MODR 2640 Lecture Notes - November 3, Truth Table, Logical Equivalence

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brownmuskrat867

19 Nov 2012

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The conditional when antecedent is the conjunction of the premises and whose consequent is the conclusion (a b) c. Argument is valid iff corresponding conditional is a tautology. A set of statements is consistent if it is possible that all are true. Valid = impossible for all premises to be true and conclusion false. Then impossible p1 true, p2 true, and c false. So, set p1, p2, and ~c is inconsistent. Argument valid iff set consisting of all premises and negation of conclusion is inconsistent. Valid = impossible all premises true and conclusion false. Inconsistent = impossible that all premises are true. Any argument with a tautology as a conclusion is valid. To determine whether an argument is a tautology, contradiction, or contingent statement. Two statements always have same truth value-- then equivalent. If there is no row in which all premises true and conclusion false, then valid. If a row in which all statements are true, then consistent.

Related Questions

1. Consider the following argument: All fish can swim. You are a fish. Therefore, you can swim. Which of the following best describes this argument?

A. It is valid but unsound.

B. It is valid and sound.

C. It is invalid and unsound.

D. It is inductively weak.

2. In a valid deductive argument: (circle the correct answer)

A. the premises must all be true.

B. it is impossible for the premises to be true and the conclusion false.

C. the premises must be false if the conclusion is false.

D. it is impossible for the premises and the conclusion to be false together.

sangriagoose906

Just The Second Part, Thanks!

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coppergnu515

For example, consider the following argument:
"Measles can't be cured by antibiotics, since Measles is caused by a virus, and antibiotics can't cure a viral infection."

We can see that the argument contains the word "since," which is a premise indicator. We know that what follows "since" will be the premises. We also know, through the process of elimination, that what precedes the word "since" is the conclusion. So my standardized argument will look like this:

1) Measles is caused by a virus. 2) Antibiotics can't cure a viral infection. therefore, 3) Measles can't be cured by antibiotics.

Now we can see the relationship of support between the premises and conclusion. We are asked to accept the conclusion, "Measles can't be cured by antibiotics," based on the two supporting premises. Notice that all of the premises and the conclusion are statements, that is, complete sentences that are either true or false. Also, notice that the premise indicator "since" has been omitted. We always omit premises and conclusion indicators when putting arguments into standard form and make sure that the components of our argument are statements, that is, complete sentences that are either true or false.

For credit on this assignment, do the following:

1) Put the following arguments into standard form:

a) "All dogs are carnivores, consequently, Max is a carnivore, for the reason that Max is a dog."

b) "Rebecca does not pray at the mosque, for she is not a Muslim and only Muslims pray at the mosque."

c) "To every existing thing God wills some good. Hence, since to love any thing is nothing else than to will good to that thing, it is manifest that God loves everything that exists."

2) Create your own argument:

a) Construct an argument of your own using two different premise indicators and one conclusion indicator with the following conclusion: "Now, more than ever, everyone needs to take a class in logic."

b) Then put the argument into standard form.

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MODR 2640 Lecture Notes - November 3, Truth Table, Logical Equivalence

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