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## Wireless Philosophy

### Course: Wireless Philosophy>Unit 2

Lesson 3: Language

# Language: Conditionals, Part 2

Justin Khoo invites us to think about conditional sentences ("if P then Q"). Perhaps surprisingly, the question of what these sentences mean has vexed philosophers for thousands of years. In part 2 of the series on conditionals, Justin discusses some of the challenges facing the material conditional theory.

Speaker: Dr. Justin Khoo, Assistant Professor, M.I.T.

## Want to join the conversation?

• Would "I think, therefor I am" be considered a conditional statement? If so, when I use it in a truth table it seems not to make sense on the third line. I think(false) ---> Therefor I am(true)= True? Is it true because in the statement saying "I am" is true, makes it true?
(1 vote)
• Any argument may be rendered into a conditional - read a book on logic to find out.

The argument ''I think. Therefore I am'' can be rephrased into a conditional as IF I think, THEN I am.

Look at the meaning of this conditional. It asserts: given ''I think'' is true, ''I am'' MUST BE true.
Note the conditional statement does NOT assert anything about the situation ''I think'' is false. Therefore, any situation in which 'I think' is false lies outside the claim of the conditional. Thus all situations in which ''I think'' is false CANNOT falsify the conditional. Well, if something CANNOT be false, it MUST BE true. Thus, the situation you describe: I think (false), I am (true) makes the conditional true. This is how I understand it. Does it work for you?
• Also how do you know what to write in the last column of the truth table
• The sum of the measures of complementary angles is 90. Write if then form
(1 vote)
• There is a problem with the coding in the captions. You probably put the <br> element in the part that shows the captions.
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• Im confused about the material conditional theory; with the two parts to it. Im confused about using "and" and using "or"
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• Concerning the section beginning at :
I've been thinking about the suggestion of a paradox in the Material Conditional Theory. Essentially, what Justin's argument boils down to is "If A, then not A". I believe he errs in assuming that this statement is false; consider that we assume not A. Then, logically and from our truth table, if we assume our antecedent to be false, then regardless of the truth value of our consequent, we must conclude that our statement as a whole is true. So, essentially, I see an error in Justin's reasoning that the initial "f, then" statement is false. If we assume "God does not exist", then our antecedent is false, which makes our "if, then" statement true (and therefore contradicts the suggestion that the statement is false. I think a better statement would have been "EITHER our statement is FALSE (and therefore our antecedent is TRUE, as shown in this video), OR our antecedent is FALSE". And so it is shown that our antecedent may be either true or false, which does not create a paradox nor argue either way for the existence of a god.

Does anyone else have thoughts on this matter or can anyone clarify, refute, or argue for the presented paradox? I'm not sure I've worked through the reasoning properly (I'm new to using logic in the philosophical sense!).
(1 vote)
• I think you're mistaken at the last part of your argument. P = god exists; -P = god doesn't exist. You're correct that if P is set to F in the truth table, then "P -> -P" is set to T.

However, we also know from reasoning that P -> -P can not be set to T. P -> -P intuitively is F.

Therefore, we have to accept a situation where P -> -P is set to F, and the only situation where that happens according to Material Conditional Theory is the one where P is T and -P is F. And if P is T, then God must exist.
(1 vote)
• High school math conditional proof
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