Each of the following passages contains a single argument. Using the letters "P" and "C," identi

Each of the following passages contains a single argument....

Key Concepts

Premise

A premise is a statement or proposition in an argument that provides reasons or evidence to support the conclusion. Premises form the foundation upon which the argument builds its case by offering factual or logical support.

Conclusion

The conclusion is the main claim or assertion that an argument is trying to establish, drawing from the evidence or reasons provided by the premises. It is the endpoint that the premises lead towards in logical reasoning.

Argument Structure

The argument structure refers to the organized relationship between premises and the conclusion, outlining how individual statements support the overall claim. Understanding this structure is essential for evaluating the validity and soundness of reasoning.

Indicator Words

Indicator words are terms or phrases within an argument that signal the introduction of premises or the conclusion. They help in identifying the logical moves in the argument, although they may be omitted once the argument has been fully delineated.

Declarative Sentences

Expressing premises and conclusions in the form of declarative sentences means writing them as clear, assertive statements that can be independently evaluated for their truthfulness. This practice helps in isolating and analyzing the components of an argument.

Transcript

00:01 So here we're asked what relevant conclusion or conclusions we can make using the premises given and explain the rules of inference we use to come up with these conclusions.

00:14 So for a, we know the premises, if i play hockey, then i am sore the next day.

00:24 We know if i am sore, then i use a whirlpool and i did not use a whirlpool.

00:30 So let's break it down.

00:33 So p is i play hockey.

00:44 Q is i am sore.

00:53 And r is i use the whirlpool.

01:07 So let's step and reason.

01:14 So we'll write everything out in order to form the conclusion.

01:17 And this also shows you how the conclusions were formed.

01:20 So, one, if i play hockey, then i am sore the next day.

01:28 That's a premise.

01:34 Two, if i am sore, then i use the whirlpool.

01:41 That's another premise.

01:46 Three, let's write the other premise.

01:50 I did not use a whirlpool premise.

01:55 Now, using these premises, we could come up with different conclusions.

02:00 All right so four we know if we look at premises one and two and we take a look at the table one of the rules of interference if we take a look at the hypothetical syllogism so if p then q and if q then r we know that p r so this is hypothetical syllogism for one and two for one and two so this tells us if i play hockey, then i use a whirlpool.

02:46 So five, we know that we didn't use a world pool.

02:54 So using three and four and taking a look at the table of the rules of inference, we find that i didn't use a world pool.

03:07 So if i play hockey, then i use a world pool, then we know that i didn't play hockey by modus tollens.

03:17 Tolins for three and four, three and four.

03:29 So this is one conclusion, and we could also draw using two and three.

03:37 The same modus tollens will tell us, i am not sore.

03:44 Modus tolens of two and three.

03:58 So these are the two conclusions for a.

04:02 One is i did not play hockey and the other is i am not sore.

04:21 So now let's get rid of this to answer b.

04:33 So b we do the same step.

04:38 We know that well signed.

04:42 We know the premises that if i work then it is sunny or partly sunny.

04:48 I worked on monday or i work on friday.

04:54 It is not partly sunny on friday and it is not sunny on tuesday.

05:00 So let us assign p is, i worked.

05:13 Actually let's do p of x.

05:16 I worked x as the day.

05:22 Q of x, x is sunny.

05:35 R of x.

05:38 X is partly sunny.

05:48 So let's write down the premises.

05:50 In order to come up with different conclusions.

05:55 So we'll do the same thing.

05:56 Step here and the reason here.

06:04 So let's write down the premise.

06:07 So we know if i work, then it is either sunny or party sunny premise.

06:28 Write down another premise.

06:31 I worked on monday or i worked on friday.

06:39 That's another premise.

06:42 All right, let's step three.

06:48 So let's write this.

06:51 I worked on monday or friday.

06:54 Therefore, monday or friday were either sunny or partly sunny.

07:00 And this is thanks to modus ponin of one and two.

07:12 Because we know that if i work, then it's either sunny or partly sunny.

07:17 And we know that i worked on sunday or i worked on monday or i worked on monday or i worked on friday.

07:23 That's how i found this one.

07:25 So next step.

07:29 It was not partly sunny on friday.

07:34 That's a premise.

07:41 So we know that five.

07:48 If i worked on friday, then it was sunny or partly sunny.

07:58 That's a universal instantiation of one using friday.

08:10 Since we know it was not partly sunny we could say if we worked on friday then it was sunny and we'll say this is disjunctive syllogism of four and five why is this? well four using five if we worked on friday then we know friday was either sunny or partly sunny and one of the premise is that it was not partly sunny on friday therefore we know it was sunny on friday if we worked.

08:57 Number seven, we're given the premise.

09:06 It was not sunny on tuesday, the premise.

09:19 So we could say if we worked on tuesday, then it was partly sunny.

09:29 Same reason for number six, disjunctive syllogism using one and seven.

09:45 So these two are the conclusions.

09:50 If we worked on friday, it was sunny.

09:53 We worked on tuesday, it was partly sunny.

09:56 So friday, it was sunny, tuesday, partly sunny.

10:13 And there are other, a few other conclusions, but these are just two of them.

10:22 Let's get rid of this to do part c.

10:29 So c, we know a few premises.

10:37 We know that every insect has six legs.

10:43 We know that dragonflies are insects, and we know that spiders do not have six legs, and we know that spiders eat dragon flies.

10:55 So let's assign some variables to them.

11:00 So p of x, x is an insect, q of x, x has six legs, and r, x of x and y, eats y so now let's do the same thing we were doing step and reason and here we'll write down the premise and use the premise to come up with different conclusions so one it tells us all insects have six legs so we could write that using the universal quantifier if you're an insect then you have six legs reason it's a premise.

12:19 Second step.

12:25 Well, dragonflies are insects.

12:29 We could say d is for dragonfly.

12:33 Dragonflies are insects.

12:35 It's a premise.

12:39 A third step is spiders do not have six legs.

12:47 S for spiders.

12:49 It's another premise.

12:56 We know that spiders eat dragonflies.

13:00 So spiders eat dragonflies.

13:04 Premise okay and now we'll start using the premise premises found so start making some conclusions so you look at one it says all insects have six legs so let's put that into use so if a spider is an insect then a spider has six legs right that we could use universal instantiation from one however we already know that spiders do not have six legs so if we take a look at three and five and the table of rules of inference we look at modus modus tolins and we conclude that spiders are not insects modus tollens using three and five why is this well we know that all insects have six legs.

14:32 We know that spiders do not have six legs, therefore spiders are not insects.

14:40 Now let's do a little more step reason.

14:49 So step seven, we know that spiders eat dragonflies...

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