Abstract: A deductive argument's premises
provide conclusive evidence for the truth of its conclusion. An
inductive argument's premises provide probable evidence for the truth
of its conclusion. The difference between deductive and inductive
arguments does not specifically depend on the specificity or generality
of the composite statements. Both kinds of arguments are characterized
and distinguished with examples and exercises.
The central concern of logic is the evaluation of arguments. In general,
arguments can be evaluated as deductive or inductive.[1]
Brian Skyrms defines the difference this way:
“When an argument is such that the truth
of the premises guarantees the truth of the conclusion, we shall
say that it is deductively valid.
When an argument is not deductively valid but
nevertheless the premises provide good evidence for the conclusion,
the argument is said to be inductively
strong.”[2]
In all cases, valid deductive arguments are about certain or
necessary inference; whereas, correct inductive arguments are about
probable or likely inferences.
Deduction: an argument whose
premises, if true, provide conclusive evidence for the truth
of its conclusion.
Let's take the classic example which must be mentioned at
least once in this course:
All men are mortal. Socrates is a man.
Therefore, Socrates is mortal.
Note how the grammatical structure of this argument form
makes the conclusion necessarily follow — not with
probability, but with certainty. One way to remember this
relationship is to think about it in this way:
All B is [in] C.
All A is [in] B.
∴ All A is [in] C.
Deductive arguments are commonly defined in accordance with
an intentional account: viz, arguments whose
premises are claimed or intended to provide
conclusive reasons for their conclusion — the claim
that it is absolutely impossible for the premises to be true
unless the conclusion is true also.[3]
This explanation, as you might have noticed is not
entirely complete. Some invalid deductive arguments
are correct inductive arguments — if logic is deemed
a prescriptive discipline, and the definition is not
based on a dialogical or contextual factor of intentions.
The reader has probably already noticed that the AAA-2
syllogism has been used in these notes in different places
as both an invalid deductive argument and a weak inductive
argument in nondialogical contexts.
is used since some deductive arguments do not meet
this claim and are therefore are called deductively
“invalid.”
However, if such arguments are evaluated as probable
arguments, they would be correct inductive arguments if the
premises were to provide good evidence for their respective
conclusions.
If the premises are true and they necessitate the truth
of the conclusion, then the argument is said to be deductively
valid and sound. In such a case, it is
impossible for the conclusion to be logically inconsistent with
the premises.
The following examples reveal some common kinds of deductive arguments;
note how some of the described types are not exclusive categories and
can overlap somewhat.
Analytic Inferences: the conclusion necessarily
follows from the interrelated meanings of the words used.
”Peter is John's brother,
so John must be Peter's brother.”
The argument is deductive since it relies
on the lexical definition of “brother.”
(Note this trivial deductive argument has no general statements.)
In sum, in analytic inferences, the conclusion follows necessarily
from the premises. An analytical inference differs from a valid
formal deductive inference in that an analytical inference is
not valid due to its grammatical form or structure, but is valid due
to the meanings of the statements within it.
The validity in this case depends upon the meanings of its terms (so-called
“material factors”) rather than the form of its grammar.
The next example requires some careful thought in order to
assess whether or not the conclusion follows with certainty:
“Mystery is delightful, but unscientific,
(2) since it depends upon ignorance.“[4]
Implicitly we know that science involves knowledge, and ignorance
is the opposite of science, so anything depending upon ignorance
is unscientific.
Finally, the following example, which is claimed to be a
deductive argument, is in one sense only hypothetically so:
c.“Grant that the phenomena of
intelligence conform to laws; grant that the evolution of
intelligence in a child also conforms to laws; and it follows
inevitably that education cannot be rightly guided without a
knowledge of those laws.”[5]
The claim is deductive since the author, Herbert Spencer,
declares that the conclusion follows inevitably. If his claim is
correct the argument is valid. If his claim is incorrect, then the
argument is invalid.
Specifically, if it can be proved either empirically or logically
that education can be rightly guided without knowing the laws
he mentions, then the argument is deductively invalid.
This deductive argument is in a sense hypothetical since the truth of
the premises have not been established. So if Spencer could prove
that the premises are true, then the conclusion would necessarily also
be true.
Syllogistic Inferences: A syllogism is a two premise
argument containing three terms, each of which is used twice. The
logic is based on fact that two different things related to a third
thing ought to be related to each other. In the following example,
one of the premises is not stated since it is implicitly assumed:
No druggist is a chemist.
That's because all apothecaries are chemists.
The conclusion follows conclusively only if we supply the
questionable implicit premise that no apothecaries are druggists:
All [apothecaries] are [chemists].
→{No [apothecaries] are [druggists]}
No [druggists] are [chemists].
Note that [apothecaries], the middle term, is the term by which
the other two terms are related. (This argument is valid, but is not
a sound argument if at least one apothecary
is found to be a druggist as well.)
Mathematical inferences: idealizations of logical or
mathematical calculations in the empirical sciences.
