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logic > Basic Concepts > Flashcards

Basic Concepts Flashcards

1
Q

An argument is factually correct if and only if…

A

all of the premises are true

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2
Q

An argument is sound if and only if…

A

it is both factually correct and valid.

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3
Q

An argument is valid if and only if…

A

the conclusion follows from the premises.

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4
Q

What are conclusion markers?

A

Words or phrases that might indicate the presence of a conclusion.

“Therefore” “hence” “thus” “in conclusion”

A lack of conclusion markers does not mean a lack of conclusion.
The presence of conclusion markers does not necessarily mean a conclusion is present.

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5
Q

What is the counter-example method?

A

A way of proving the invalidity of an argument by showing an invalid counter-example of the same form.

If an argument admits a counter-example of the same form, with true premises and a false conclusion, the original argument is invalid.

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6
Q

What is the difference between imply and infer?

A

Not to be confused.

  • Something is implied when presented information suggests but does not directly state that something
  • Something is inferred when a reasoning entity deduces that something based on presented information
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7
Q

Premise Markers

A

Words or phrases that suggest the presence of a premise.

“since” “for” “because”

Not all premises will use recognizable markers so it is important to be able to identify a premise by reasoning.
Conversely, the presence of a marker does not necessarily indicate the presence of a premise.

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8
Q

What is the Principle of Counter-examples?

A
  • An argument (form) is invalid if it admits a counter-example.
  • An argument (form) is valid as long as it admits no counter-examples

By demonstrating that an argument admits a counterexample of the same form with a false conclusion, you demonstrate that the argument form is invalid as it is a substitution instance of that form.

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9
Q

Probably but fallible is a quality of…

A

a conclusion found in inductive reasoning.

While the premises of an inductive argument make the conclusion more likely (probable), there is still room for error (fallible).

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10
Q

The form of a statement is a function of…

A

the arrangement of its terms.

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11
Q

The form of an argument is a function of…

A

the form of the individual statements that comprise it.

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12
Q

True or False: A factually correct argument is always valid.

A

False: Any argument with all true premises can have a false conclusion. Any argument with all true premises and a false conclusion is invalid.

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13
Q

True or False: a lack of counter-examples proves an arguments validity.

A

False: While no counter-examples might make an arguments validity more likely, it may simply be the case that a counter-example has yet to be found.

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14
Q

True or False: a proposition can have multiple statements.

A

True: A statement can be formulated in multiple ways or languages to communicate a proposition.

  • The snow is white.
  • Der schnee ist weiss.
  • La neige est blanche.
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15
Q

True or False: a single statement has only one proposition.

A

False: A single statement can have multiple propositions depending on context and speaker.

“I am hungry” has different propositions when spoken by different people.

It can also imply something other than a physical need for food. “I am hungry (for action)”

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16
Q

True or False: A valid argument can be made from the argument form derived from an invalid argument.

A

False

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17
Q

True or False: A valid argument has all true premises.

A

False: An argument is valid if the truth of its conclusion is necessitated by the truth of its premises. That is to say that an argument with false premises can still be valid if the arguments conclusion follows if the premises were true.

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18
Q

True or False: Any argument with the same form as a valid argument is also valid.

A

True

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19
Q

Valid or Invalid: An argument with all true premises and a false conclusion.

A

Invalid

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20
Q

Valid or Invalid: An argument with all true premises and a true conclusion.

A

Undetermined. More information needed.

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21
Q

Valid or Invalid: An argument with not all true premises and a false conclusion.

A

Undetermined. More information needed.

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22
Q

Valid or Invalid: An argument with not all true premises and a true conclusion.

A

Undetermined. More information needed.

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23
Q

What are classes in syllogistic logic?

A

In syllogistic logic all descriptive terms refer to classes (or groups) of a particular thing.

All Lutherans are Protestants

24
Q

What are descriptive terms?

A

The nouns that replace letters in an argument form.

25
Q

What are four known valid syllogistic argument forms?

A

1) All X are Y, all Y are Z / all X are Z
2) All X are Y, some X are Z / some Y are Z
3) All X are Z, no Y are Z / no X are Y
4) No X are Y, some Y are Z / some Z are not X

26
Q

What are logical terms?

A

The words in an argument that establish the relation between descriptive terms.

27
Q

What are terms in logic?

A

Terms are the words that make up a statement or argument, and are divided into two classifications.

Descriptive terms which are the nouns and concepts within the argument.
Logical terms which establish the relation between descriptive terms.

28
Q

What are the three basic levels of logical analysis?

A
  • Syllogistic
  • Sentential
  • Predicate
29
Q

What are two basic definitions of validity?

