Tarski's World

The program Tarski's World is located at /LocalApps/math/tarski.

The exercises are located in /LocalLibrary/Tarski/NXercise.

Open the Tarski program. Click on file in the upper left hand corner; then on open.

Select open; select world; navigate through the directories to /LocalLibrary/Tarski/NXercise and then click on wittgens.wld.

Select open; select sentences; navigate through the directories to /LocalLibrary/Tarski/NXercise and then click on wittgens.sen

The formal sentences like Large(a) describe properties which may or may not be true of the named object in Wittgenstein's world. Consider the inspector on the lower hand corner of your screen. To see whether an expression is true actually has three stages. First you must see if it is well-formed . (For example if Large was supposed to describe a single object, Large(a,b) would not be well-formed). To check this click yes or no for wff ( well-formed formula) and click on verify to check your answer. Then check whether the expression is a sentence (either true or false: 2x = 3 is not a sentence because its truth depends on the choice of x). Finally, in the third line check whether it is true. Do this for various sentences in Wittgens.sen. You can also make new sentences or modify the ones given using the keyboard in the upper right. After you are comfortable with these sentences and world proceed to the next task.

Problem 1. Open Lestrade.sen and Lestrade.wld. You will notice that none of the objects in this world has a name. Your task is to assign them names in such a way that all the sentences in Lestrade.sen come out true.

To assign names; click on sentence in the inspector window and choose block. Now click on one of the blocks in Lestrade's world. It characteristics will appear in the inspector window. Now you can click on a letter to name the block.

Problem 2. How many of the names you chose in Problem 1 were forced on you? That is how many of the names could you have assigned to other objects and had all the sentences come out true.

Homework 1. Do the Ox expressions for homework assignment that is handed out.

Homework 2: Go to the lab and open Austin.sen and Wittgens.wld. Evaluate each of the 6 sentences; write the sentences in a column on a piece of paper and write the answer (T or F ) next to each sentence. Guess what would happen to some of the sentences if you rotated the world. Now rotate the world (go to display and press either rotate left or rotate right.) Now write down the truth values of each sentence in the rotated world in a second column. (You can do this more easily by clicking on edit and then verify all but first record your reading so you can check what these predicates really mean.) Rotate the world again (in the same direction) and check the values. Repeat until the world has come a full circle.

Are there any patterns in your table. Are any sentences always true or always false; can you explain why? Can you explain why some rows alternate in value and others have three falses and only one true. (These are really geometry questions; not logic questions). Write down in English a definition of when Frontof(a,b) is true (in terms of the rows and columns that a and b are on.