A. Modal Logic
What is it?Traditional Logic has two values- true and false. (Binary Logic)
Modal Logic- refers to three value logic. The three values are true, false, and modality (Modality being necessity, and possibility/impossibility).
Some propositions are contingently true (Meaning it must be true). Others are necessarily true (Meaning things could have been different).
Turning the words into language of Possible Worlds helps that possibility factor be understood.
Heuristic Device: teaching tool. Sort of a metaphor for helping us understand things. Example: styrofoam models of the solar system.
The doctrine of possible worlds is a heuristic device. It's not meant to be literal or straightforward.
B. Review on Propositions
Difference between a sentence and a proposition. Propositions are best understood as the meaning of a sentence.Example:
John is the husband of Mary.
Mary is John's wife.
Clearly, these aren't the same sentence, but the meaning (proposition) of both of them is the same. They share the same truth.
Truth is a property of propositions.
Another example- Languages. Ordering between English and Spanish/German/French are different, but the proposition can be the same. Even if word choice is different, because of synonyms the essence of a sentence can be preserved.
C. State of Affairs
Example:Sentence: GW Bush is president in 2001. (Remember, that's when this lecture was recorded)
State of Affairs: GW's being president in 2001.
In order to turn a proposition (Or truth from a sentence) into a "State of Affairs", first make the subject possessive and then change the verb to gerrant ("is" turns to "being").
State of Affairs is really just the reality which is referred to by the proposition.
When the State of Affairs is true, we say it "obtained". When it is false, it did not "obtain".
Nash says here-
Most of this stuff is common sense/Not hard to figure out. The biggest part is vocab. (I sort of disagree... I think it gets a bit heavy at times, but he's a philosophy doctor, and I'm a junior in highschool...)
D. Eternal Entities
Claim- propositions and states of affairs are eternal. (Regardless of being true or false. They are eternally one of those).For example: The Cleveland Indians won the 1948 world series. (Nash likes the Indians)
This state of affairs can't be changed or erased. It has always existed in the mind of God.
It's the same thing as the number one, or the pythagorean theorem.
What about "now" statements? Can the be eternal?
Yes, because "now" refers to a state of affairs at a specific point in time, not the continual state of affairs in a constant "now" state.
For example:
I am typing right now.
This state of affairs in this proposition is this: My doing the action of typing in this specific point in time. The proposition is not saying that "now" is whenever the proposition is read- because then it has no chance of being true. The "now" refers to 7:53 pm on Friday, October 5th, 2012. Because of the time parameter, this state of affairs is eternal.
Other factors play into the truthfulness of a state of affairs. Some propositions are true, but they haven't closed off those possibilities yet, so they feel false. For example- The dog is barking. This could be a true statement, but because I haven't elaborated, you have no reason to believe it. However, if I were to say, "My dog charlie is barking at 8:32 am on Saturday morning, October 5th, 2012, in Indianola Iowa, United States of America, Planet Earth." There really isn't any room for another possibility. That state of affairs is eternal- it has always existed in God's mind.
My bit:
This possible worlds thing is pretty cool. I don't know how people sit down and think up this stuff. (I'm not saying they make it up, just that they process/discover it). It blows my mind. It's not too difficult to understand, I mean- it's just another metaphor, but to be a pioneer for this kind of thinking- that's impressive.More to come on Possible Worlds in the Next Post. Stay tuned, I think a bit of application is on the way. :)
Is this what he meant when he said the number 'one' was eternal? If so, he is using the word 'eternal' in a different way than I would normally use it. Perhaps it is a bit of philosophic jargon. I mean each place has their own set of jargon. Jargon isn't bad. To people who understand it, it makes communication easier. But to those of us who don't use the word that way, it makes the communication tougher.
ReplyDeleteSo he uses the word 'eternal' to refer to a very specific statement of something that is happening at a specific time. And this statement could either be eternally true (or just true) or eternally false (or just false). If he is using the word 'eternal' this way, then what would be an example of a claim that is not an 'eternal' claim?
Ya, sometimes he uses jargon that doesn’t get fully explained, and it can make things difficult.
ReplyDeleteI interpreted his use of ‘eternal’ as a property of propositions, regardless of time frame. So whether something was at a specific point or not, it could still be an eternal state of affairs. I would sort of disagree with the ‘just’ true or false part. Following Nash’s train of thought (I may be wrong here), since being eternal is a property of truth or falsehood, if something is true or false, it would be eternally so.
Since he uses the state of being eternal as a property of propositions, the existence of a finite claim would depend on what you meant by ‘claim’. If the claim was a proposition, there would be no way for it to be finite. If it was not a proposition however, it wouldn’t be necessarily eternal (Not to say that it isn’t, just that it wouldn’t have to be). Now, my question for Nash would be the same as yours, What in the world would be an example of something that isn’t a proposition (and therefore a finite statement)?
Let me get your thought on this: How would you define the word 'proposition' ?
ReplyDeleteA statement that is either true or false... and in the case of Modal logic- possible or impossible. (But it has to be verbalized... so maybe non-propositions would include not-verbalized things? Like Moods, Attitudes, etc. ??)
ReplyDeleteHow about " The show is funny. " It could be either true or false, I suppose.
ReplyDeleteThats true. It would vary from person to person depending on their world view.
ReplyDelete