All particles have mass
All electrons are particles
All electrons have mass
All fish swim
All sharks are fish
Therefore, all sharks swim
Deductive and Inductive Arguments
A deductive
argument is an argument in which it is thought that the premises provide a
guarantee of the truth of the conclusion. In a deductive argument, the premises
are intended to provide support for the conclusion that is so strong that, if
the premises are true, it would be impossible for the conclusion to be false.
argument is an argument in which it is thought that the premises provide a
guarantee of the truth of the conclusion. In a deductive argument, the premises
are intended to provide support for the conclusion that is so strong that, if
the premises are true, it would be impossible for the conclusion to be false.
An inductive
argument is an argument in which it is thought that the premises provide
reasons supporting the probable truth of the conclusion. In an inductive
argument, the premises are intended only to be so strong that, if they are
true, then it is unlikely that the conclusion is false.
argument is an argument in which it is thought that the premises provide
reasons supporting the probable truth of the conclusion. In an inductive
argument, the premises are intended only to be so strong that, if they are
true, then it is unlikely that the conclusion is false.
The difference
between the two comes from the sort of relation the author or expositor of
the argument takes there to be between the premises and the conclusion. If the
author of the argument believes that the truth of the premises definitely
establishes the truth of the conclusion due to definition, logical entailment
or mathematical necessity, then the argument is deductive. If the author of the
argument does not think that the truth of the premises definitely establishes
the truth of the conclusion, but nonetheless believes that their truth provides
good reason to believe the conclusion true, then the argument is inductive.
between the two comes from the sort of relation the author or expositor of
the argument takes there to be between the premises and the conclusion. If the
author of the argument believes that the truth of the premises definitely
establishes the truth of the conclusion due to definition, logical entailment
or mathematical necessity, then the argument is deductive. If the author of the
argument does not think that the truth of the premises definitely establishes
the truth of the conclusion, but nonetheless believes that their truth provides
good reason to believe the conclusion true, then the argument is inductive.
The noun “deduction”
refers to the process of advancing a deductive argument, or going through a
process of reasoning that can be reconstructed as a deductive argument. “Induction” refers to the process
of advancing an inductive argument, or making use of reasoning that can be
reconstructed as an inductive argument.
refers to the process of advancing a deductive argument, or going through a
process of reasoning that can be reconstructed as a deductive argument. “Induction” refers to the process
of advancing an inductive argument, or making use of reasoning that can be
reconstructed as an inductive argument.
Because deductive arguments are those in which the
truth of the conclusion is thought to be completely guaranteed and not just
made probable by the truth of the premises, if the argument is a sound one, the
truth of the conclusion is “contained within” the truth of the
premises; i.e., the conclusion does not go beyond what the truth of the
premises implicitly requires. For this reason, deductive arguments are usually
limited to inferences that follow from definitions, mathematics and rules of
formal logic.
truth of the conclusion is thought to be completely guaranteed and not just
made probable by the truth of the premises, if the argument is a sound one, the
truth of the conclusion is “contained within” the truth of the
premises; i.e., the conclusion does not go beyond what the truth of the
premises implicitly requires. For this reason, deductive arguments are usually
limited to inferences that follow from definitions, mathematics and rules of
formal logic.
For example, the following are deductive arguments:
• There are 32 books on the top-shelf of the
bookcase, and 12 on the lower shelf of the bookcase. There are no books
anywhere else in my bookcase. Therefore, there are 44 books in the bookcase.
bookcase, and 12 on the lower shelf of the bookcase. There are no books
anywhere else in my bookcase. Therefore, there are 44 books in the bookcase.
• Bergen is either in Norway or Sweden. If
Bergen is in Norway, then Bergen is in Scandinavia. If Bergen is in Sweden,
then Bergen is in Scandinavia. Therefore, Bergen is in Scandinavia.
Bergen is in Norway, then Bergen is in Scandinavia. If Bergen is in Sweden,
then Bergen is in Scandinavia. Therefore, Bergen is in Scandinavia.
Inductive arguments, on
the other hand, can appeal to any consideration that might be thought relevant
to the probability of the truth of the conclusion. Inductive arguments,
therefore, can take very wide ranging forms, including arguments dealing with
statistical data, generalizations from past experience, appeals to signs,
evidence or authority, and causal relationships.
the other hand, can appeal to any consideration that might be thought relevant
to the probability of the truth of the conclusion. Inductive arguments,
therefore, can take very wide ranging forms, including arguments dealing with
statistical data, generalizations from past experience, appeals to signs,
evidence or authority, and causal relationships.
Inductive Arguments
Govier lists four characteristics of inductive arguments:
1. Premises and conclusion are all empirical
propositions.
propositions.
2. Conclusion is not deductively entailed by
premises.
premises.
3. Reasoning used to infer the conclusion is based
on the assumption that the regularities described in the premises will persist.
on the assumption that the regularities described in the premises will persist.
4. Inference is either that unexamined cases will
resemble examined ones or that evidence makes an explanatory hypothesis
probable.
resemble examined ones or that evidence makes an explanatory hypothesis
probable.
