When already died (I guess you mean dead?), saying the he cannot die, sounds like some tautology or meaningless proposition to make. — Corvus
Not sure about not legitimate - never came across that term in the Logic books. — Corvus
When socrates died, he has already died, so the premise that socrates couldn't have died when he died seems invalid. — Corvus
nor did he die when he was dead, since he would have died twice. — Sextus Empiricus
When someone is already dead, it is not valid to declare, he cannot die. — Corvus
Is the mooted standard Metre Rule, the one in Paris from which all others are copied, a metre long? How could you tell - by measuring it against itself? But that's not performing a measurement. — Banno
Did the 'postmodern condition' actually happen? — Kenosha Kid
At a point before the election, with 'win's understood as 'will win', then R v A is true.
At a point after the election, with 'wins' understood as 'won', then R v A is true. — TonesInDeepFreeze
It's just a case of the so called “paradoxes of material implication”. — Amalac
That is incorrect. To accept a proof does not require accepting the truth of the premises. — TonesInDeepFreeze
It only proves G is true if all the axioms used in the proof are true. So, since G is an axiom used in the proof, if it is false, then, though we have proved G, we have not proved that G is true. — TonesInDeepFreeze
No, it's not just an assertion. It's a theorem about propositional logic. And it is reducible, in a sense, to a theorem about Boolean algebra. And its proof is reducible to finitary operations, which are reducible to auditing the execution of an algorithm. So (heuristically speaking) we may say that at the root of the question is ability to audit the execution of an algorithm. Of course, it's hard to imagine such an ability in a person who was so delusional that they claimed to witness '0' and '1' written in the same space when only one of them was written in that space. But that is not the same as going all the way back up the chain of reductions I just described to say that LNC must be an axiom. — TonesInDeepFreeze
I recommend 'Logic: Techniques Of Formal Reasoning' by Kalish, Montague, and Mar. Within about a chapter you could assign yourself the easy exercise of deriving LNC in the natural deduction system there. — TonesInDeepFreeze
If you do nothing to the baby, it exists. — TheMadFool
Ergo, if it doesn't exist, you did something to the baby! — TheMadFool
Crying, wet and pouting lips searching for the mother's breast for milk. — TheMadFool
Fetus aborted. No crying, no wetness, no pouting, in short no actual baby — TheMadFool
If nothing was done to an actual baby where is the baby? — TheMadFool
X aborts the fetus. X doesn't give birth to the baby
X did something to the fetus. Something happened to the baby — TheMadFool
In other words, it's not possible that X can do something to the fetus & X can have a baby (that's what abortion is all about). — TheMadFool
If you say that doing something to the fetus does nothing to the baby then this should be possible: X does something to the fetus & X can have a baby (like X did something to the tooth and X can have a baby). This is impossible. — TheMadFool
Ergo, To do something to the fetus implies to do something to the baby. — TheMadFool
Not to do something to the baby implies not to do something to the fetus. — TheMadFool
I can't do anything to the actual baby if I have an abortion i.e. if I destroy the fetus. — TheMadFool
an actual baby should be born even if I destroy the fetus. — TheMadFool
So, if I destroy the fetus, I destroy the baby. That's what I meant from the get go. — TheMadFool
Non sequitur/ straw man, that's not another way of saying that at all.
Obviously, if a woman wants to have a baby, she must not destroy the fetus that she plans on having become a baby (the baby that the fetus will become), but that doesn't mean that destroying the fetus has effects on some non-existent baby.
Anyway, here's a consecuence of your “argument”:
1. Doing something to the potential tree (seed) implies doing something to the actual tree.
2. If 1 were false, destroying the seed should have no effect on the tree, which is just another way of saying that you could destroy the seed and still grow a tree (the tree that the seed would have become if it hadn't been destroyed).
3. Therefore, since 2 is preposterous, cleaning scattered seeds in a garden is deforesting, and should be punished in the same way as burning the same number of trees. — Amalac
1. Doing something to the potential baby (fetus) implies doing something to the actual baby. — TheMadFool
If 1 were false, destroying the fetus should have no effect on the baby — TheMadFool
which is just another way of saying you could destroy the fetus and still give birth to the baby. — TheMadFool
Destroying the fetus, destroys the baby, no? — TheMadFool
Remember, a woman's concern is the actual baby — TheMadFool
To do something about the actual baby, the woman does something to the potential baby — TheMadFool
It's crystal clear to me as it should be to you. — TheMadFool
What I was aiming at is that logic is the handmaid of what is the case. One of the things we do with language is that when it doesn't seem to show us what is the case we change what we are saying.
DO you agree with that? — Banno
That's a very silly question. I don't know it, since it is not the case, and I can't know that which is not the case. Are you trolling me?
