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Each of the following passages contains a single argument. Using the letters "P" and "C," identify the premises and conclusion of each argument,...

Question

Each of the following passages contains a single argument. Using the letters "P" and "C," identify the premises and conclusion of each argument, writing premises first and conclusion last. List the premises in the order in which they make the most sense (usually the order in which they occur), and write both premises and conclusion in the form of separate declarative sentences. Indicator words may be eliminated once premises and conclusion have been appropriately labeled. The

Each of the following passages contains a single argument. Using the letters "P" and "C," identify the premises and conclusion of each argument, writing premises first and conclusion last. List the premises in the order in which they make the most sense (usually the order in which they occur), and write both premises and conclusion in the form of separate declarative sentences. Indicator words may be eliminated once premises and conclusion have been appropriately labeled. The exercises marked with a star are answered in the back of the book. Corn is an annual crop. Butcher's meat, a crop which requires four or five years to grow. As an acre of land, therefore, will produce a much smaller quantity of the one species of food than the other, the inferiority of the quantity must be compensated by the superiority of the price.



Answers

Lewis Carroll Exercises 39–44 are from problems in Lewis Carroll’s book Symbolic Logic. Write each premise in symbols, and then give a conclusion that uses all the premises and yields a
valid argument. Source: The Complete Works of Lewis Carroll.

Let d be “it is a duck,” p be “it is my poultry,” o be “one is an officer,” and w be “one waltzes.”
a. No ducks waltz.
b. No officers ever decline to waltz.
c. All my poultry are ducks.
d. Give a conclusion that yields a valid argument.

For this question, we're gonna have three statements that we know are all through and have true conclusions will be needed to determine the validity of them. So I think it would be easiest to start from the back and work our way in just toe start from the highest degree of broadness and work our way in. So we know that all houses have nails. So for and representatives from Oiler diagram And we want to say that some things have nails. So we're gonna represent that with this red circle of things that have nails. And we know that all houses have nails, so a house would be somewhere inside here. I'm not gonna add it yet, but we'll know that Ah, house is gonna be somewhere inside here. We'll add that in later. But this is all things that have nails, which is gonna be generally our broadest circle. The next statement we have is that all roofs have nails. So when we know that all roofs have nails, that means another circle of roofs would be somewhere inside here, so we'll see in which order to place them in later. And the last name is that All houses have roofs so all houses have roofs then what we know will we know that all houses have roofs means that when we're layering everything, we know that this could be the state. This is the circle of roofs and this is the circle of houses. So Oops. So when we write everything in, does everything check out? But we say that all houses have roofs, all roofs have nails and all nails are all houses have must therefore have nails. So all the statements that we have are valid if we take all their conclusions to be true and everything checks out.

Now, in this argument, we have three premises. The 1st 1 is that all mammals have fur. So we start off with larger set of all things that have for and then inside, that we have this subset of all mammals. So all things that have for this could include coconuts, plata pie, anything really, that has for and on this one, we have mammals, which is a smaller set of all things that have for humans, I guess. And inside that we also have to say that all tigers up for which is our second premise. So we're gonna sail tigers have for gonna have toe draw a new domain for tigers and insert that inside for and we say that all tigers now have for and our third and final argument is that all the tigers are mammals. Well, can we really say that? Because if all tigers were mammals than what you would expect more, so is that you would have this entire blue circle within the green circle. However, the way that the statements and the premises were given, all of the information that we have is that all tigers out for weaken. It could necessitate that all tigers are mammals and it probably does. But based on the way the conclusions are given, we can draw. It's like this. We can also draw it like an intersection point. Or we can draw it where the tigers air within mammals, but nothing that we have necessitates anything being in one of those three directions. Therefore, the arguments are invalid.

This problem is a rearrangement of problem 27 where now we are keeping the premise that all mammals have fur, so we're gonna have the larger domain of things that have for within that we're gonna have a sub domain of mammals. Now, our second premise is that all tigers are mammals. So now that set of tigers is contained within. Now, when we're labeling this, this is things that have for mammals was gonna write. It is, um and this is Tiger because it s a T and now our last premises that all tigers have for So if the tiger was within mammals, which is but in for it necessitates that tigers have for all of these.

So for this statement, it's a little bit worthy. So it's kind, dissect it and go along. So the first thing that we're gonna do is define what has done that at one time or another that where the expression we're just gonna assign it a p of X and move on. So, with a p of X aside for that expression, what else could we say about the phrase so says there is no one here. So the way that phrase is mentioned, a kind of points out to be an existential. There is no one here, so there exists no one I It's probably the negation of of an existential Okay, So if there exists no one who has not done that at one time or another. So there exists no one which we're gonna characterizes this who has not done that at one time or another than not pre fixing r p of X is gonna be inside our brackets or not p of X. So now when we have this statement, we can rewrite it as and universal, and we carry the negation side. Since the double negation, it's gonna be a p of X. So when we When we say it again, it's gonna be Everyone here has done it at one time or another.


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