See 'fuzzy logic' for possible alternative formalisms. — fresco
A heap is what I call a heap; a non-heap is what I call a non-heap. The transition is therefore up to me, since the ultimate judge for me who decides between heaps and non-heaps is myself. At least I, for one, accept this judge's judgement. — god must be atheist
Can you explain further? My problem is how can a bunch of lies (multiple corroborative observations each by itself not-true/false) add up to the truth (objectivity)? — TheMadFool
That makes sense but the definition of "heap" in this case would be private and others will probably disagree with you. — TheMadFool
That makes sense but the definition of "heap" in this case would be private and others will probably disagree with you.
— TheMadFool
You're absolutely right. That's why I made no bones about it, and did not declare that my proposition is the ultimate answer. I came out straight away and said under what circumstances my opinion holds. — god must be atheist
But what about the big picture, a poll of judgements, or of individual thresholds? What if the tail end of such a distribution (of thresholds) reaches back to a single grain? — bongo fury
What if the tail end of such a distribution (of thresholds) reaches back to a single grain? — bongo fury
Then, for some enthusiasts at least, this play of the game is over. From their point of view, you won't play. You decline to agree that a single grain is absolutely not a heap. You admit that this grain is, in the current idiom, "on the spectrum" of (usage of) heap. Albeit at one far end of that spectrum. You've lost one of the two required (and puzzlingly opposed) intuitions that we are trying to reconcile — bongo fury
What if the tail end of such a distribution (of thresholds) reaches back to a single grain?
— bongo fury
Can you expand on that? — TheMadFool
a situation where the idea of 'a heap of sand' has been an issue ! — fresco
One grain of sand doesn't a heap make. Adding another will still not be a heap but carry this on for some time and we arrive at a heap of sand. The paradox is basically about how one grain of sand doesn't count and yet continue this for an adequate length of time and we have a heap of sand. Mathematically I think it can be stated as how 0+0+0+0+0+0+0+0 > 0? Each step doesn't count and yet after a certain time we have something that matters. I think it's about vagueness primarily because a heap is vague term. Any way what you should keep in mind about the paradox is simply that many nothings add up to something. — TheMadFool
Coming to objectivity we can consider it a method for arriving at truth. There may be many definitions of objectivity but what I want to stress on is the requirment that there be an adequate number of observations. A single person's testimony amounts to very little these days. Each claim , whatever it may be, needs corroboration if it's to fly in any epistemological setup. What is notable is just like one grain of sand, a single person or observation fails to be objective. Yet, just like many grains of sand in a heap, multiple people or observations make them objective. — TheMadFool
I think it's about vagueness primarily because a heap is vague term. — TheMadFool
What lots of people say only tells you what lots of people say. — Terrapin Station
If we wanted to be more specific, we could tighten it up. — T Clark
Which, when you want to know about usage, is what you want to know. — bongo fury
Well, or if you want to know what people like (their preferences), or what their opinions about something are, etc., sure. — Terrapin Station
But otherwise, we can use it as it is. With certain embarrassing difficulties on slippery slopes, admittedly. — bongo fury
Yes. I think the vagueness of the word matches the vagueness of what it describes. — T Clark
So you need both intuitions, clarity and fuzziness. The heap game, and other natural incursions by logical thought, can make you doubt this is possible, so you abandon one or the other. Then you come to, and realise you are in a mess without both. E.g. IMO fuzzy logic: analog-digital interfacing in wolf's clothing. Or e.g. Brexit. — bongo fury
What this illustrates is that some concepts are simply vague and didn't require precise definitions because despite their vagueness conversation/discourse wasn't hampered. — TheMadFool
what is unambiguous to ALL is the starting point itself - one single grain of sand is definitely not a heap. — TheMadFool
I can't think of a situation where vagueness is a crucial aspect. Do you have an example? — TheMadFool
I think one of the reasons why the Sorites Paradox is important and comes up so frequently isn't not only that we have a problem with vagueness. It's also that mathematics, as we understand it today, is built upon or founded on the practical need for counting. Hence we start with counting natural numbers. Now math has developed from this practical need, but it's logical foundations might not be good to be chained to counting. Now a heap confuses this thinking that "Let's start with counting" and we tend to just think of it as problem of mixing math with definitions from a spoken language.An important area of difference between the sorites paradox and objectivity is the former is physical and sand grains have volume and becoming a heap isn't that difficult to imagine. — TheMadFool
But does your conception of vagueness allow you to deny absolutely that a single grain is a heap? — bongo fury
Basically you have incommensurability between a heap and an exact number of grains. The paradox rises when we don't take into account the incommensurability between the two. — ssu
So that's what's wrong. Simply that we think every logical system can be reduced to a simple system of arithmetic. — ssu
Based on that, I'm willing to state that a single grain is not a heap. Absolutely? Nothing in language, or anything else, is absolute. — T Clark
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