I appreciate the author's dispensation with fuzzy logic as a suitable answer to the problem of the heap, but I'm not sure that his answer (a lack of knowledge) is any more persuasive.
As evidenced by his formulation of the sorites paradox, we all seem to have an intuitive notion of when a heap transitions to a less-than-heap (for lack a better word) or individual. One possible description (which I don't claim is final) that aligns with this intuition is that the whole stands out more than its parts. A heap, then, is when an object exists more on its own than as of other objects. The same might be said for crowds, flocks of birds, &c.
I like to consider the difference between 'one','a couple','a few','several','many'. e.g 1,2,3-6,5-12,10+ respectively.
>Vagueness isn’t a problem about logic; it’s a problem about knowledge.
I think it's more to do with context. The transition from 'a grain' to 'a pile' to 'a heap' where those terms are actually useful is normally clear in the context of whatever problem we're trying to solve.
The confusion arises from the fact that 'a grain' is considered to be well-defined without context and that language refers to it directly. Thus we lament that we can't adequately define 'heap'. Whereas in fact all language is metaphorical and indirect, and definitions can't rescue us from this. So even the label 'a grain' is fuzzy if you look deeply and scientifically enough.
You can't have a heap if the objects aren't stacked, and stacking nonrectangular objects generally requires 4 if you want it to be a stable heap. 3 as the base, 1 on top.
>The transition from 'a grain' to 'a pile' to 'a heap' where those terms are actually useful is normally clear in the context of whatever problem we're trying to solve.
That's the position of pragmatist philosophers, the existential-phenomenologists and the analytic philosophers influenced by the later Wittgenstein.
In Western philosophy, there are two competing ideas about the metaphysical status of basic concepts. According to one, as in Platonism, dualism, and materialism, concepts concerning the real world are perfect, like mathematical ideas. In the other view, concepts are the products of the great complexities of human living, and so are inherently vague, complex, and contextual. In the last century or so, I would say the later idea has been winning out, though many philosphers still hold the former one.
A few months ago I bookmarked a 1923 talk/essay by Bertrand Russell that is actually entitled Vagueness. I thought it was extremely interesting to read the perspective of a cleary-brilliant thinker prior to the computer age.
How do you discuss this issue without bringing up the problems with essentialism?
A "heap" is an under-defined term and if you treat it like it isn't you confuse yourself. More interestingly, so is "alive". Fuzzy logic doesn't apply.
It's pretty fantastic that we can use vagueness and metaphor to communicate so richly, unfortunate that we get so used to it we often confuse ourselves.
Alternatively you could consider a functional definition. If you need to consider a group of grains collectively, and they are stacked touching each other, they are a heap.
Likewise, is it a boat if you make it and never plan to put it in the water, but use it as a table? Is it a boat if you lie on a block of foam and paddle?
If you think things have some sort of platonic essence, these concepts are hard. If you think the definition of a thing is the role it fills, this particular problem is easier.
I don't understand the author's point about the two heaps. Clearly there are two separate propositions at play -- the "heapness" of either pile, and whether or not the two heap-like entities are identical. The first requires fuzzy logic because the definition of "heap" is vague. The second does not because the rules (take a grain off one for each grain removed from the other) are precisely defined. There is no inherent contradiction just because two different systems are in use at once.
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[ 2.4 ms ] story [ 33.5 ms ] threadAs evidenced by his formulation of the sorites paradox, we all seem to have an intuitive notion of when a heap transitions to a less-than-heap (for lack a better word) or individual. One possible description (which I don't claim is final) that aligns with this intuition is that the whole stands out more than its parts. A heap, then, is when an object exists more on its own than as of other objects. The same might be said for crowds, flocks of birds, &c.
Just my two cents.
>Vagueness isn’t a problem about logic; it’s a problem about knowledge.
I think it's more to do with context. The transition from 'a grain' to 'a pile' to 'a heap' where those terms are actually useful is normally clear in the context of whatever problem we're trying to solve.
The confusion arises from the fact that 'a grain' is considered to be well-defined without context and that language refers to it directly. Thus we lament that we can't adequately define 'heap'. Whereas in fact all language is metaphorical and indirect, and definitions can't rescue us from this. So even the label 'a grain' is fuzzy if you look deeply and scientifically enough.
I think that overstates the problem. Just don't use 'heap' in a context where greater precision is needed; there are alternatives.
A heap is more than three.
You can't have a heap if the objects aren't stacked, and stacking nonrectangular objects generally requires 4 if you want it to be a stable heap. 3 as the base, 1 on top.
That's the position of pragmatist philosophers, the existential-phenomenologists and the analytic philosophers influenced by the later Wittgenstein.
In Western philosophy, there are two competing ideas about the metaphysical status of basic concepts. According to one, as in Platonism, dualism, and materialism, concepts concerning the real world are perfect, like mathematical ideas. In the other view, concepts are the products of the great complexities of human living, and so are inherently vague, complex, and contextual. In the last century or so, I would say the later idea has been winning out, though many philosphers still hold the former one.
http://www.personal.kent.edu/~rmuhamma/Philosophy/RBwritings...
A "heap" is an under-defined term and if you treat it like it isn't you confuse yourself. More interestingly, so is "alive". Fuzzy logic doesn't apply.
It's pretty fantastic that we can use vagueness and metaphor to communicate so richly, unfortunate that we get so used to it we often confuse ourselves.
Likewise, is it a boat if you make it and never plan to put it in the water, but use it as a table? Is it a boat if you lie on a block of foam and paddle?
If you think things have some sort of platonic essence, these concepts are hard. If you think the definition of a thing is the role it fills, this particular problem is easier.