Philosophy Final

Statistical Inferences

an inference based on an ability to generalize. An observed pattern can be used to create an inference that uses statistical regularity

Causal Inference

an inference based on knowledge of either causes or effects

Analogical Inferences

an inference based on the idea that two things that share some relevant characteristics probably share other characteristics as well. Some characteristics help to prove certainty more than others

Categorical Syllogism

an inference constructed entirely of categorical statements.

Strong Inference

an inference for which logical analysis verifies that the premises, if true, provide evidence that the conclusion has a high probability of being true (at least a 90% chance of being true)

Moderate Inference

an inference for which logical analysis verifies that the premises, if true, provides evidence that the conclusion has a good chance of being true (greater than 50% chance of being true, but less than 90%)

Weak Inference

an inference for which logical analysis verifies the premises, if true, provides very little or no evidence that the conclusion is true (less than 50%)

Inductive Inference

an inference in which it is asserted that the conclusion has a high probability of being true if the premises are true. Claims that the truth of the conclusion is highly probable given the truth of all its premises. Probably, most of the time, likely

Deductive Inference

an inference in which it is asserted that the conclusion is guaranteed to be true if the premises are true. Claims to guarantee the truth of the conclusion, given the truth of all its premies

Valid Inference

an inference in which it is impossible for the conclusion to be false if the premises are true

Invalid Inference

an inference in which it is possible for the conclusion to be false even if the premises are true. Not all of these arguments are bad arguments, but they are not deductively valid arguments, they are not guaranteed

Not Cogent

an inference is weak (based on the analysis of the logical component) and/or it has at least one false premise (based on the analysis of the truth content)

Conditional Inference

an inference that has a conditional statement as one of its premises

Subjectivist Theory

situations can arise where neither a priori nor relative frequency methods will work. The subjectivity of these probability determinations occur when we do not have total knowledge regarding an event.

Truth Value

statements have one of two possible truth values--true or false

Truth Content

the actual truth or falsity of a statement and the methods of its determination

Subject Term

the class designated by the first term in a categorical statement

Predicate Term

the class designated by the second term in a categorical statement

Sufficient Condition

the condition that meets the minimum requirement to ensure that another event does occur

Analogical Structure

the designation, placement, and role of the premises and conclusion that reveal the logical structure of an analogical inference.

Conclusion

the end point of an inference; the statement that is meant to follow from the premises. What the argument is trying to get you to believe.

Equivocation

the intentional or unintentional use of different meanings or references for words or phrases in an inference.

Disanalogy

the introduction of relevant and significant differences between the entities mentioned in an analogy. The less trivial the traits, the more basic the situation is, the stronger the disanalogy and the weaker the original analogy.

Logical Certainty

the kind of certainty achieved by a valid inference

Truth Table

the listing of all possible combinations of the truth values of a statement

Logical Relationship

the logical connection between premises and conclusions

Logical Component

the logical relationship between premises and a conclusion

Main Logical Operator

the logical symbol that determines the statements final truth value

Modus Ponens

the method of affirming the antecedent

Modus Tollens

the method of denying the consequent

Restricted Conjunction Method

the method used for situations dealing with two (or more) independent events, where the occurrence or nonoccurrence of the other event. Method--> Pr(A and B) = Pr(A) X Pr(B)

Logical Commitments

the necessary requirements for a statement to be true

Negation

the operation of logically changing the truth value of a statement to its opposite truth value. Negates the truth value of the statement that follows it

Probability Calculus

a branch of mathematics that can be used to compute the probabilities of compound events from the probability of simple events

Counteranalogy

a competing analogy that compares the entity mentioned in the conclusion of the original analogy to a different entity. When can create this stronger than the original one, gives more reason not to believe the conclusion. Counter the original analogical inference

Conditional Statement

a complex statement having the form "If P, the Q" where the variables P, Q get replaced by statements. Will never get a case where P is true and Q is false

Truth-functional Statement

a complex statement whose truth value is determined by an analysis of the individual components (the simple statements) together with the logical operator(s)

Necessary Condition

a condition that must be met before another event can occur

Venn Diagram

a diagram that uses overlapping circles to represent categorical statements and to illustrate the validity or invalidity of a categorical inference

Unintended Consequence of the Analogy

a direct result of an analogy that is unacceptable to the person presenting the analogy. If can think of these, then can have the person making the argument give reasons to accept or disaccept such consequences

Fallacy of Affirming the Consequent

a fallacy with a form that resembles modus ponens

Fallacy of Denying the Antecedent

a fallacy with a form that resembles modus tollens

Class

a group, set, or collection of objects that have a common characteristic attributed to each member

Statement

a sentence that is either true or false

Inference

a set of statements whereby the premises are offered as support for a conclusion

Logical Loop

a situation in which we miss alternatives because our minds are locked into one path of analysis. Involves making the conclusion false and trying to get all the premises true at the same time

Premise

a statement (or set of statements) offered as support for a conclusion

Self-contradiction

a statement that by its logical form is necessarily false. Always false

Tautology

a statement that by its logical form is necessarily true. No matter what you substitute for P, you will always get a true statement -> valid argument

Existential Import

a statement that has existential import when it implies that something exists

Categorical Statement

a statement that uses sets, categories, or groups of objects (real or imaginary) to replace the variables in one of four specific forms. Every one either affirms that the subject term is related partially or completely to the predicate term or denies that the subject term is related partially or completely to the predicate term.

Noncontingent Statement

a statement whose truth or falsity is based on its logical form, not on truth content

Contingent Statement

a statement whose truth or falsity is not based on its logical form but is dependent on other factors; it is therefore possible for the statement to be either true or false. Has both true and false results in the main operator's column.

