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Autobiographical subject matter: This section will focus on a future goal or aspiration. It can be an educational, professional, or personal goal. Choose a goal you have for at least a year or two in the future.
Logical skills involved:
- Expressing conditional claims in propositional logic
- Using the conditional derivation rule in a proof
Worksheet instructions: State your goal as an atomic sentence. Choose a letter to represent it, and add it to the key.
Think of an initial activity or condition that would help you start making progress toward that goal. Choose a letter to represent it, state it as an atomic sentence, and add it to the key.
Write a chain of three conditionals that expresses a sequence of steps that you anticipate needing to take in order to accomplish the goal. Make a key and give the form of the three conditionals.
- The antecedent of the first should be the initial activity that you just identified above.
- The consequent of the first should match the antecedent of the second.
- The consequent of the second should match the antecedent of the third.
- The consequent of the third should be the goal that you stated above.
Making this chain of conditionals will require adding two more atomic sentences to your key. Then give the form of those three conditionals.
Give a formal proof in which the three conditionals in the chain are premises. The conclusion of your proof should be a conditional stating that if the initial activity/condition is met, then your goal follows. Derive the conclusion using the conditional derivation rule. No additional premises should be needed.
Advice and things to keep in mind
You may find it easier to draft your chain of three conditionals in English first, then put them in symbolic form and fill out the key. Just the key, symbolic forms, and proof are on the worksheet, but be sure your chain of conditionals makes conceptual sense before formalizing it!
Of course, in life there are often many different steps one could take while aiming to accomplish a certain goal. There is no need to capture all the possibilities; just use the sequence of conditionals that seems most realistic, sensible, or promising to you.
Goal or Aspiration Worksheet
GOAL:
INITIAL ACTIVITY:
KEY:
_____ = ________________________________________________________________
_____ = ________________________________________________________________
_____ = ________________________________________________________________
_____ = ________________________________________________________________
CONDITIONAL FORMS:
- __________________
- __________________
- __________________
PROOF:
