No, your reading of it is incorrect because you seem to think it is saying:
All dogs have four legs
Lassie has four legs
Lassie is a dog
...is valid in symbolic logic. It doesn't say that. It says the exact opposite, that this is not valid. — Count Timothy von Icarus
If in a given interpretation, P is true, then per that interpretation, for any statement Q, Q->P is true. — TonesInDeepFreeze
"Dogs have four legs, and Lassie has four legs, therefore Lassie is a dog" is not a valid argument. The conclusion ("Lassie is a dog") may be true, but it has not been proved by this argument. It does not "follow" from the premises.
Now in Aristotelian logic, a true conclusion logically follows from, or is proved by, or is "implied" by, or is validly inferred from, only some premises and not others. The above argument about Lassie is not a valid argument [correct -TIDF] according to Aristotelian logic.Its premises do not prove its conclusion. And common sense, or our innate logical sense, agrees. [correct -TIDF] However, modern symbolic logic disagrees. [incorrect - TIDF] One of its principles is that "if a statement is true, then that statement is implied by any statement whatever."
modern symbolic disagrees that the Lassie argument's premises do not prove the conclusion. — TonesInDeepFreeze
That is what the paper says. The paper is incorrect. — TonesInDeepFreeze
There's a paper that says the premises prove the conclusion of this argument? — flannel jesus
It's quoted in a post earlier in this thread. — TonesInDeepFreeze
Dogs have four legs, and Lassie has four legs, therefore Lassie is a dog" is not a valid argument. The conclusion ("Lassie is a dog") may be true, but it has not been proved by this argument. It does not "follow" from the premises.
Now in Aristotelian logic, a true conclusion logically follows from, or is proved by, or is "implied" by, or is validly inferred from, only some premises and not others. The above argument about Lassie is not a valid argument according to Aristotelian logic. Its premises do not prove its conclusion. And common sense, or our innate logical sense, agrees. However, modern symbolic logic disagrees. One of its principles is that "if a statement is true, then that statement is implied by any statement whatever.
In fact it says it isn't valid tout court up above. — Count Timothy von Icarus
If that was the point, it could have been stated much clearer — Count Timothy von Icarus
If they wanted to make the point you ascribe to them why wouldn't they use an example like:
All monkeys have tails.
Garfield the cat has a tail.
Therefore Garfield is a monkey. — Count Timothy von Icarus
I somehow find it more plausible that they were trying to highlight the incongruity between the fact "Lassie has four legs" does not imply Lassie is a dog in symbolic logic in the argument:
All dogs have four legs
Lassie has four legs
Therefore Lassie is a dog
And the fact that "Lassie has four legs" does imply Lassie is a dog if "Lassie is a dog" is true. — Count Timothy von Icarus
the straightforward purpose given the context — Count Timothy von Icarus
the text is not particularly hostile towards symbolic logic aside from arguing that it isn't particularly helpful for most people's use cases. — Count Timothy von Icarus
This, rather than assuming they are trying to imply an falsehood to cast shade on symbolic logic in an extremely roundabout way using an example obfuscates their point (if that was the point they were making)—doing all this to try to suggest something that is easily verifiable as false for ... what purpose? — Count Timothy von Icarus
IDK, maybe I am letting the principle of charity run amok. — Count Timothy von Icarus
In fact it says it isn't valid tout court up above. — Count Timothy von Icarus
"Winston Churchill was French" does not imply a contradiction. But that does not imply that "Winston Churchill was French" is true. — TonesInDeepFreeze
As in the concept/meaning of self as "that which is purple and square" vs. "that which is orange and circular" or any some such? And this in relation to "there both is and is not a self"? — javra
This makes no sense to me. — Janus
That said, the self has no definitive definition, so introducing such a thing in the context of discussing whether anything could be the same in different contexts or thought under different perspectives seems incoherent from the get-go. — Janus
Consider the following substitutions which do not suffer from such ambiguities: Render (A implies B) as "the presence of water implies the presences of oxygen" and (A implies notB) as " the presence of water implies the absence of oxygen": do the two statements not contradict one another? — Janus
"the presence of water implies the presences of oxygen" and (A implies notB) — Janus
the proposition that A entails both B and notB will be logically contradictory — javra
Would allow simplifying that to:
For any statement A, it is not the case that both A and not-A. — TonesInDeepFreeze
If I understand, you take
It is not the case that both water can be green and water can be not-green.
as an instance of the law of contradiction. (?) — TonesInDeepFreeze
An interpretation, aka 'a model'. — TonesInDeepFreeze
But that does not imply that "Winston Churchill was French" is true in all interpretations, but it does imply that "Winston Churchill was French" is true in at least one interpretation. — TonesInDeepFreeze
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