Some dictionaries define “deduction” as reasoning from the general to specific and
“induction” as reasoning from the specific to the general. While this
usage is still sometimes found even in philosophical and mathematical contexts,
for the most part, it is outdated. For example, according to the more modern
definitions given above, the following argument, even though it reasons from
the specific to general, is deductive, because the truth of the premises
guarantees the truth of the conclusion:
“induction” as reasoning from the specific to the general. While this
usage is still sometimes found even in philosophical and mathematical contexts,
for the most part, it is outdated. For example, according to the more modern
definitions given above, the following argument, even though it reasons from
the specific to general, is deductive, because the truth of the premises
guarantees the truth of the conclusion:
The members of the Williams family are Susan,
Nathan and Alexander.
Nathan and Alexander.
Susan wears glasses.
Nathan wears glasses.
Alexander wears glasses.
Therefore, all members of the Williams family wear
glasses.
glasses.
Moreover, the following argument, even though it
reasons from the general to specific, is inductive:
reasons from the general to specific, is inductive:
It has snowed in Massachusetts every December in
recorded history.
recorded history.
Therefore, it will snow in Massachusetts this
coming December.
coming December.
Mathematical Premises
It is worth noting, therefore, that the proof
technique used in mathematics called “mathematical induction”, is,
according to the contemporary definition given above, actually a form of
deduction. Proofs that make use of mathematical induction typically take the
following form:
technique used in mathematics called “mathematical induction”, is,
according to the contemporary definition given above, actually a form of
deduction. Proofs that make use of mathematical induction typically take the
following form:
Property P is true of the number O.
For all natural numbers n, if P holds of n then P
also holds of n + 1.
also holds of n + 1.
Therefore, P is true of all natural numbers.
When such a proof is given by a mathematician, it
is thought that if the premises are true, then the conclusion follows
necessarily. Therefore, such an argument is deductive by contemporary
standards.
is thought that if the premises are true, then the conclusion follows
necessarily. Therefore, such an argument is deductive by contemporary
standards.
Because the difference between inductive and
deductive arguments involves the strength of evidence which the author believes
the premises to provide for the conclusion, inductive and deductive arguments
differ with regard to the standards of evaluation that are applicable to them.
The difference does not have to do with the content or subject matter of the
argument. Indeed, the same utterance may be used to present either a deductive
or an inductive argument, depending on the intentions of the person advancing
it. Consider as an
deductive arguments involves the strength of evidence which the author believes
the premises to provide for the conclusion, inductive and deductive arguments
differ with regard to the standards of evaluation that are applicable to them.
The difference does not have to do with the content or subject matter of the
argument. Indeed, the same utterance may be used to present either a deductive
or an inductive argument, depending on the intentions of the person advancing
it. Consider as an
For example, the following are Inductive arguments:
Dom Perignon is champagne, so it must be made in
France.
France.
It might be clear from context that the speaker
believes that having been made in the Champagne area of France is part of the
defining feature of “champagne” proper and therefore the conclusion
follows from the premise by definition. If it is the intention of the speaker
that the evidence is of this sort, then the argument is deductive. However, it
may be that no such thought is in the speaker’s mind. He or she may merely
believe that most champagne is made in France, and may be reasoning
probabilistically. If this is his or her intention, then the argument is
inductive.
believes that having been made in the Champagne area of France is part of the
defining feature of “champagne” proper and therefore the conclusion
follows from the premise by definition. If it is the intention of the speaker
that the evidence is of this sort, then the argument is deductive. However, it
may be that no such thought is in the speaker’s mind. He or she may merely
believe that most champagne is made in France, and may be reasoning
probabilistically. If this is his or her intention, then the argument is
inductive.
It is also worth noting that, at its core, the
distinction has to do with the strength of the justification that the author or
expositor of the argument intends that the premises provide for the conclusion.
If the argument is logically fallacious, it may be that the premises actually
do not provide justification of that strength or even any justification at all.
Consider the following argument:
distinction has to do with the strength of the justification that the author or
expositor of the argument intends that the premises provide for the conclusion.
If the argument is logically fallacious, it may be that the premises actually
do not provide justification of that strength or even any justification at all.
Consider the following argument:
All odd numbers are integers.
All even numbers are integers.
Therefore, all odd numbers are even numbers.
This argument is logically invalid. In actuality,
the premises provide no support whatever for the conclusion. However, if this
argument were ever seriously advanced, we must assume that the author would
believe that the truth of the premises guarantees the truth of the conclusion.
Therefore, this argument is still deductive. A bad deductive argument is not an
inductive argument.
the premises provide no support whatever for the conclusion. However, if this
argument were ever seriously advanced, we must assume that the author would
believe that the truth of the premises guarantees the truth of the conclusion.
Therefore, this argument is still deductive. A bad deductive argument is not an
inductive argument.
ANSWER: QUESTION 3
Where G is true, W is true, G.W is true, where G
and W is false, G.W is false, where G is false and W is true G.W is false and
where G is false and W is false G.W is false.
and W is false, G.W is false, where G is false and W is true G.W is false and
where G is false and W is false G.W is false.
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G
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W
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G.W
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T
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T
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T
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T
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F
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F
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F
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T
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F
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F
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F
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F
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