Re: In need of the all-out revision of symbolic logic



Charlie-Boo wrote:
herbzet wrote:
Charlie-Boo wrote:
Eukie_M_SHIRAISHI wrote:

In the Fregean Theory of Logic (the standard theory of logic in the
20th century),
?p implies q? has had been defined to mean ?not-p or q?.

Here let P be ?A lion is a mammal? and Q be ?A lion and a whale are
both mammals?
It is clear that Q implies P but P does not imply Q.
Hence ?P implies Q? is a falsity.
On the other hand, ?not-P or Q? is a truth.

You're mixing meanings - being inconsistent in how you interpret these
sentences.

Do you mean that the OP is using a word in different senses in
different sentences? Which word in which sentences?

Add quantifiers to show we are talking about our world vs. all worlds.

How is the OP being inconsistent in how he interprets these sentences?


It is not true than in all worlds if P is true then Q is true.

Do you mean "It is false that P implies Q"?

Do you mean "It is false that P implies Q"?

It is true that in our world if P is true then Q is true.

Do you mean "It is true that P implies Q"?

Do you mean "It is true that P implies Q"?

You could still formalize this distinction, however.

What name would you use in the two cases to describe the relation
between P and Q?

What name would you use in the two cases to describe the relation
between P and Q?

What would you call the case when it is not true that in our
world if P is true then Q is true, but it is true in some
worlds that if P is true then Q is true?

What would you call the case when it is not true that in our
world if P is true then Q is true, but it is true in some
worlds that if P is true then Q is true?


Therefore, it is a mistake to define ?p implies q? to mean ?not-p or
q?.

Since implication is one of the most fundamental concepts in logic,
all-out revision
is needed in the Fregean Theory of Logic.

Have a look at the following Web site:- <http://www.age.ne.jp/x/eurms/
PNG/Key/Honron-2.html#02-2>- Hide quoted text -

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hz
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