@fast,
fast;117402 wrote:
Sometimes, the word "believe" is the word of choice by those that know but fear to claim knowledge. A person that sees that proposition X is the same as proposition Y may fear saying so and claim instead that they're equivalent, but I suspect that you even deny that proposition X and proposition Y are equivalent (let alone the same).
The sentence, "Sandy bit Charlie" is not the same as (nor equivalent to) the sentence, "the girl with the red hair sunk her teeth down into the guy with square glasses," but what can be meant by the expression of those sentences in certain unique situations can be the same (or at least very similar), so what can be expressed by a person (or different people) uttering those sentences (making statements) can be the same. There is certainly more to a statement than a sentence.
For example, the first eyewitness said, "Sandy bit Charlie," and the second eyewitness said, "the girl with the red hair sunk her teeth down into the guy with square glasses." It is clear to all involved that both eyewitnesses are referring to the same girl and guy and mean virtually the same thing by what they say. The statements made to the cop by the eyewitnesses are virtually the same (yet each used different ways to express the same proposition), or at the very least, they are consistent. We have two people (and not just one person) saying that the girl bit the guy.
What's up with the italics?
The two sentences in your example have the same referents, but they do not mean the same. You can see this by making up a possible scenario where they differ in referents. That's your exercise for tomorrow. :p
---------- Post added 01-05-2010 at 11:29 PM ----------
fast;117412 wrote:Maybe the word, "logically" is throwing me. It seems to me that two different statements can be the same or similar or altogether different. If something is close to being the same but not quite the same, then I might say they're similar. What does "logically equivalent" mean anyway if not similar?
Logical equivalence
P and Q are logically equivalent iff P logically implies Q and Q logically implies P.
Logical implication
P logically implies Q iff there is no possible world where P is the case and where Q is not the case.
Keep that in mind.
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This is, BTW Fast,
yet another thing you could have learned if you had just read the book I referred you to to begin with. Here I will do it again: Swartz and Bradley,
Possible Worlds, 1979.
As for you Z. This is a reason to learn from that particular logic textbook. It covers a lot of things that you have been discussing on this forum. Maybe you ought to start with it. Tho I admit that it is kinda technical and it took me a while to read it. It was
the book that taught me the most.