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The ancient Sorites paradox,

1 grain of wheat does not make a heap. If 1 grain doesn’t make a heap, then 2 grains don’t. If 2 grains don’t make a heap, then 3 grains don’t. … If 999,999 grains don’t make a heap, then 1 million grains don’t. Therefore, 1 million grains don’t make a heap.

can be easily applied to all terms with vague boundaries: being tall, old, red, fat and so on. In short, it can be applied to any thing that is subject to change over time or composed by parts.

The term "heap", however, as well as the others, refers to a flexible range, related to the observer and the context of the observation. A person may perceive a group of grains differently from another one, depending on their personal attitudes or the context in which they are located - in the same way as the same amount of money looks scarce to a rich and abundant to a poor one. Even a single observer can perceive a certain number of grains sometimes as a heap and sometimes not, depending on the context. Similarly, it is very likely that, faced with the same situation, similar brains who have undergone a similar education will agree to the use of the word "heap". It's the use of the term "heap" that decrees what a heap is, not vice versa. Although the word occurs on similar circumstances, its use is always specific and must be evaluated one situation at a time, because any identity is precisely defined only through the totality of its relations. The paradox easily applies to any term isolated from a relational context, but it dissolves as soon as it is situated in a relationship ('being taller than', 'less bald than', 'old for', etc): vagueness appears if we consider just a part of the relationships that define something.

Does accepting relationism resolve the Sorites paradox?

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  • There is no doubt that "heap" is context dependent. But the paradox appears whenever we start piling up grains even if the context is otherwise fixed. Modus ponens combined with induction simply leads to a contradiction. Vague predicates are those to which induction does not apply.
    – Conifold
    Commented Oct 7, 2018 at 22:21
  • Thank you for your comment. I don't see how the paradox appears with a fixed contest. i.e I see a pile of grains with n grains and I call it "heap", or I start piling grains until I decide to call it "heap". Whatever the reasons why I call it "heap" in a determinate context (and time), even if I don't know them (let's suppose they are unconscious), that's an heap relationally defined. Let's say I remove a grain and I decide it's still an heap, there's no paradox here, just a labeling decision, like when I say "enough" while someone pours water in my glass.
    – Francesco D'Isa
    Commented Oct 8, 2018 at 8:16
  • Once you decided that 1 grain is not a heap and adding a grain to not a heap does not turn it into a heap you do not get to decide what to call a heap anymore if you want to stay coherent. The context is moot.
    – Conifold
    Commented Oct 8, 2018 at 17:46
  • @Conifold my proposal is that the use of the term "heap" establish what a heap is, not the other way around. The reasons why the label is or is not applied are to be found in the particular cases, and have not to be coherent; the context is unknown, not moot.
    – Francesco D'Isa
    Commented Oct 8, 2018 at 19:19
  • The problem exploited in the paradox is that we do not just decide on the use of a word one situation at a time, we want that use at a minimum to satisfy some logical constraints. So if I understand you correctly your proposal is either moot or incoherent.
    – Conifold
    Commented Oct 8, 2018 at 19:39

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To introduce relationism is an interesting angle but I don't think it punctures the paradox. The fact that you and I might disagree on whether X, a pile of beans, constitutes a heap can readily be conceded but that can still leave us with individual sorites problems.

Regardless of what you think - out of relation to it - I may have my own sorites problem because in fact I might not be able to decide whether X is a heap. And you - out of all relation to me or anyone else - might not be able to decide whether Y is a heap.

If the question whether X constitutes a heap is to be determined 'only through the totality of its relations with others', any such totality is impossible to serve as a criterion or metric. Imagine enumerating and specifying the totality of anything's relations to others. It's a theoretically possible but practically unreal possibility - and sorites problem are all too practical.

But an intriguing line of approach.

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  • Thank you for your interesting answer! I don’t think we can have ‘private’ sorites, since language is a common praxis and I would simply use the rules I learned to judge what an heap is. Moreover, there could be a part of my mind in relation to another one that label ideas and words. I agree that is practically impossibile to specify the totality of the relations, but I disagree that Sorite is just a practical issue. When it’s practical, it’s a problem but not a paradox, since it’s always related to the subjective use of words and ideas (I.e when a fetus is a person)
    – Francesco D'Isa
    Commented Oct 7, 2018 at 16:11
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    Thank you. I didn't mean 'private' and certainly not 'logically private' sorites. I meant that even within a common community and a shared language we can and do have individual problems about e.g. what counts as a heap. I liked your question and am glad that you found my answer interesting. Best - Geoffrey
    – Geoffrey Thomas ♦
    Commented Oct 7, 2018 at 16:20

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