Deleted lines 7-9:
Aristotle's ''Metaphysics'':
@@@To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, or of what is not that it is not, is true.@@@
Added lines 9-14:
*Aristotle's ''Metaphysics'':
@@@To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, or of what is not that it is not, is true.@@@
* According to Athenaeus, a gravestone on the Greek Island of Cos contains this poem:
@@@O Stranger: Philetas of Cos am I,\\
'Twas the Liar who made me die,\\
And the bad nights caused thereby.@@@
Changed lines 14-19 from:
* L1 is true → "L1 is false" is true \Rightarrow L1 is false \Rightarrow L1 is
both true and false.
* L1 is false \Rightarrow "L1 is false" is true \Rightarrow L1 is true \Rightarrow L1 is
both true and false.
to:
* L1 is true → "L1 is false" is true → L1 is false → L1 is both true and false.
* L1 is false → "L1 is false" is true → L1 is true → L1 is both true and false.
Changed lines 18-20 from:
\Rightarrow L1 is not true and L1 is not false.
to:
* Assumption #1 → L1 is not true and L1 is not false.
* Assumption #2 : if L1 is not true then it is false.
* Assumption #1 & #2 → L1 is both false and not false.
Changed lines 24-33 from:
* One might argue (though not everyone would agree)
that a sentence fails to be true or false if
has a false
fails to
still need to explain why L1 does not have a truth
4 Explanation #1 : truth-values require proper grounding
to:
* One might argue (though not everyone would agree) that a sentence fails to be true or false if (a) it has a false presupposition, or (b) the subject term fails to refer.
* But L1 does not seem to fall into either case. So we still need to explain why L1 does not have a truth value.
!!Explanation #1 : truth-values require proper grounding
Changed lines 30-40 from:
2 : The truth (or falsity) of a sentence
depends on something distinct from itself
Example :
* Whether "Socrates had red hair" is true depends on
the state of certain physical objects.
* But whether L1 is true or not does not depend on
anything else external to it.
to:
* Assumption #3 : The truth (or falsity) of a sentence depends on something distinct from itself (truth-makers).
**Whether "Socrates had red hair" is true depends on the state of certain physical objects.
** But whether L1 is true or not does not depend on anything else external to it.
Changed lines 34-56 from:
* What about "this is a sentence"?
* What about logical truths?
sentence whose truth depends on a fact that can be
expressed without using the concept of
* If only an example, what is the general definition?
* The proposal is not plausible if it is taken as a
general definition. Consider "Penguins do not have
the concept of truth."
* Perhaps what is meant is : the truth of a sentence
has to depend on some fact that is independent of
whether the sentence is true or false (Assumption #3).
* L1 fails this test.
* Also sentence L2 : "L2 is true."
to:
** What about "this is a sentence"?
** What about logical truths?
* Sainsbury : "an example" of proper grounding is a sentence whose truth depends on a fact that can be expressed without using the concept of truth.
** If only an example, what is the general definition?
** The proposal is not plausible if it is taken as a general definition. Consider "Penguins do not have the concept of truth."
** Perhaps what is meant is : the truth of a sentence has to depend on some fact that is independent of whether the sentence is true or false (Assumption #4).
** L1 fails this test.
** Also sentence L2 : "L2 is true."
Changed lines 45-61 from:
* If L1 does not have a truth-value, then we can draw
two conclusions
* (a) L1 is not true.
* (b) L1 is not false.
compatible with
So L1 is false after
and not false. So we have a contradiction, as
Sainsbury points out.
to:
* If L1 does not have a truth-value, then we can draw two conclusions :
** (a) L1 is not true.
** (b) L1 is not false.
** L1 says of itself that it is false. This is compatible with (a).
** But since (b) is true, it is false that "L1 is false." So L1 is false after all.
* So if L1 is neither true nor false, then L1 is both false and not false. So we have a contradiction, as Sainsbury points out.
Changed lines 54-62 from:
* Sentence L3 : "L3 is not true."
* L3 is true \Rightarrow "L3 is not true" is true \Rightarrow L3 is not true.
\Rightarrow L3 is not true \Rightarrow L3 is true
* L3 is neither true nor false\Rightarrow L3 is not true \Rightarrow L3 is
true
to:
@@@(L3) L3 is not true.@@@
* L3 is true → "L3 is not true" is true → L3 is not true.
* L3 is false → L3 is not true → L3 is true
* L3 is neither true nor false → L3 is not true → L3 is true.
Changed lines 61-69 from:
* The proper grounding theory as it stands cannot
solve the paradox.
* It is not clear how solutions which postulate
semantic defects in the liar sentences can deal
with L3 since a sentence with semantic defects
would not be true, which is what L3 says.
to:
* The proper grounding theory as it stands cannot solve the paradox.
* It is not clear how solutions which postulate semantic defects in the liar sentences can deal with L3 since a sentence with semantic defects would not be true, which is what L3 says.
Changed lines 68-72 from:
Footnote 3 of Sainsbury on page 113 says "This
derivation shows that one could not regard L1 as a
basis for a straightforward proof of G." What does he
mean by this claim?
to:
@@Footnote 3 of Sainsbury on page 113 says "This derivation shows that one could not regard L1 as a basis for a straightforward proof of G." What does he mean by this claim?@@