Reasoning with Games #liespy

Our second mini project is much like the first, though this assignment calls on you to posit your own argument with a tenable objection to your own view and why you ultimately win out.  My previous post will still be helpful when making this project; however, here are some additional thoughts on how one can go about making an argument of such nature.

When making objections, it’s often helpful to think about what it would mean for a premise if it were true and then work your way back to see if something absurd follows (this form of argument is called reductio ad absurdum).  If we assume something is true and then the result is something we would never maintain, then we know the premise cannot be true.  Consider the following game:

A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet three inhabitants: Tom, Sue and Bill. Tom tells you that Bill is a knave. Sue tells you, `Only a knave would say that Bill is a knave.’ Bill claims that Tom and Sue are the same.  

Who is a knight and who is a knave?

Here is how to go about solving the game using this specific form of argument:

Round 1

Let’s assume that Tom is a knave.  This would mean that Bill is a knight, considering that Tom is lying.  If Bill is a knight, it would mean that Sue is also a knave (because Bill is telling the truth).  However, if Sue is a knave, it would mean that she would be telling the truth we she says that only a knave would say that Bill is a knave (because Tom is a knave), which can’t be the case because knaves always lie.  So, Tom must be a knight.

Round 2

Let’s assume that Tom is a knight.  If Tom is a knight, then we know that Bill is a knave (because knights always tell the truth).  If Bill is a knave, this means that he is lying when he says that Tom and Sue are the same, so we know they are different.  Since we assume Tom is a knight, it would mean that Sue is lying when she says that only a knave would say that Bill is a knave.  So, since we assume that Tom is a knight and we know that he and Sue are not the same (because Bill is lying), Sue is a knave.

We get these results:  Tom is a knight, Sue is a knave, and Bill is a knave.

Even though this is just a game, it nevertheless is a valuable model for considering how to reason and show that a view is false.  Consider the Twain example from my previous post with the first premise of his argument:

Premise 1: All necessities of our circumstances are virtues

Let’s assume this is true.  If it is, it would mean that everything that is a necessity is virtuous.  As I wrote before, this would mean things like eating and sleeping are virtues because they are necessary components of life. This would also seem particularly complicated in various contexts of “necessary”: killing and stealing for survival seems necessary at times, though again, not virtuous.  So, unless we are willing to accept all of this, it would seem like Premise 1 is false.

When testing your own arguments, think about what they would necessarily entail if they were sound and whether this is a problem (it can also be done with the objections you consider to your own view).


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