E.g., “Since a shell weighing 64 lbs leaves a
gun with a velocity of 3,000 feet per second, and arrives at a
target with a striking velocity of 500 feet per second, 11,250
BTU of heat resistance is generated.”[6]
I.e., these types of inferences follow from the truths of
mathematics where the empirical facts and scientific equations are
assumed true. Mathematical inferences are one type of analytical
inferences.
So, if the premises are true and the formula for energy
conversion into heat is correct, then the conclusion follows with
certainty. Note that it's the calculation that is deductive. The
actual exact physical quantities stated cannot be known with certainty
and most empirical background conditions are ignored, so these aspects
of the inference are assumed nonempirical idealizations.
Logical inferences: arguments which can be described by
symbolic notation in order to simplify the relationships among the
structures (rather being evaluated from the meaning of the statements
themselves).
E.g., “If you work hard, then you will succeed,
and if you succeed, then you will be happy; therefore, if
you work hard, you will be happy.”
Given w→s→h, it
follows w→h
(These types of inferences follow from the truths of logic. The logic
rule used here is called a hypothetical syllogism.)
Induction: an
argument whose premises, if true, provide some evidence for the truth
of its conclusion.
Inductive arguments can range in probability from very low to
very high, but always less than 100%. The probability of the conclusion
drawn from an inductive argument is only an estimate and usually not
known exactly.[7]
(Note that the mathematical calculations in statistical reasoning are
deductive even though the conclusions themselves are only probable. In
other words, in statistics, the probability expressed in the conclusion
follows from the premises with mathematical necessity.)
Often (but not always!) induction is the sort of inference which
attempts to reach a conclusion concerning all the members of a class or
group on the basis of the observations of only some of them. So to put
it another way, the conclusion of a very strong inductive argument with
true premises is improbably false.
Inductive arguments are often said to be empirical because they
depend on observations or experience about the world. This is a
typical weak observational argument:
“I've seen many persons with creased earlobes who have had
heart attacks, so I conclude that (all) persons who have creased
earlobes are prone to have heart attacks.”[8]
Since the argument is weakly inductive, it would be an error to infer
the conclusion is probably true. All that can be safely said is that
there is some indication that the conclusion might be true.
Words indicating probability-qualifying terms in
statements such as “may,” “might,”
“could.” “should,” “must”
“ought,” as well as “likely,” “possibly,”
“probably,” “maybe”
probabilistic inferences, including use of modal verbs in conclusions.
For example:
“Aristophanes is the most material of ancient poets:
nevertheless great, and in his department, classic, from his
copious imagination and keen poetic invention. He. may,
therefore, by all means, in this capacity, rank with the
great Tragic writers.”[9]
In this example, “may” indicates the conclusion possibly
follows.
The use of existing information as a basis to discover or predict
additional or future information: (1) the approximate calculation from
the known value of something to a predicted unknown value if current trends
continue or (2) the estimation of the future value of something from known
values by means of some method.
inferring by some method unknown information from known information.
For example:
“A systematic evaluation of genotoxic responses will
allow us to determine how genotoxic effects in rodents
extrapolate to similar effects in humans. Research has already
indicated that human cells may be more capable than rodent
cells of repairing at least some DNA lesions, implying that
human cells may be less sensitive to genotoxic agents.”[10]
Here, the word “implying” separates the premises from the
conclusion; note also the modal verb “may.”
Predictive Techniques: the future will likely
continue to be like the past.
“Since past experience indicates that irrigation is
necessary for sustained production, the cost of a commercial
grove with irrigation facilities would probably be at least
$200.00 per acre higher than the official estimate.”[11]
In addition to the prediction of a higher cost being based on past
experience, a second clue to this argument being inductive is the use
of the word, “probably.”
Some Parts to All Parts: Reasoning from the qualities
of some members of a group to a conclusion about the qualities of all
the members.
Since some of the individual parts have a characteristic; it could be
that all of the individual parts have that characteristic.[12]
One bird species with one color-form in the same population has
been shown to be relatively stable over time, so all bird species
with one color-form in that same population will remain relatively
stable over time, as well.
Notice that this example is not reasoning from the properties of a
part of something to a property of the whole of that thing.
Generally speaking, what is thought to be true of the members of a
class individually is not true of the class considered as a whole
because a term is used in a distributive sense (about each and every
individual thing) in the premises and an a collective sense (about the
whole itself) in the conclusion.
Here's another argument from parts of a class:
“According to a Jenkins Group survey, 42% of college
graduates will never read another book. Since most people read
bestsellers printed in the past 10 years, it follows that
virtually no one is reading the classics.”[13]
Note that the word “virtually” in this example hints that
the conclusion does not follow with absolute certainty.
Causal Reasoning: Since one event often precedes another
event, the first is sometimes considered a probable cause of the second.
(Cf., post hoc ergo
propter hoc).
”[The reason] as to why productivity has slumped since
2004 is a simple one. That year coincided with the creation of
Facebook.”[14]
Usually examples like this post hoc example are
considered instances of the fallacy of false cause because correlation
does not imply causation. Yet, such premises sometimes provide weak
evidence for the truth of the conclusion.
