T2.2: 7 of 7
Good, let's review the connectives before moving on to adding names. You can also find this table in the Chapter 2 Reference (so you need not print it out now).
|Connective Name||Resulting Sentence Type||Component Names||Typical English Versions||English Statement||Symbolization in SL|
|&||Ampersand||Conjunction||Conjuncts||"and", "both ... and ... "||Agnes and Bob will attend law school.||A&B|
|>||Horseshoe||Conditional||Antecedent, Consequent||"if ... then ... "||If Agnes attends, then Bob will.||A>B|
|~||Tilde||Negation||Negate||"it's not the case that", "not"||Agnes will not attend law school.||~A|
|v||Wedge||Disjunction||Disjuncts||"or", "either... or... "||Either Agnes or Bob will attend law school.||AvB|
|=||Triple Bar||Biconditional||Bicomponets1||"if and only if", "just in case"||Agnes will attend law school just in case Bob will.||A=B|
Look carefully at this table to make sure you've caught the basics...then on to names and predicates as we try to disect the atomic sentences a bit .
Names and Predicates
We'll continue to think about connectives and compound sentences. But we can also symbolize the names that occur in sentences.
So far in this tutorial, we have symbolized simple sentences (like "Agnes will go to law school") with a single symbol.
But at other times we'll want to break an English sentence up to analyze it.
We'll use lower case letters as proper names of our symbolic language to stand for objects. So, we might take 'a' as a name of Agnes. We'll typically set out our definition of a proper name, an interpretation, this way:
In such a case, we will say that 'a' refers to Agnes.
And we'll use upper case letters as predicates or to stand for kinds, properties, or just incomplete thoughts (corresponding to incomplete sentences). So, we could use 'L' to stand for "will go to law school". Because predicates are something like incomplete sentences, we'll write their interpretation with a blank:
L_: ___ will go to law school.
Agnes will go to law school
can be symbolized simply as
Yes, it's a little backward from the English. But we'll get used to it! You may want to read this as "Go to law school will Alice". But I suspect it's best to just read 'La' and say to yourself "Alice will go to law school."
In addition to representing predicates, we will somtimes still to use upper case letters to stand for simple English sentences when there are no names or predicates to do the job. You'll be able to tell from context.
'La' counts as a new sort of atomic sentence. Let's see what we can build with it.
1. Agnes will go to law school and Bob will go to law school.
Before we had names in our symbolic language, we would symbolize 1 simply as 'A&B'. If our interpretation so defines 'A' and 'B', then this is fine.
But when we have 'a' as a name for Agnes and adding 'b' as a name for Bob, we can symbolize 1 as
2. If Agnes will go to law school, then she will be miserable for the first year.
can be symbolized as:
(Hint: if this still looks confusing, enter a question mark in a field, i.e., in one of the boxes, then hit the TAB key to get the answer. For this little quiz, you'll be entering things like "La>Mb". AND you can learn alot by making mistakes and trying to correct them. If at first everything seems a little confusing, do the problems, get them wrong, redo and see if the material doesn't get clearer.)
a: Agnes, b: Bob
L_: ___ will go to law school.
M_: ___ will be miserable.
Don't forget that the greater than sign is for the horseshoe AND the '=' sign for the triple-bar.