Critical Thinking:
Textbook
Chapter 1: What Logic Studies:
- Argument = group of statements in which conclusion is claimed to follow from
the premise
o An argument can have one or more premises, but only one conclusion
- Statement = sentence that is true or false
- Premise = information intended to provide support for a conclusion
- Conclusion = statement that is claimed to follow from the premise of an argument;
the main point of an argument
- Logic = the study of reasoning and the evaluation of arguments
Statements and Arguments:
- “Statement” refers to a specific kind of sentence: declarative sentence
o This declares, asserts, claims, or affirms that something is the case
o Every statement is either true or false and these are called truth values
- “Proposition” is the information content imparted by a statement – the meaning of
a statement
- “Inference” is used by logicians to refer to the reasoning process that is expressed by
an argument
o The act of reasoning from premises to a conclusion can be referred to
as “drawing an inference”
- Arguments are created in order to establish support for a claim and the premises
are supposed to provide good reasons for accepting the conclusion
Recognizing Arguments:
- Conclusion indicator = words and phrases that indicate the presence of a conclusion
o Shared language provides us conclusion indicators which are useful words
that people use to conclude something
o Examples:
▪ Therefore, Thus, Consequently, It proves that, It suggests that, So, It
follows that, Implies that, Hence, We can infer that, We can conclude
that
- Premise indicator = words and phrases that help us recognize arguments by
indicating the presence of premises
o Examples:
▪ Because, Since, Given that, Assuming that, As shown by, As indicated
by, The fact that, For the reason that, It follows that
- When premise and conclusion indicators aren’t present, simple strategies used
to identify parts of an argument are:
o First: locate conclusion, try placing word therefore in front of the statements
o Second: try placing the word because in front of the statements to
identify premises
, - To determine whether an argument is present:
o At least one of the statements has to provide reason or evidence for some
other statement (must be a premise)
o Must be a claim that the premise supports or implies a conclusion
▪ If the passage expresses a reasoning process – that the conclusion
follows from the premises – then we say that it makes an inferential
claim
- Inferential claim = if a passage expresses a reasoning process – that the conclusion
follows from the premises
o Objective feature of an argument and can be implicit or explicit
o Explicit inferential claims can often be identified by the premise and
conclusion indicator words and phrases
o Implicit inferential claims can still contain inferential relationship between
premises and conclusion even though it does not have explicit indicator
words
Arguments and Explanations
- Explanation = provides reasons for why or how an event occurred
o By themselves, not arguments but can form part of an argument
Truth and Logic
- Truth value analysis = determines if the information in the premises is accurate,
correct, or true
- Logical analysis = determines the strength with which the premises support
the conclusion
- A thorough analysis of arguments requires an active separation of the truth value
from the logic
Deductive and Inductive Arguments
- Logical analysis of an argument is concerned with determining the strength of inference
- Inference = the claim that the conclusion follows from the premises
- Deductive argument = one in which it claimed that the conclusion follows
necessarily from the premises
o It is claimed that under the assumption that the premises are true it is
impossible for the conclusion to be false
- Inductive argument = one in which it is claimed that the premises make the
conclusion probable
o It is claimed that under the assumption that the premises are true it
is improbable for the conclusion to be false
o Ex: Some parts of the United States have had severe winters for the last 10
years. The Farmer’s Almanac predicts another cold winter next year. Therefore,
probably some parts of the United States will have a severe winter next year.
- Looking for key words to identify deductive arguments:
o Necessarily, certainty, definitely, and absolutely
- Key words for inductive arguments:
, o Probably, likely, unlikely, improbable, plausible, implausible
- Look for strength of inferential connection between premises and conclusion
o Conclusion does follow necessarily from premises that are assumed to be
true, then the argument is deductive
o Assuming that the premises are true, the conclusion is necessarily true
o Ex: all vegetables contain vitamin C. Spinach is a vegetable. Therefore,
spinach contains vitamin C.
o In other words, if we assume that it is true that all vegetables contain vitamin
C, and if we also assume that it is true that spinach is a vegetable, then it is
impossible for spinach not to contain vitamin C, therefore this argument is
deductive
Deductive Arguments: Validity and Soundness:
- Logical analysis of a deductive argument is concerned with determining whether
the conclusion follows necessarily from the premises
- “Assuming the premises are true, is it possible for the conclusion to be false?”