Sample

a subset of a population; information about specific characteristics of a sample are often generalized to a population

Logical Operator

a term such as and, or, or not, which performs a specific logical function that determines the logical possibilities of truth and falsity for a complex statement

Relative Frequency Theory

a theory in which probability is defined as the relative frequency with which members of a class exhibit some attribute. Relies on direct observation of events. Probabilities can be computed by dividing the number of favorable cases by the total number of observed cases

A Priori Theory

a theory in which the probability ascribed to a simple event is a fraction between 0 and 1, of which the denominator is the number of equiprobable outcomes, and the numerator is the number of outcomes in which events in question occurs. Rely on hypothetical reasoning based on the assumptions that all the possible outcomes of a given situation can be determined and that each of the possible outcomes has an equal probability of occurring

Indirect Truth Table

a truth table for which truth values are assigned specifically to reveal the possibility of true premises and a false conclusion

Exclusive Disjunction

a type of disjunctive statement where both the disjuncts cannot be true at the same time

Inclusive Disjunction

a type of disjunctive statement where it is possible for both disjuncts to be true at the same time

Technically Valid Inference

an inference that has a tautology as its conclusion is technically valid because it is impossible for the conclusion to be false. An inference that has a self-contradiction as one of its premises is technically valid because it is impossible for all the premises to be true

Unsound Inference

an inference that is invalid (based on the analysis of the logical component) and has at least one false premise (based on the analysis of the truth content)

Sound Inference

an inference that is valid (based on the analysis of the logical component) and has all true premises (based on the analysis of the truth content)

Deductive Analysis

analysis of an inference with the specific goal of determining the logical question of validity or invalidity. Even if the premises are true, they cannot guarantee that the conclusion is true as well

Population

any group of objects (real or imaginary) that is the subject of investigation

Syllogism

any inference that has exactly two premises and one conclusion

Statistical Generalization

based on a sample, a claim is made that a certain percentage of a given population has a specific characteristic.

Universal Generalization

based on a sample, a claim is made that every member of a given population has a specific characteristic

Contradiction

conclusion must be false but P1...Pn is true

If

designates the antecedent of a conditional statement

Only If

designates the consequent of a conditional statement

Consistent Statements

for truth-functional statements, if there is at least one line on their respective truth tables where the truth values are both true. Some way the world can be such that both statements are true. Need not be the case that that is actually how the world is

Inconsistent Statements

for truth-functional statements, if there is not even one line on their respective truth tables where the truth values are both true. For two statements to be such, it must be impossible for both statements to be true at the same time. There is no way the world could possibly be such that both statements are possibly true

Enthymemes

inference with missing premises, missing conclusions, or both

Truth Preservation

the premises, if true, guarantee that the conclusion will be true

Biconditional

the relation captured by the logical operator "≡." The truth table for material equivalence shows that it is true when the components have the same value, otherwise it is false. Means if and only if

Universal Affirmative Statement

the statement form "All S are P," which asserts that all members of the subject term are members of the predicate term

Universal Negative Statement

the statement form "No S are P," which asserts that no members of the subject term are members of the predicate term

Particular Affirmative Statement

the statement form "Some S are P," which asserts that some (at least more than one) members of the subject term are members of the predicate term

Particular Negative Statement

the statement form "Some S are not P," which asserts that some (at least one) members of the subject term are not members of the predicate term

Antecedent

the statement that follows the "if" in a conditional statement

Consequent

the statement that follows the "then" in a conditional statement

Order of Operations

the step-by-step method of generating a complete truth table by correctly identifying the order of handling the logical operators within a complex statement

Probability Theory

the theoretical frameworks that make it possible to calculate the chance that events will occur

Inductive Analysis

the type of analysis that makes it possible to investigate the strengths and weaknesses of certain inferences, such as analogical, statistical, and causal inferences

Logical Structure

the underlying logical relationship of an inference

Cogent

this inference must be strong or moderate (based on the analysis of the logical component) and have all true premises (based on the analysis of the truth content)

Analogy

to indicate that two or more things are similar by listing the relevant (significant) characteristics they have in common

Well-formed Formula

truth-functional statements that have been translated symbolically and are syntactically (grammatically) correct

Logically Equivalent Statements

truth-functional statements that have identical truth tables

Conjunction

two or more statements connected by the logical operator "and". In order for it to be true, both its parts have to be true

Disjunction

two or more statements connected by the logical operator "or". One or the other is true. In order to be false, both parts must be false

Contradictory Statements

two statements that have opposite truth values on every line of their respective truth tables. Means that no matter facts, if one is true the other is false; if one is false the other is true. No possible way the world can be as such both true or both false

Equiprobable

when each of the possible outcomes of an event has an equal probability of occurring

Representative Sample

when the characteristics of a sample are correctly identified and matched to the population under investigation. An example of the fallacy of hasty generalization. Must ensure that every member of the population has an equal chance of getting into the sample

Truth Content Error

when the information given is determined to be false. At least one of the premises is false.

Logical Component Error

when the premises of an inference, even if true, logically allow the conclusion to be false. Something or other is wrong with the relationship between the premises and the conclusion. Even if the premises are true, the conclusion might be false.

Principle of Charity

when we have to choose between different reconstructions of another person's inference. We should choose the reconstructed inference that gives the benefit of the doubt to the person presenting the inference

Conclusion Indicator Words

words or phrases that indicate the probable existence of a conclusion. Therefore, thus, so, hence, consequently, in conclusion, it follows that, we can infer that, it proves that, suggests that, implies that, we can conclude that...

Premise Indicator Words

words or phrases that indicate the probable existence of a premise. Because, since, given that, assuming that, as shown by, for the reason(s) that, as indicated by, the fact that, it follows from...