Copyright © 2004, S. Marc Cohen Revised 9/29/04
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12. Write these additional sentences:
Adjoins(a, b) FrontOf(a, b)
SameSize(a, b) Between(a, b, d)
13. Now play with the blocks (move them around) and verify the sentences (ctrl-F) each time
you move them. That way, you’ll see under what conditions these sentences are true, and
learn first-hand the meanings of the predicates. Write some more sentences, using the other
predicates in the blocks language, and continue to experiment.
14. You will notice, for example:
• Adjoins(a, b) requires that a and b be on squares that share a side; they cannot be
“diagonally” adjacent.
• FrontOf(a, b) requires no more than that a be closer to the front than b; it does not have
to be anywhere near b, or even in the same row or column.
• A sentence containing a name that does not name any block in a given world does not
have any truth value in that world. To make Between(a, b, d) have a truth value, we had
to assign the name d to one of the blocks in the world.
• Between(a, b, d) requires that a, b, and d be in a straight line: either in the same row,
column, or diagonal. Note that it is the first named block (a in the sentence above) that is
the one in the middle.
• If you try to move blocks in such a way that a large block adjoins another block, you
cannot do it! In Tarski’s World, no large block can adjoin any other block. (That is
because the large blocks are so large they overlap their borders and infringe on the
adjacent block.)
• SameSize(a, a), SameShape(a, a), SameRow(a, a), SameCol(a, a), and a = a are
always true.
• Larger(a, a), Smaller(a, a), Adjoins(a, a), FrontOf(a, a), BackOf(a, a), RightOf(a,
a), LeftOf(a, a), and a ≠ a are always false.
•
Between(a, a, a), Between(a, a, b), Between(a, b, a), and Between(b, a, a), etc. are
always false. A Between sentence cannot be true unless it contains three different
names. (Although even then it may still be false.)
15. These facts all express features of the meanings of the predicates in the blocks language,
which closely (although not exactly) match the meanings of their English counterparts. For
example, it is part of the meaning of larger than that a thing cannot be larger than itself; it is
part of the meaning of is in the same row as that a thing cannot fail to be in the same row as
itself.
16. The predicates of the blocks language are determinate, not vague. There is no gradation of
sizes between small and medium, and any two objects that are both are small are considered
to be of the same size. Hence, every sentence of the blocks language is either true or false.
Nor are there degrees of truth and falsity—a sentence is either (entirely) true or (entirely)
false, and no true sentence is “truer” than another.
Be sure to do the You try it on p. 24.