Exercise 3.18 Question

I am struggling to find a sentence that is equivalent to (a = d) without using the identity symbol. I know I need to find a sentence that can not be true of two different blocks, but I am not sure I understand how else to indicate that one block has two names. Is there another way I should be thinking about this sentence?

4 thoughts on “Exercise 3.18 Question

  1. Clayton Hucks

    Hi! I know this is after the deadline (sorry) but I still think it important to share for future assignments. This one stumped me for a bit too but then I realized what it truly meant to be equal in Tarski’s world. For example, let’s pretend these letters are people: Ben and Benjamin. Let’s say we need to prove that Ben=Benjamin. If this is a dorm building and Ben is in his room, that mean that Benjamin is in the same room. In order to be in the same room, you must be on the same floor and in the same “row” position on the hallway. Now think of this in terms of Tarski’s world… there are rows and colmuns. If a=d, that means they are both in the same….. 🙂

    Hope this helped!

    Best,
    Clayton

  2. Isabel Larson

    Hi Isabel! Think about what it means for two shapes to be the same in Tarski’s world. What properties must they share? Try to break equivalency up into its components and think about how you would write those individual elements rather than grouping them all together under the equals sign. Hope this helps! -Isabel

  3. Carlos Serrano

    This one stumped me for a bit too, but I think I managed to figure it out. Think of it this way; if a = d WAS true, it means that a and d must be the same block. Is there any other way to express this without simply writing d = a? Think of what a = d means in terms of location on Tarski’s World. If they were the same, they’d have be in the same row AND column.

    Hope this helps. If anyone else want to help or correct me if I am wrong please feel free.

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