A
  1. An argument is valid if and only if it is impossible for the conclusion to be false while all premises are true.
  2. An argument is valid if and only if the truth of its premises necessitates the truth of its conclusion.
30
Q

What basic questions should you ask yourself when analyzing an argument?

A
  1. Are all of the premises factually correct?

2. Does the conclusion follow from the premises?

31
Q

What challenges surround inductive reasoning?

A

Conclusions drawn ultimately have some level of fallibility and as a result there is no consensus on what makes an inductive argument valid.

32
Q

What does it mean for arguments to have the same form?

A

Multiple arguments have the same form when they are uniform substitution instances of the same argument form.

33
Q

What is a concrete argument?

A

Creates a fleshed out, specific argument by replacing placeholder letters from an argument form.

34
Q

What is a concrete sentence?

A

A sentence that replaces, with descriptive terms, the placeholder letters in a sentence form.

35
Q

What is a non-substitution instance?

A

An argument that does not follow the structure of an argument form is a non-substitution instance of that form.

36
Q

What is a premise?

A

A statement within an argument that attempts to support the conclusion.

37
Q

What is a sentence form?

A

Sentence forms are derived from concrete sentences, replacing descriptive terms with placeholder letters allowing for easier analysis of the sentence structure.

38
Q

What is a statement?

A

A sentence that can be judged either true or false.

Not an exclamatory, interrogative or imperative sentence.

39
Q

What is a substitution instance?

A

A concrete sentence/argument created from a sentence/argument form.

40
Q

What is a syllogism?

A

The type of argument studied in Syllogistic logic.
Uses logical terms “all” , “some” , “no” , “not” , “is” , “are”
Contains exactly two premises and one conclusion
All statements within a syllogism follow a form similar to:
1) all A are B
2) some A are C
3) no A are D
4) some A are not E

41
Q

What is a uniform substitution instance?

A

A substitution instance of an argument form where distinct descriptive terms replace and correspond to distinct placeholder letters in the argument form.

42
Q

What is an argument form?

A

Derived from an argument, replacing descriptive terms with letters so that the argument structure can be more easily analyzed.

43
Q

What is an argument?

A

A collection of statements consisting of a concluding statement and supportive premises.

44
Q

What is deductive reasoning?

A

A form of logic in which the truth of the premises necessitates the truth of the conclusion. If the argument is valid, then the conclusion must be true if the premises are true.

45
Q

What is inductive reasoning?

A

Reasoning in which the truth of the premises only makes the conclusion more likely, not absolute.

46
Q

What is logic?

A

Logic is the study of distinguishing correct reasoning from incorrect reasoning.

An unemperical science, similar to math, in that it does not rely on observational or experimental data.

47
Q

What is reasoning?

A

The process of making inferences based on available information.

48
Q

What is the difference between a statement and a proposition?

A

Statement are the words organized to attempt to represent a proposition.

A proposition is the thing or state of a thing a statement attempts to represent.

“The dog is hairy” is a statement.
The entity that is a dog or its quality of hairiness is the proposition the statement attempts to communicate.

49
Q

What is the difference between form and content?

A

Dependent on the complexity of logical analysis.
Form is concerned with the factual correctness of an argument and whether its conclusion follows from the premises.
Content is concerned with the factual correctness of each statement in the argument.

50
Q

What is the Fundamental Principle of Logic?

A

An arguments validity or invalidity is determined by its form.

Validity is a function of form.

51
Q

What is the primary concern of logic?

A

Logic is only concerned with whether a conclusion C is correct by premises P1, P2, P3,…

Logic is not concerned with the processes by which an entity comes to conclusion C by P1, P2, P3,…

52
Q

What is the Trivial Principle?

A

If an argument has all true premises and a false conclusion, it is invalid.

53
Q

What logical terms are associated with Predicate logic?

A

All terms associated with both Syllogistic and Sentential logic.

  • all
  • some
  • no
  • not
  • is
  • are
  • and
  • or
  • if… then
  • only if
54
Q

What logical terms are associated with Sentential logic?

A
  • and
  • or
  • if… then
  • only if
55
Q

What logical terms are associated with Syllogistic logic?

A
  • all
  • some
  • no
  • not
  • is
  • are
56
Q

Why are statements important in logic?

A

Statements are the building blocks of an argument. Statements are used to create a logical structure from which conclusions may be drawn.

57
Q

Why is logic concerned with statements, not propositions?

A

Statements are concrete and easy to analyze based on their form.

Propositions are elusive and difficult to understand or communicate.

logic (2 decks)

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