Logic And Critical Thinking Flashcards

Front 1

Explain why we may not be justified in believing any arbitrary list of propositions.

Back 1

We may not be justified in believing any arbitrary list of propositions because the truth values of propositions themselves necessitate the truth values of certain other propositions.

Front 2

Explain the difference between logical relations and causal relations.

Back 2

Causal relations are relations between events ore states of affairs in the world. That is when one event or state of affairs brings about another state of affairs the two events are causally related. Logical relations are relations between the truth values of propositions. Logical relations only hold between propositions, that is things that can have a truth value and thus are meaningful.

Front 3

What two constraints determine the truth values of propostions.

Back 3

The two constraints on the truth values of propositions are that their truth values depend on the states of affairs, and on the truth values of certain other logically related propositions.

Front 4

Explain the difference between contradictory pairs of propositions and contrary pairs of propositions.

Back 4

The difference between contradictory pairs of propositions and contrary pairs of propositions is that in a contrary pair both propositions can be false.

Front 5

What do contradictions and tautologies tell us about the world? Why are contradictions and tautologies important?

Back 5

Contradictions and tautologies tell us nothing about how the world is; they are empty of informational content. Tautologies and contradictions are important because they have their truth values as a matter of necessity. That is that Tautologies must be true, and Contradictions must be false. Contradictions help us eliminate sets of propositions from our descriptions and theories about the world as logically impossible. Tautologies require us to accept certain propositions as true and others as false, depending on the truth values of other propositions.

Front 6

What are the three important general features of relations of logical implication?

Back 6

1. Logical implications are not symmetric. This means that although P implies Q, it need not be true that Q implies P.
2. Logical implications are reflexive. This means that every proposition implies itself. That is for every proposition P, P implies P.
3. Logical implications are transitive. This means that for any three proposition P,Q, and R, if P implies Q and Q implies R, then P implies R.

Front 7

What is the difference between an conditional proposition that expresses a logical implication adn a conditional proposition that expresses a materail conditional?

Back 7

Logical implications are different from truth functional conditionals because the implied proposition in logical implications are implied with necessity.

Front 8

What is the difference between two propositions that are materially equivalent and two propositions that are logically equivalent?

Back 8

Material equivalence is when propositions have the same truth value. A Logically equivalent set of propositions is that way because the equivalence is necessary, that is it is impossible for two propositions to have different truth values.

Front 9

What are modal concepts?

Back 9

Modal concepts indicate the manner in which a proposition’s truth value is presented. This includes whether propositions are actually true or actually false, possibly true or impossible, necessarily true, necessarily false, contingently true or continently false.

Front 10

How are modal concepts connected with the assessment of dediuctive reasoning?

Back 10

3. The assessment of deductive reasoning depends fundamentally on different modalities, on what is possibly true and what is necessarily true or necessarily false. A deductive argument is valid if the premises are true then the conclusion must be true: that is a relationship of necessity, and the premises actually being true.

Front 11

Define a truth functional connective.

Back 11

an expression is a truth functional connective if and only if it functions to construct compound propositions such that the truth values of those compound propositions depend soley on the truth values of their component propositions.

Front 12

Name and state all four laws of logic. What is a law of logic?

Back 12

1. The law of bivalence: Each proposition is either true or false.
2. Law of truth values: no proposition is both true and false
3. The law of Contradiction: a proposition P and it's negation "It is not the case that P" cannot both be true
4. The law of excluded middle: A proposition P and its negation "it is not the case that P" either P is true or its negation "it is not the case that P" is true.
A law of logic states a condition that is necessary before it is possible for any proposition to have a truth value.

Front 13

Why do we need to define truth functional operators and connectives by using truth tables?

Back 13

A truth table shows how the truth values of the compound propositions depend on the true values of their parts.

Front 14

Give arguments that demonstrate that the truth table for logical negation can be derived from the laws of logic.

Back 14

A. 1) A proposition "P" and its negation "It is not the case that P" cannot both be true
2) A proposition must be either true or false.
3) (underlined) The propostion P is true
Therefore 4) Propostion "it is not the case that P" is false
B.
1) For every proposition P and its negation "it is not the case that P" either P is true ore its negation "it is not the case that p" is true
2) (underlined) The proposition P is false
Therefore 3) The proposition "It is not the case that P" is true

Front 15

Explain how to construct a truth table for two independent propositions.

Back 15

We construct a truth table for two propositions whose truth values are independent of one another.

Front 16

Using examples, explain the difference between inclusive and exclusive uses of the word or.

Back 16

A. Is incluseive because it covers a range and can be any of the situations: Employees may have paid days off either for illness or for family emergencies.
2. Is exclusive because it cannot be both possibilities: Sue will go to the concert at 8 tonight, or sue will go to a movie at 8 tonight.

Front 17

Explain the relationship between causal relations and causal conditionals.

Back 17

Causal relations connect states of affairs in the world so that one event, called the cause, brings about the occurance of the other event called the effect. The conditional states that there is a causal connection between a cause and an effect.

Front 18

Using an example, explain how the converse of a conditional is formed. Give an example of two propositions that are converses of one another.

Back 18

The converse of a conditional is formed when the antecedent is true and the consequent is false. It is sunny I am at the beach. So it would be false if it was sunny and I was not at the beach.

Front 19

Usion an example, explain why a conditonal propostition and its converse do not always have the same truth value. How is the truth value of a condtional related to the truth value of its converse.

Back 19

p q p then q q then p
T T T T
T F F T
F T T F
F F F T
A converse is only true when the antecendent is false and the consequent is true

Front 20

what kind of propositions express necessary and sufficient conditions?

Back 20

Conditional

Front 21

Explain the relationship between necessary and sufficient conditions and conditinal propositions.

Back 21

A state of affairs or event "s" is a sufficient condition for a state of affairs or event "n" if and only if the occurance of S must occur for N to occur.

A state of affairs or event N is a necessary condition for a state of affairs or evnet S if an only if N must occur for S to occur.
Conditional, if sufficient then necessary.

Front 22

Using an example explain why a sufficient condition need not also be a necessary condition.

Back 22

Sue is a citizen of colorado is a sufficient condition for er to be a citizen of the united states. If sue is a citizen of the united states she does not have to be a resident of COlorado, she could be a resident of one of the 49 other states

Front 23

Using an example exlain why a necessary condition need not also be a sufficient condition.

Back 23

Sue is a citizen of colorado is a sufficient condition for er to be a citizen of the united states. If sue is a citizen of the united states she does not have to be a resident of COlorado, she could be a resident of one of the 49 other states

Front 24

Explain why biconditionals are appropriate for stateing definitions. Describe and explain the general form of such definitions.

Back 24

in stating a definitaonal claim, the definition of a general ter is supposed to give both necessary and sufficient conditions for applying that general term to its examples.
Something is a prime number when X Y and Z.