- Valid deductive argument = an argument in which, assuming the premises are true, it
is impossible for the conclusion to be false
- Invalid deductive argument = an argument in which, assuming the premises are true, it
is possible for the conclusion to be false
- Determining the validity of an argument rests on logical analysis
o We rely on the assumption that the premises are true in order to
determine whether the conclusion necessarily follows
o Truth value does have a role in the overall analysis of deductive arguments
▪ The determination that a deductive argument is valid rests on
the assumption that the premises are true
▪ A valid deductive argument can have premises or a conclusion whose
actual truth value is false
- Sound argument = deductive argument is sound when argument is valid, and
premises are true
- Unsound argument = when argument is invalid or if at least one of the premises is false
Argument Form:
- In categorical logic, an argument form is an arrangement of logical vocabulary and
letters that stand for class terms such that a uniform substitution of class terms for the
letters results in an argument
- In categorical logic, a statement form is an arrangement of logical vocabulary and
letters that stand for class terms such that a uniform substitution of class terms for the
letters results in a statement
- Substitution Instance = in categorical logic, a substitution instance of a statement
occurs when a uniform substitution of class terms for the letters results in a statement
, - Substitution Instance of an Argument = occurs when a uniform substitution of
class terms for the letters results in an argument
Counterexample:
- A counterexample to a statement is evidence that shows the statement is false
- A counterexample to an argument shows the possibility that premises assumed to
be true do not make the conclusion necessarily true
- A single counterexample to a deductive argument is enough to show the argument
is invalid
Inductive Arguments: Strength and Cogency
- Often our arguments are not expected to achieve validity
- The results of analysis of inductive arguments are not all-or-nothing
- Deductive arguments can be only valid, invalid, sound, or unsound and one
deductive argument cannot be more valid than another
- One inductive argument can be classified as stronger or weaker than another
inductive argument
- We can compare them by determining the probability that their respective
conclusions are true, under the assumption that the premises are true
- Logical analysis of an inductive argument asks, “if the premises are assumed to be
true, then is it improbable for the conclusion to be false?”
- Strong inductive argument = an argument such that if the premises are assumed to
be true, then the conclusion is probably true
o If the premises are assumed to be true, then it is improbable that the
conclusion is false
- Weak inductive argument = an argument such that if the premises are assumed to
be true, then the conclusion is not probably true
- Cogent argument = an inductive argument is cogent when the argument is strong
and the premises are true
- Uncogent argument = an inductive argument is uncogent if either or both one of the
following conditions hold: the argument is weak, or the argument has at least one
false premise
Reconstructing Arguments:
- People often take shortcuts when creating arguments and sometimes people might
intentionally leave out important information because he or she thinks that the
missing information is already understood
- Arguments with missing premises, missing conclusions, or both are called enthymemes
o The missing information is therefore implied
- Enthymemes are context-driven
o Our recognition and subsequent reconstruction of the argument depends on
the setting in which the information appears
Textbook
Chapter 1: What Logic Studies:
- Argument = group of statements in which conclusion is claimed to follow from
the premise
o An argument can have one or more premises, but only one conclusion
- Statement = sentence that is true or false
- Premise = information intended to provide support for a conclusion
- Conclusion = statement that is claimed to follow from the premise of an argument;
the main point of an argument
- Logic = the study of reasoning and the evaluation of arguments
Statements and Arguments:
- “Statement” refers to a specific kind of sentence: declarative sentence
o This declares, asserts, claims, or affirms that something is the case
o Every statement is either true or false and these are called truth values
- “Proposition” is the information content imparted by a statement – the meaning of
a statement
- “Inference” is used by logicians to refer to the reasoning process that is expressed by
an argument
o The act of reasoning from premises to a conclusion can be referred to
as “drawing an inference”
- Arguments are created in order to establish support for a claim and the premises
are supposed to provide good reasons for accepting the conclusion
Recognizing Arguments:
- Conclusion indicator = words and phrases that indicate the presence of a conclusion
o Shared language provides us conclusion indicators which are useful words
that people use to conclude something
o Examples:
▪ Therefore, Thus, Consequently, It proves that, It suggests that, So, It
follows that, Implies that, Hence, We can infer that, We can conclude
that
- Premise indicator = words and phrases that help us recognize arguments by
indicating the presence of premises
o Examples:
▪ Because, Since, Given that, Assuming that, As shown by, As indicated
by, The fact that, For the reason that, It follows that
- When premise and conclusion indicators aren’t present, simple strategies used
to identify parts of an argument are:
o First: locate conclusion, try placing word therefore in front of the statements
o Second: try placing the word because in front of the statements to
identify premises
, - To determine whether an argument is present:
o At least one of the statements has to provide reason or evidence for some
other statement (must be a premise)
o Must be a claim that the premise supports or implies a conclusion
▪ If the passage expresses a reasoning process – that the conclusion
follows from the premises – then we say that it makes an inferential
claim
- Inferential claim = if a passage expresses a reasoning process – that the conclusion
follows from the premises
o Objective feature of an argument and can be implicit or explicit
o Explicit inferential claims can often be identified by the premise and
conclusion indicator words and phrases
o Implicit inferential claims can still contain inferential relationship between
premises and conclusion even though it does not have explicit indicator
words
Arguments and Explanations
- Explanation = provides reasons for why or how an event occurred
o By themselves, not arguments but can form part of an argument
Truth and Logic
- Truth value analysis = determines if the information in the premises is accurate,
correct, or true
- Logical analysis = determines the strength with which the premises support
the conclusion
- A thorough analysis of arguments requires an active separation of the truth value
from the logic
Deductive and Inductive Arguments
- Logical analysis of an argument is concerned with determining the strength of inference
- Inference = the claim that the conclusion follows from the premises
- Deductive argument = one in which it claimed that the conclusion follows
necessarily from the premises
o It is claimed that under the assumption that the premises are true it is
impossible for the conclusion to be false
- Inductive argument = one in which it is claimed that the premises make the
conclusion probable
o It is claimed that under the assumption that the premises are true it
is improbable for the conclusion to be false
o Ex: Some parts of the United States have had severe winters for the last 10
years. The Farmer’s Almanac predicts another cold winter next year. Therefore,
probably some parts of the United States will have a severe winter next year.
