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- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/01%3A_Propositional_Logic/1.05%3A_AndThe sentence in the last column is a negation of (P→Q), so the definition of “¬” tell us that ¬(P→Q) is true when (P→Q) is false, and ¬(P→Q) is false when (P→Q) is true.
- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/02%3A_First_Order_Logic/2.03%3A_Reasoning_with_quantifiersSymbolize this argument, and prove that it is valid. (The second sentence is perhaps best symbolized not using one of the eight forms, but rather using a conditional, where both the antecedent and the...Symbolize this argument, and prove that it is valid. (The second sentence is perhaps best symbolized not using one of the eight forms, but rather using a conditional, where both the antecedent and the consequent are existential sentences.) Do you believe this argument is sound?
- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/01%3A_Propositional_Logic/1.02%3A_Ifthen._and_It_is_not_the_case_that.The sentence we want to test is “For each of these four cards, if the card has a Q on the letter side of the card, then it has a square on the shape side of the card”. Let Q stand for “the card has a ...The sentence we want to test is “For each of these four cards, if the card has a Q on the letter side of the card, then it has a square on the shape side of the card”. Let Q stand for “the card has a Q on the letter side of the card.” Let S stand for “the card has a square on the shape side of the card.” Then we could make a truth table to express the meaning of the claim being tested:
- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/01%3A_Propositional_Logic/1.03%3A_Good_Arguments[5] In nearly all these cases, the deaths were caused by what appeared to be the same illness, commonly called “childbed fever”. Worse, these numbers actually understated the mortality rate of the Fir...[5] In nearly all these cases, the deaths were caused by what appeared to be the same illness, commonly called “childbed fever”. Worse, these numbers actually understated the mortality rate of the First Clinic, because sometimes very ill patients were transferred to the general treatment portion of the hospital, and when they died, their death was counted as part of the mortality rate of the general hospital, not of the First Clinic.
- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/01%3A_Propositional_Logic/1.08%3A_Reductio_ad_AbsurdumSo, Galileo reasons, if there are many numbers in the group of natural numbers that are not in the group of the square numbers, and if there are no numbers in the group of the square numbers that are ...So, Galileo reasons, if there are many numbers in the group of natural numbers that are not in the group of the square numbers, and if there are no numbers in the group of the square numbers that are not in the naturals numbers, then the natural numbers is bigger than the square numbers.
- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/01%3A_Propositional_Logic
- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/02%3A_First_Order_Logic/2.01%3A_Names_and_predicatesWhen we say, “a predicate of arity n is true or false of each n objects from our domain of discourse”, what we mean is that an arity one predicate must be true or false of each thing in the domain of ...When we say, “a predicate of arity n is true or false of each n objects from our domain of discourse”, what we mean is that an arity one predicate must be true or false of each thing in the domain of discourse; and an arity two predicate must be true or false of every possible ordered pair of things from the domain of discourse; and an arity three predicate must be true or false of every possible ordered triple of things from our domain of discourse; and so on.
- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/01%3A_Propositional_Logic/1.07%3A_OrThey favor the definition where a disjunction is true if its two parts are true; this is sometimes called the “inclusive ‘or’”. Of course, all that matters is that we pick a definition and stick with ...They favor the definition where a disjunction is true if its two parts are true; this is sometimes called the “inclusive ‘or’”. Of course, all that matters is that we pick a definition and stick with it, but we can offer some reasons why the “inclusive ‘or’”, as we call it, is more general than the “exclusive ‘or’”.
- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/03%3A_A_Look_Forward/3.01%3A_Some_advanced_topics_in_logicIf a function f is 1-to-1 on A and is into B, then we know that |B| ≥ |A|. (Such a function has every member of A in its domain, and for each such member picks out exactly one member of B; but because...If a function f is 1-to-1 on A and is into B, then we know that |B| ≥ |A|. (Such a function has every member of A in its domain, and for each such member picks out exactly one member of B; but because we only know that the function is into B, we do not know whether there are members of B that are not in the range of the function, and we cannot be sure that there is some other 1-to-1 function on A and onto B.)
- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/01%3A_Propositional_Logic/1.10%3A_Summary_of_Propositional_LogicAn indirect proof (or indirect derivation, and also known as a reductio ad absurdum) is: an ordered list of sentences in which every sentence is either 1) a premise, 2) the special assumption for indi...An indirect proof (or indirect derivation, and also known as a reductio ad absurdum) is: an ordered list of sentences in which every sentence is either 1) a premise, 2) the special assumption for indirect derivation (also sometimes called the “assumption for reductio”), or 3) derived from earlier lines using an inference rule. If our assumption for indirect derivation is ¬Φ, and we derive as some step in the proof Ψ and also as some step of our proof ¬Ψ, then we conclude that Φ.
- https://human.libretexts.org/Bookshelves/Philosophy/A_Concise_Introduction_to_Logic_(DeLancey)/02%3A_First_Order_Logic/2.05%3A_Relations_functions_identity_and_multiple_quantifiersHow would we translate the expression, “Steve is the father of Tom”? We could add to our language a predicate, “… is the father of …”. However, it is interesting that in this expression (“Steve is the...How would we translate the expression, “Steve is the father of Tom”? We could add to our language a predicate, “… is the father of …”. However, it is interesting that in this expression (“Steve is the father of Tom”), the “is” is identity.
