27
votes
What's the solution to Sorites paradox?
The solution is to realise that the problem as posed is based on a false assumption that there is always a clear dividing line between two opposing classifications of degree. Take long and short, ...
- 13.5k
26
votes
What is the meat paradox?
There is no necessity for a solution because there is no paradox. This falsely called "paradox" is just a misinterpreted and biased statement, sustained by fallacies and political arguments:
...
- 6,831
15
votes
Why would this not resolve the Sorites paradox?
Your proposed solution does not solve the paradox.
The whole point of the paradox is that the term 'pile' is vague. That is, given an object (e.g. a collection of grains of sand) it is indeterminate ...
- 6,466
12
votes
Accepted
What the Preface paradox tells us about the principle of explosion
I agree with Just Some Old Man's answer, but to expand on it a little...
If we think of all the statements in the textbook as propositions A1, A2, ..., An then the situation we are trying to describe ...
- 22.9k
12
votes
Is there a distance so small it can't be further divided?
Is there a distance so small it can’t be further divided?
The modern solution to this problem is the use of infinitesimals, as used by Leibniz and Newton in their development of the calculus. ...
- 6,140
12
votes
Is there a distance so small it can't be further divided?
The time it takes for the arrow to reach one half of the distance, is one half of the time.
So the total length traveled by the arrow is one half the distance, plus one half of one half, plus one half ...
- 573
11
votes
Accepted
Is a set containing itself already a paradox?
Russell's paradox arises within naïve set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of ...
- 36.2k
11
votes
Irresistible force paradox as an inconsistent formal theory
This dilemma doesn't really makes sense in modern physics because any macroscopic force accelerates any mass no matter how large, but if you were to axiomatize it in pre-modern physics then yes, it ...
- 7,600
11
votes
What is the meat paradox?
I'm joining the other answers in stating that the so-called "meat paradox" isn't a paradox. Rather, it's an example of the logical fallacy of all or nothing thinking.
I strongly disagree ...
- 807
11
votes
What's the solution to Sorites paradox?
The answer is in the definition of a heap.
I offer the definition that a heap must have at least one layer stacked upon a base layer.
For grains of sand you need at least 3 grains in a base layer to ...
- 211
10
votes
Accepted
What's the current status of the "paradox of analysis"? And are there any strong and widely accepted resolutions?
A good paper to read on this subject is an old classic: Gilbert Ryle's Systematically Misleading Expressions. (Proceedings of the Aristotelian Society, 32: 139-170 (1932). Also in his Collected Papers,...
- 22.9k
10
votes
Why would this not resolve the Sorites paradox?
This is all about the difference between natural language and formal language. In formal language, a term cannot be used unless it's well-defined according to the standards of the language. In ...
- 27.2k
10
votes
Is finding truth possible?
You've stumbled upon an old problem in philosophy, The Paradox of Inquiry, first formulated in Plato's Meno.
The problem can be reformulated as follows:
Either you know the answer to a question, or ...
- 6,466
10
votes
What qualifies as the solving of a paradox?
Technically speaking, a paradox isn't a problem to be solved in and of itself. A paradox points at a weakness, misconception, or internal contradiction of the philosophical/analytical structures we ...
- 18.5k
10
votes
Accepted
What is the meat paradox?
Humans are irrational. There are countless examples of individual behaviour that shows inconsistency of beliefs. Christians condemn murder, but many will quite happily support the idea of war. People ...
- 13.5k
10
votes
What's the solution to Sorites paradox?
One solution would be to say that even 1 grain is a heap. That would be defining "heap" more precisely than its informal, intuitive meaning. What does "heap" precisely mean anyway? ...
- 2,402
9
votes
Accepted
Was Kant anticipating Gödel's incompleteness in his antinomies?
This reminds me of the older question Was Wittgenstein anticipating Gödel? There is more to it in the case of Kant than there was in the case of Wittgenstein though, at least in spirit. One could ...
- 42.5k
9
votes
Accepted
Why would this not resolve the Sorites paradox?
The previous answers betray a lack of familiarity with the literature. Your solution, using the least number principle, essentially works. It is a known argument for epistemism about vagueness, the ...
9
votes
What is the meaning of “to fight a Catch-22 is to accept it”?
The definitive way to answer the question is to read the book. Here is how it is presented in the book itself (copied from here):
Yossarian: “You mean there’s a catch?”
“Sure there’s a catch,” Doc ...
- 1,543
9
votes
What if all sets contain themselves?
I think that disallowing the empty set will cause the resulting theory to lose too much. For example, the intersection of two disjoint sets, which would be the empty set, is now undefined. You will ...
- 2,402
9
votes
Accepted
What if all sets contain themselves?
I think we can find a contradiction with ZFC immediately:
Let S = {A, B} with A =/= B.
WLOG, by your hypothesis, assume that A = S. (One of these elements needs to equal the whole set!)
Then, also ...
- 114
8
votes
Accepted
Can it be rational to have beliefs one knows to be inconsistent?
It can. Ramsey put it nicely in his "last papers" written around 1929 under the influence of Peirce's pragmatism (quoted from Marion, Wittgenstein, Ramsey and British Pragmatism):
"We want our ...
- 42.5k
8
votes
What is the meaning of “to fight a Catch-22 is to accept it”?
By fighting the rule, you are accepting that it is something you have to deal with, whether obeying, evading, or fighting.
If, for instance, soldiers were allowed to leave base before 9 with permits ...
- 1,968
8
votes
What if all sets contain themselves?
The axiom of foundation is not (usually) taken for a logical truth (although see about predicativism for an attempt to situate well-foundedness on the level of predication theory). Accordingly, its ...
- 12.1k
7
votes
How do mathematicians reconcile that an infinite set does not have to be larger than its proper subset?
There is a long controversy as to what should count as the "size" of an infinite set, and there provably does not exist a notion that satisfies both the bijectivity principle, a.k.a. Hume's ...
- 42.5k
7
votes
Accepted
Is it possible that a question has only two answers?
Answer 1 - 'yes'
Suppose I ask, 'Can Tom walk ?' I am asking about the truth-value of the proposition, 'Tom can walk'. I expect the answer 'Yes' or 'No'. The answer, 'Yes', is right if Tom can walk ...
- 35.4k
6
votes
Shouldn't Last Thurdayism be able to be proved wrong by Physics?
I think you're misunderstanding the idea behind "Last Thursdayism" on two fronts.
First, as can be seen from the selection of "Thursday", the main point of the posit is to point out a problem in ...
- 24.6k
6
votes
Accepted
Is "Intolerance of intolerance" equivalent to the Liar's Paradox?
If you take a really silly literal view of the sentence the statement is a performative contradiction but not equivalent to the liar's paradox.
Let's say being intolerant of something is along the ...
- 1,956
6
votes
What's the solution to Sorites paradox?
So I would say that two possible answers to the paradox are
Rigorously define a 'heap' to explicitly consider the number of grains of sand, or
Keep the fuzziness around heaps, and observe that tiny ...
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