- Looking for key words to identify deductive arguments:
o Necessarily, certainty, definitely, and absolutely
- Key words for inductive arguments:
, o Probably, likely, unlikely, improbable, plausible, implausible
- Look for strength of inferential connection between premises and conclusion
o Conclusion does follow necessarily from premises that are assumed to be
true, then the argument is deductive
o Assuming that the premises are true, the conclusion is necessarily true
o Ex: all vegetables contain vitamin C. Spinach is a vegetable. Therefore,
spinach contains vitamin C.
o In other words, if we assume that it is true that all vegetables contain vitamin
C, and if we also assume that it is true that spinach is a vegetable, then it is
impossible for spinach not to contain vitamin C, therefore this argument is
deductive
Deductive Arguments: Validity and Soundness:
- Logical analysis of a deductive argument is concerned with determining whether
the conclusion follows necessarily from the premises
- “Assuming the premises are true, is it possible for the conclusion to be false?”
- Valid deductive argument = an argument in which, assuming the premises are true, it
is impossible for the conclusion to be false
- Invalid deductive argument = an argument in which, assuming the premises are true, it
is possible for the conclusion to be false
- Determining the validity of an argument rests on logical analysis
o We rely on the assumption that the premises are true in order to
determine whether the conclusion necessarily follows
o Truth value does have a role in the overall analysis of deductive arguments
▪ The determination that a deductive argument is valid rests on
the assumption that the premises are true
▪ A valid deductive argument can have premises or a conclusion whose
actual truth value is false
- Sound argument = deductive argument is sound when argument is valid, and
premises are true
- Unsound argument = when argument is invalid or if at least one of the premises is false
Argument Form:
- In categorical logic, an argument form is an arrangement of logical vocabulary and
letters that stand for class terms such that a uniform substitution of class terms for the
letters results in an argument
- In categorical logic, a statement form is an arrangement of logical vocabulary and
letters that stand for class terms such that a uniform substitution of class terms for the
letters results in a statement
- Substitution Instance = in categorical logic, a substitution instance of a statement
occurs when a uniform substitution of class terms for the letters results in a statement
, - Substitution Instance of an Argument = occurs when a uniform substitution of
class terms for the letters results in an argument
Counterexample:
- A counterexample to a statement is evidence that shows the statement is false
- A counterexample to an argument shows the possibility that premises assumed to
be true do not make the conclusion necessarily true
- A single counterexample to a deductive argument is enough to show the argument
is invalid
Inductive Arguments: Strength and Cogency
- Often our arguments are not expected to achieve validity
- The results of analysis of inductive arguments are not all-or-nothing
- Deductive arguments can be only valid, invalid, sound, or unsound and one
deductive argument cannot be more valid than another
- One inductive argument can be classified as stronger or weaker than another
inductive argument
- We can compare them by determining the probability that their respective
conclusions are true, under the assumption that the premises are true
- Logical analysis of an inductive argument asks, “if the premises are assumed to be
true, then is it improbable for the conclusion to be false?”
- Strong inductive argument = an argument such that if the premises are assumed to
be true, then the conclusion is probably true
o If the premises are assumed to be true, then it is improbable that the
conclusion is false
- Weak inductive argument = an argument such that if the premises are assumed to
be true, then the conclusion is not probably true
- Cogent argument = an inductive argument is cogent when the argument is strong
and the premises are true
- Uncogent argument = an inductive argument is uncogent if either or both one of the
following conditions hold: the argument is weak, or the argument has at least one
false premise
Reconstructing Arguments:
- People often take shortcuts when creating arguments and sometimes people might
intentionally leave out important information because he or she thinks that the
missing information is already understood
- Arguments with missing premises, missing conclusions, or both are called enthymemes
o The missing information is therefore implied
- Enthymemes are context-driven
o Our recognition and subsequent reconstruction of the argument depends on
the setting in which the information appears
