Truth Table Word Problem [Mathematics: Liberal Arts]

**Politicians argue in favor of positions all the time. The key to being an informed voter is to listen carefully to the arguments made.**

a)Find two simple logical arguments made in the last Presidential election

b)Write these arguments in symbols (define variables)

c)Use truth tables to analyze the arguments and determine if they are valid.

Please I am having so much difficulty with this!

Re: Truth Table Word Problem [Mathematics: Liberal Arts]

This may look like a cute problem that demonstrates relevance of formal logic in everyday life, but I think this relevance is overestimated. I doubt that even in politics it is easy to find an argument that is wrong from the standpoint of propositional logic. On the contrary, I found that when people invoke and stress formal logic during a discussion of subtle and complicated topics like politics and religion, they are oversimplifying things. The reason for the difference of opinions in these areas is not that people don't know (at least intuitively) or disagree on the law of excluded middle or contraposition, but that they take different sets of facts into consideration, assign different values to evidence, have different moral axioms and so on.

For this reason one of Murthy's laws says, "Logic is a systematic method of coming to the wrong conclusion with confidence" (other logic-related quotes on that page are also interesting). This is not because correct real-world reasoning is inherently illogical. Rather, in order to apply formal logic, one has first to come up with a mathematical model of a real-world situation, and such models are always simplifications and don't take everything into account. In some cases, my feeling was that people who invoked formal logic did so to hide the fact that they did not consider an issue in its fullness but wanted to give an impression that they were taking it seriously.

I think it is much more likely that errors in political discourse are of this kind than those detected by truth tables.

So I would recommend not looking too far but finding a couple of simple and valid arguments. For example: Borrowing rates are low iff foreign investors' confidence is high. Confidence is high iff deficit is low. Deficit is reduced by increasing taxes or reducing spendings. Our ideology prohibits us to increase taxes. Therefore, to keep borrowing rates low it is necessary to reduce spendings.

Re: Truth Table Word Problem [Mathematics: Liberal Arts]

I see, your example is perfect, Its actually similar to mine regarding taxes - how would one put that in a truth table then?

Re: Truth Table Word Problem [Mathematics: Liberal Arts]

First, simple propositional logic deals with, well, propositions, i.e., something that is true or false. It cannot express goals, desires, temporal reasoning, etc. So, formulate the argument in terms of what is true/false now. For example, "Deficit is reduced by increasing taxes or reducing spendings" would become "If taxes are increasing or spendings are being reduced, then deficit is being reduced." "Our ideology prohibits us to increase taxes" would become "Taxes are not increasing." This alone shows how restrictive propositional logic is.

Then identify propositions, i.e., indivisible statements, and denote them with letters. Write the assumptions and the conclusions symbolically. Then construct a truth table listing all combinations of propositional variables' truth values and the corresponding values of formulas.

Re: Truth Table Word Problem [Mathematics: Liberal Arts]

Last question - my proposition would then be p(iff(q and (p and r)) yes?

Re: Truth Table Word Problem [Mathematics: Liberal Arts]

What is your proposition? And what are p, q, and r?