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propositional truth trees 3 mp4

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Okay, we are up to conditionals. The rule for a conditional tells us to branch and on the right branch we have the consequent, just as it was. And on the left branch we want the negation of the antecedent. Okay? Right branch exactly the same, left branch we negate. I've given us a longer one to try as well. Notice, what is the main operator? It's the dot, so this is not a conditional to start off with, so let's recall the dot rule. It tells us to put each conjunct underneath the sentence. Okay? So there I've done the conjunct rule. And now look what I've gotten: I have two horseshoes, and so I can perform the horseshoe rule. We're gonna perform them one at a time. I'll do the first one first. So, this horseshoe we're gonna draw a branch underneath. And it's fine, it's not going to be directly underneath right here cause there's no room. It's just wherever the tree stops below it we will draw our branch. On the right side, the consequent exactly as it was. On the left side, the negation of the antecedent. Then we check that and now here's something that we haven't seen yet. I wanna perform the rule on this statement. Now, whenever you perform a rule you perform it below where it is on the tree and you perform it on every path. that's open below it. I have two open paths. We'll see in a later video why paths sometimes close off. So the horseshoe rule tells us to branch and you have to do that branch on any open row below it. and I've got two open rows. And the rule says to put the consequent just as it is A wedge C, negation of the antecedent. and we'll perform that in both of these two places. So we performed it here and we performed it here. And now, actually, I can show you why something is closing off. See this tilde B? and the B? In a tree, whenever you have something and its negation, in a pathway, so see that pathway? We can put an "X" and close off that path. Notice that this tilde B and this B do not close off. because they are not in the same path. When you draw the path you always have to just go up. You can't go up and then down, only up. I can check off this conditional and I also have these two statements that aren't broken down and we already have talked about the wedge rule So I can do that every place that's open underneath it There's only one place underneath each one. And now there's more things that I can cross off A... tilde A So I can close that one off. And anything else? C... nope. A... nope. C... nope. Okay, so I've got some paths closing off. The way I like to remember this rule for conditional is the material implication rule from our deduction rules. Remember we can change horseshoes into wedges? And the right side stayed the same and the left side, the antecedent, gets a tilde added when you go from a horseshoe to a wedge. And that's basically the move that's happening here. Right? We go from a horseshoe to a wedge.

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Duration: 4 minutes and 39 seconds
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Language: English
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Posted by: herna130 on May 31, 2017

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