Or maybe you meant to type: How do you know that they also don't prove it is not a theorem? — TonesInDeepFreeze
That's one notion. But another definition of 'axiom' is purely syntactical. — TonesInDeepFreeze
The proofs can be mechanically audited whether the auditer knows of LNC as an axiom or not. Indeed, even for everyday reasoning, probably most people haven't even heard of LNC, especially the notion of it is an axiom. And that does not contradict that good reasoning (other than dialethistic) conforms to LNC and sometimes uses it - either as an explicit or implicit principle. — TonesInDeepFreeze
It is fine to have it as a logical axiom, since it is logically true. Sceptics should learn that it is logically true. — TonesInDeepFreeze
First, it is possible for one to assert and deny a proposition. And it is even ubiquitous that people assert propositions that are inconsistent with other propositions. So probably what you mean is that it is not possible to be correct while both asserting and denying a proposition. Then your question seems to be how do we know that contradictions are not the case. But the question of how we know things is different from the question of what axioms we choose. We may know that a proposition is true by reasoning from different axioms that each yield the proposition as a theorem. It is not required that LNC be one of the axioms. If, as we ordinarily do, we require a system that is complete in the sense of proving all validities then it is only required that LNC at least be a theorem even if not an axiom. — TonesInDeepFreeze
I think this because logic is about what we can say, and not about the way things are — Banno
I think this because logic is about what we can say, and not about the way things are. — Banno
The belief in the law of contradiction is a belief about things, not only about thoughts.
His “only” implies that he holds that the belief in the Law of Contradiction is both about thoughts and about things. — Amalac
But no difference between Amalac and Amalac. — Banno
Even as Amalac is both a word and you. — Banno
They prove it as a theorem. Of course, our motivation for the system would include proving it as a theorem. — TonesInDeepFreeze
Talk meaningfully" is a large and undefined rubric. — TonesInDeepFreeze
Not all proofs use the law. Indeed, the law is not even usually one of the logical axioms. — TonesInDeepFreeze
(1) Trivial. If the law is an axiom then it also provable by the rule of putting an axiom on a line. — TonesInDeepFreeze
Perhaps it would help to think of it like this: Russell supposes that either the law of noncontradiction is a fact int he world or a figment of language. — Banno
The belief in the law of contradiction is a belief about things, not only about thoughts. — Russell
Even as Amalac is both a word and you. — Banno
But perhaps the best way to proceed would be for you to set out exactly what you think Russell's argument is in the piece you quote; because I don't see an argument there — Banno
When we have seen that a tree is a beech, we do not need to look again in order to ascertain whether it is also not a beech; thought alone makes us know that this is impossible. But the conclusion that the law of contradiction is a law of thought is nevertheless erroneous. What we believe, when we believe the law of contradiction, is not that the mind is so made that it must believe the law of contradiction. This belief is a subsequent result of psychological reflection, which presupposes the belief in the law of contradiction. The belief in the law of contradiction is a belief about things, not only about thoughts. It is not, e.g., the belief that if we think a certain tree is a beech, we cannot at the same time think that it is not a beech; it is the belief that if the tree is a beech, it cannot at the same time be not a beech. Thus the law of contradiction is about things, and not merely about thoughts; and although belief in the law of contradiction is a thought, the law of contradiction itself is not a thought, but a fact concerning the things in the world. If this, which we believe when we believe the law of contradiction, were not true of the things in the world, the fact that we were compelled to think it true would not save the law of contradiction from being false; and this shows that the law is not a law of thought. — Russell
1. If you destroy the fetus then you destroy the baby (that's what abortion is - potential) — TheMadFool
2. If you can't destroy the baby then you can't destroy the fetus (1 contra) — TheMadFool
7. If you destroy the seed then you destroy the tree (potential) — TheMadFool
8. If you can't destroy the tree then you can't destroy the seed (7 contra) — TheMadFool
11. If a seed is not a tree then you can destroy the seed (your claim) — TheMadFool
Yes but the value of a seed lies in its potential (tree), not in itself. — TheMadFool
"It is both a wave and a particle"; — Banno
That's a different question. A possible world comes about as the result of a "what if..."; then we can see if that "what if..." leads to a consistent story or not. If it is inconsistent, then there can be no such possible world.
That is, logic gives us a grammar with which to judge our statements. — Banno
Possible worlds are constructed by fiat, not discovered. — Banno
So do the proofs you mention indeed first prove there exists a unique individual with such and such properties that is then named 'God'? — TonesInDeepFreeze
Especially, one can't just assert without proof that there does exist a unique individual having certain properties and then go on to demonstrate that that individual then has other properties for a QED. — TonesInDeepFreeze
But it would mean something like: Necessarily, there exists/is an x (God), such that a (the greatest conceivable being/ subject of all perfections) = x. — Amalac
How does a system of modal logic talk about its own semantics? I'm not saying it can't be done, but I'd like to know how it works. — TonesInDeepFreeze
That strikes me as being an additional premise. Of course we can't rule out that additional premises have consequences. — TonesInDeepFreeze
The actual world is one among the possible worlds (this again follows in some systems of modal logic). If one admits that god exists in all possible worlds, that would imply that god exists in the actual world.
And so, if one accepts that it is possible that it is necessary that god exists in all possible worlds (meaning: in some possible worlds, necessarily God exists in all possible worlds), then it follows that in all possible worlds, god exists in all possible worlds, and therefore “god exists in all possible worlds” is true in the actual world, which is one of the possible worlds in which that statement is true, and therefore god exists in the actual world.
All this follows if one accepts system B of modal logic, from the corollary of axiom B (if the modal ontological argument is valid):
◇□X → X (If it is possible that it is necessary that X, then X is the case).
Likewise in system S5, the corollary of axiom 5:
◇□X → □X — Amalac
Now, suppose an individual is a member of a certain universe, of course that individual is not a member of certain other universes. So, yes, there is no individual that is a member of every universe. — TonesInDeepFreeze