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How is this different from :Some rectangles are squares. So, a rectangle is a square. Some rectangles are not squares. So, a rectangle is not a square. It follows by conjunction introduction that "a rectangle is a square and a rectangle is not a square." But the quoted statement is a contradiction. Therefore, by the principle of explosion, trivialism is true. This concludes the argument.
browser32 wrote:Previous content regarding the argument, including a depicted variation of the argument, can be located through https://twitter.com/paulemok/status/970444013512871936.
Some rectangles are squares. So, [any] rectangle is a square.
fuse wrote:of course, non-trivialism must also be true
fuse wrote:why privilege just one side of the trivial coin?
fuse wrote:The implied [any] is the mistake in your premises.
fuse wrote:First rule of making a good argument: eliminate ambiguity/assumption/hinted implication from your terms.
browser32 wrote:Some rectangles are squares. So, a rectangle is a square.
browser32 wrote:Changing or formalizing a statement to make it more suitable for a particular argument may change the properties of the statement.
A square is a rectangle with particular distinguishing characteristics, just as a cat is a mammal with particular distinguishing characteristics.Your argument involving mammals and cats involves different categories as my argument involving rectangles and squares. Your argument involves the categories mammal and cat, but my argument does not involve those categories. Instead, my argument involves the categories rectangle and square, which are categories your argument does not involve.
browser32 wrote:Argument. It is given that some rectangles are squares. The given statement is conventionally taken to mean that at least one rectangle is a square. Otherwise, since the word rectangles is plural, it is taken to mean that at least two rectangles are squares. In either case, at least one rectangle is a square. Since at least one rectangle is a square, it is also true that one rectangle is a square. The implication of the previous statement is similar to the implication that if at least five peaches fell off of a peach tree today, then it is also true that five peaches fell off of the tree today. Since one rectangle is a square, one rectangle that is a square is a rectangle. So, a rectangle is a square. This concludes the argument.
Carleas wrote:The principle of explosion no longer applies when you are dealing with the imprecision of every day language, as it follows from formal logic.
Carleas wrote:In every day speech, it isn't the case that two contradictory statements imply any arbitrarily chosen conclusion.
Carleas wrote:In every day speech, the same word or locution can be and often are used to mean different things.
Carleas wrote:5) Rectangle S is a square and rectangle N is not a square.
phyllo wrote:I switched from rectangles and squares to mammals and cats so that the logic would be more intuitive and not dependent on mathematical concepts and definitions.
phyllo wrote:That change has altered the meaning to "Every rectangle is a square" or alternatively "Any rectangle is a square" as Fuse pointed out.
phyllo wrote:"A cat is a mammal" is true but "A mammal is a cat" is false.
phyllo wrote:Another alternate meaning for your second statement is "A particular rectangle is a square", but in that case referring to any other rectangle and saying that it is not a square does not produce a contradiction.
Mad Man P wrote:You see all you're saying is "there is at least one rectangle that is a square and there is at least one rectangle that is NOT a square" there is no contradiction in that.
browser32 wrote:The statement "a rectangle is a square" is not logically equivalent to the statement "any rectangle is a square."
browser32 wrote:There is no implied any in my premises.
The indefinite article (a, an) is used before a noun that is general or when its identity is not known.
browser32 wrote:I agree. However, while the rectangle in the quoted statement "a rectangle is a square" may not be the same rectangle in the quoted statement "a rectangle is not a square," the quoted noun phrase "a rectangle" has the same meaning in both statements.
fuse wrote:What you must do to make your case is explain exactly the meaning of a rectangle is a square. Logical equivalence is effectively determined only after statements have been properly clarified/formalized.
fuse wrote:You've just explained that the statements reference two different, particular rectangles ("the rectangle in the quoted statement...").
fuse wrote:Thus, you would not faithfully capture the original meaning of either statement were you to substitute in the general definition: "one quadrilateral that has four right angles."
browser32 wrote:Mad Man P wrote:You see all you're saying is "there is at least one rectangle that is a square and there is at least one rectangle that is NOT a square" there is no contradiction in that.
No, I'm not saying your quoted statement. "There is at least one rectangle that is a square" is not logically equivalent to "a rectangle is a square."
browser32 wrote:Argument. It is given that some rectangles are squares. The given statement is conventionally taken to mean that at least one rectangle is a square. Otherwise, since the word rectangles is plural, it is taken to mean that at least two rectangles are squares. In either case, at least one rectangle is a square. Since at least one rectangle is a square, it is also true that one rectangle is a square. The implication of the previous statement is similar to the implication that if at least five peaches fell off of a peach tree today, then it is also true that five peaches fell off of the tree today. Since one rectangle is a square, one rectangle that is a square is a rectangle. So, a rectangle is a square. This concludes the argument.
browser32 wrote:Mad Man P:
The basis for your claim is unclear. I'm unsure how your two quotes support what you have claimed.
Mad Man P wrote:You cannot perform a deduction without a second premise
Mad Man P wrote:you may restate the first premise so long as it is a logical equivalent, but the moment you alter it's logical implications it's a non-sequitur.
Mad Man P wrote:You have no such deductive argument leading you from "at least one rectangle is a square" to "a rectangle is a square"
browser32 wrote:at least one rectangle is a square. Since at least one rectangle is a square, it is also true that one rectangle is a square. The implication of the previous statement is similar to the implication that if at least five peaches fell off of a peach tree today, then it is also true that five peaches fell off of the tree today. Since one rectangle is a square, one rectangle that is a square is a rectangle. So, a rectangle is a square.
browser32 wrote:That is not true. A deduction does not have to involve at least two premises.
Mad Man P wrote:You would have to show the SAME rectangle that is a square is also not a square for there to be a contradiction.
browser32 wrote:"a rectangle" in the statement "a rectangle is a square" and the statement's negation "a rectangle is not a square" refers to any rectangle.
Mad Man P wrote:"A rectangle is a square" does not contradict "a rectangle is not a square" unless both statements were referring to the SAME rectangle
browser32 wrote:Since I am allowed to set the referent of "a rectangle" in each of the two statements to any rectangle, I am allowed to set the referent of "a rectangle" in each of the two statements to the same rectangle and have a contradiction.
Mad Man P wrote:you are not allowed to do this by the laws of logic
Mad Man P wrote:I don't know who or what you think is "allowing" you to make that move.
browser32 wrote:"a rectangle is a square" is not logically equivalent to "any rectangle is a square." The first statement is sometimes but not always true, but the second statement is never true.
Mad Man P wrote:You would have to show the SAME rectangle that is a square is also not a square for there to be a contradiction.
browser32 wrote:Regarding my post at ...
wtf wrote:Premise three: P1 and P2 are each other's negations.
browser32 wrote:(1) If a rectangle is a square, then it is regular.
browser32 wrote:The purest negation of "a rectangle is a square" does not consider whether the rectangle in the negation is the same rectangle as in the original statement.
browser32 wrote:I am not speaking generally.
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