Conditional Countersign Routing Made Easy

Lay conditional field bulletin

we start this video with the assumption that you have a good grip on conditional statements and are able to translate any conditional sentence into a standard if then form and we're looking at the arguments that can be constructed with these conditional claims the first argument that is a valid form is the most common form of reasoning with a conditional claim and that is affirming the antecedent or often called simply modus ponens so i'll just jump right in with this example if albed is eating the whole pizza then abba will be full so we have our conditional claim and then we affirm the antecedent of the conditional sentence abed is eating the whole pizza and from that we can conclude the consequent is true that abed will be full and so here it's pretty easy to see we have p would be the sentence abbott eats the whole pizza and q abbott will be full and we can symbolize the argument like such if p then q p is true about is eating the whole pizza therefore we conclude that q is true and so that's modus ponens that is very common okay before going on to the next form of argument with conditional sentences we need to take just a moment to talk about negation and denial of sentences so a sentence might be negated in a variety of ways so let's just run through some examples if somebody says i passed the test the denial of that or the negation of that would be i failed the test now notice there is a not included in the either sentence is a not which is the most simple way of negating a sentence so for example in this case i pass the test it is not the case that i passed the test so when you're in doubt of how to negate a sentence just add the phrase it is not the case that in front of the sentence and you have the denial there are other ways of course depending on the context here so her shoelaces are tied her shoelaces are untied the second is the denial of the first the tail side is up the tail side is down again the negation and there are some background assumptions here uh he is an experienced cook and then here it's a little bit more complex of a sentence to negate so we just use that standard way of doing it it is not the case that he is an experienced cook and so in logical notation the first sentences could be represented as p and the second as not p and we use a tilde in front of the p to represent that not p and in all of these pairs both sentences cannot be true if one sentence is true the other sentence has to be false this is the relationship of contradiction okay now that we have denial of sentences down...