are 'evidently unsound, and may well have some logical defect', the author defines the problem as 'the argument from incremental differences among objects with indefinite property-complement demarcations arranged along a continuum'. It is not only philosophers who need to worry:
'We are taught to avoid these in argument, and sometimes send students in courses on critical reasoning to search through the editorial columns of newspapers . . . to detect slippery slope fallacies in the popular press, where they seem to be so abundant in careless thinking about the problems of foreign policy, euthanasia and abortion.'
Using something closely analogous to the hard logic of mathematical induction, the soft slide down the slippery slope begins with a vague concept, such as bald, heap or person, and an object that definitely does not have the property under consideration. Advancing by small degrees, one slides over the undefined partition between heap and non-heap, bald and hairy, or person and non-person.
'If a zygote at the moment of conception is not a person with a right to life protected from abortion, and if continued embryonic development a fraction of a second later does not change a non-person into a person, then no passage of subsequent time or development can do so.'
Earlier research into slippery slope paradoxes had always led to one of three conclusions: that all such arguments are logically fallacious; that there are two distinct types, respectively valid and invalid; or that there are many types, 'including conceptual, precedential and causal' which defy any classification that tells you whether they are valid.
Dr Jacquette proposes a framework for condensing and uncondensing slippery slope arguments to test their soundness. 'The concept of baldness is vague', he says, adding that 'slippery slope sophisms' trade on vagueness and ill-defined demarcation lines. 'My conclusion is that all slippery slopes can be reduced to a single category of arguments, which, when correctly interpreted, are always logically valid (though sometimes unsound).' Leader writers please note.Reuse content