Logic Week 1-2

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Fallacy of Affirming the Consequent

(INVALID) If it rained, the ground is wet; the ground is wet; the ground is wet; hence, it rained.

Premise Indictor Expression

- Since - For - Because - On Account Of - Inasmuch as - For the reason that

Conclusion Indictor Expression

- Therefore - Thus - It Follows That - So - Hence - Consequently - As A Result

Logically True

True under all possible situations

Logically Indeterminate

True under some and false under some other possible situations

(Valid/Invalid & Sound/Unsound) All gods are immortal. So all gods have always existed

Invalid/Unsound

Inconsistent

No possible situation under which all members are true

Entailment

Similar to validity but not identical. A set of sentences logically entails a sentence if and only if it is impossible for the members of the set to be true and that sentences false

How is it possible for a valid argument to have a false conclusion?

Some of the premisses of such an argument may be true, but at least one premiss must be false

(T/F) A set containing all the sentences of English is bound to be Inconsistent

TRUE

(T/F) Every set of true sentences is consistent

TRUE - If all the sentences in a set are true then it is possible for all of them to be true so set is consistent

(T/F) If the set {A,B,C} is consistent then {A,B} is also consistent

TRUE - If it is possible {A,B,C} are consistent so it is possible {A,B} are consistent

(T/F) An invalid argument must have a consistent set of premisses.

TRUE - If the argument is invalid then there is a possibility that the premisses are all true and the conclusion is false so that same possibility relates to consistency

(T/F) Every logically true sentence is true

TRUE - Logically true is true in every possible situation. If it is true in actual situation then it must be true.

(T/F) If A is logically false then the set {A,B} is inconsistent

TRUE - Suppose A is logically false so there is not possible situations A is true so there is no possible where A+B are true so the set is inconsistent

(T/F) If an argument is invalid then it conclusion is not logically true

TRUE - Suppose an argument is invalid, then there must be a possibility that the premisses re true and the conclusion is false

(T/F) If {A,B} is consistent and C is logically true then {A,B,C} is consistent

TRUE - Suppose {A,B} is consistent so there is a possible situation in which A+B are both true. Suppose C is logically true in every possible set. Therefore, there is a possible set in which A,B,C, are true

(T/F) If A is logically true and B is logically equivalent to A then B is logically true also

TRUE - Under all possible situations the two sentences have the same truth value to be logically equivalent, A is true under all situations so B is true under all situations

Logically Equivalence

Under all possible situations the two sentences have the same truth value (either both are true or both are false)

(Valid/Invalid & Sound/Unsound) All gods are immortal. So all gods shall always exist

Valid/Sound

Invalid Argument

There is a possible situation under which all the premisses are true and the conclusion is false. Famous Example - Fallacy of Affirming the Consequent

Consistent

There is possible situation under which all members are true together

Holy Grail of Logic

To be able to determine the validity of any arguments

(T/F) From the fact that an argument is not sound you cannot infer that its conclusion is false

True

(T/F) If the premisses are true and the conclusion is false then the argument is definitely invalid

True

(T/F) The conclusion of a sound argument is bound to be true

True

(T/F) There are invalid arguments with a false conclusion

True

(T/F) There are invalid arguments with a true conclusion

True

(T/F) There are valid arguments with a true conclusion

True

Sound Argument

An argument is sound if, and only if, all its premisses are true and its valid

Valid Argument

An argument is valid if, and only if, it is impossible that its premisses are true while its conclusion is false; in other words, if the premisses are true then the conclusion must be true

Predicate Logic

Branch of symbolic deductive logic that predicates and individual terms as the fundamental units of logical analysis

Sentential Logic

Branch of symbolic deductive logic that takes sentences as the fundamental units of logical analysis

What is logic concerned with?

Concerned to understand the validity of arguments

Argument

Consists of one or more statements, called the premisses, and a statement called the conclusion

(T/F) If the set {A,B} is consistent then {A,B,C} is also consistent.

FALSE - Example to Prove: {Obama is president, Kerry is Secretary of State} Consistent {Obama is president, Kerry is Secretary of State, Obama is not president} Inconsistent

(T/F) Any set containing just one sentence is bound to be consistent

FALSE - Example to Prove: {Some ducks are not ducks} Inconsistent

(T/F) If the premisses are consistent, then the argument must be invalid

FALSE - Snow is White. Snow is White. Therefore, Grass is Green (Invalid but Consistent)

(T/F) If {A,B} is inconsistent then A is not logically equivalent to B

FALSE - {Dogs are not Dogs, Cats are not Cats}

Logically False

False under all possible situations

(Valid/Invalid) No nuclear powered submarines are commercial vessels, so no warships are commercial vessels, since all nuclear powered submarines are warships.

Invalid

(Valid/Invalid & Sound/Unsound) We (in this classroom) are all mortal. So there will come a time when none of us will be alive

Invalid & Unsound

Logic Special Cases (5)

1.) An argument who conclusion is logically true. 2.) Every logical true sentence being entailed by every set of sentences, including the empty set, because it is impossible for a logically true sentence to be false and hence impossible for the members of a set, any set, all to be true and that logically true sentence false. 3.) Arguments who premises form logically inconsistent sets 4/5.) Sentences p and q are logically equivalent if and only if it is not possible for one of the sentences to be true while the other sentence is false.


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