Analogies, hunches, forecasts, and so forth:
“I share … [a] disrespect for religious
certitude, which is a simulacrum of faith; but suggest that
scientific certitude is barely less lethal. Just as we do not judge
the value of science by nuclear weapons, pollution and junk food,
we should not judge religion by its abuses.”[15]
Analogical inductive reasoning is based on the heuristic
Many accounts of the difference between induction and deduction are
stated in terms of the generality and specificity of the statements in
the arguments. However, this distinction is no longer considered correct
in logic.[16]
It is sometimes argued that in deduction particular statements are
always inferred from the general statements, as in this example:
All organisms have chromosomes.
[This fruit fly is an organism.]
∴This fruit fly has chromosomes.
(The brackets in the above argument indicate an implicit premise.)
And it is sometimes said that in induction the general is
inferred from the particular as illustrated here:
A red-eyed fruit fly has large
chromosomes.
A white-eyed fruit fly has large
chromosomes.
A Hawaiian fruit fly has large
chromosomes.
∴All fruit flies have
large chromosomes.
This form of inductive argument is termed “enumerative”
or “incomplete” induction because there are other kinds
of fruit flies.
But these definitions are misleading for several reasons. Let us
briefly note some of them.
In some kinds of deduction, the general is inferred from the
particular, e.g:
Only Plato and Aristotle were great Greek
philosophers.
Plato and Aristotle lived in Athens.
∴ All the great Greek
philosophers lived in Athens.
This form of argument is explained below as “perfect
induction” or “induction by complete enumeration”
since its general conclusion is based on a listing of all of the
possible specific instances. In other words, induction by complete
enumeration is actually a deductive argument since its conclusion
follows with certainty from its premises.
In induction by complete enumeration all the members of a
class are listed with some characteristic and then a summary
statement is made about all of them:
Each senator was present at today's
session.
∴ All senators were present
at today's session.
This example of induction by complete enumeration is a deductive
argument and so this might be a bit confusing at first. To state
the point in general terms, induction by complete enumeration is a
form of deductive argument:
Entities E1, E2, and
E3 all have property p.
Entities E1, E2, and
E3 are the only members of class M.
∴ All members of class M have property
p.
Induction by complete enumeration is only possible when knowledge
about every individual of what is talked about is known. The
conclusion is simply a summary of that information.
In some kinds of induction, the particular is inferred from
the general:
All the great Greek philosophers wrote treatises
on science.
All philosophers named Aristotle wrote
treatises on science.
This argument is only very slightly probable even though all of the
statements in it happen to be true because not enough information
about Aristotle is given in the premises to validly entail the
conclusion true. E.g., if “Isaac Newton” were
substituted for “Aristotle” in the above argument, the
argument's conclusion would be false. Both arguments, given the
information in the premises, are equally plausible.
The argument is actually very weakly inductive even though it moves
from general premises to a specific conclusion.[18]
Finally, you might remember having difficulty in distinguishing
between deduction and induction in terms of the generality or the
specificity of the statements when you studied this topic in other
classes. It's likely you and your instructor found it sometimes
difficult to distinguish between a general statement and a particular
statement in some arguments.
Consider the difficulty of distinguishing general from
specific statements in the following cases:
The whale is a mammal. [as in an encyclopedia entry]
All novelists of Waverly named Sir Walter
Scott are historical writers. [a definite description]
All present kings of France are bald. [a non-existent entity]
All ideal gases are perfectly elastic. [a theoretical entity or
nonobservable entity]
Specific statements can often be written in the form of general
statements or vice versa.
When we make a statement, especially in some theoretical areas of
science, we do not always know how many, if any, members of the
subject class of statements exist. Consequently, it could be begging the question
Also termed “circular argument” or
“petitio principii,” the
argumentative fallacy of assuming in a premise the same statement
which was to be proved. Formally the argument is valid, but is
considered by most logicians fallacious when deceptive.
to assume that a premise statement is specific
or general when the statement's reference is uncertain.
Unlike deductive arguments in which no additional evidence can be added
to make the inference more certain, inductive arguments can be made more
probable by adding additional evidence.
Inductive Arguments: Bryan Skyrms provides this example
of a strong argument whose conclusion is made more likely by adding
additional evidence:
The conclusion of this argument might seem to follow with certainty,
but additional evidence can be added to increase the probability of
the truth of the conclusion.
For example adding the information that that George has a
sprained ankle, a broken leg, and a heart condition makes it
even less likely that George can run a 4 minute mile.
However, when we add the premise that George is paraplegic,
then the argument is transformed into a deductive argument because
now the conclusion follows with certainty by the meanings of the
words used in the statements.
Deductive Arguments: In deductive arguments, the conclusion
cannot have any empirical information which is not specifically included
in the premises, and the conclusion cannot be more be more general in
scope than the premises.
For example, in induction by complete enumeration (which is
a deductive argument, as described above), the conclusion is
simply a summary of information about the all of the different
instances enumerated in the premises:
Two performers in the Kronos Quartet
play violin, one plays viola and another plays cello.
∴ The Kronos Quartet is
composed of performers who all play stringed instruments.
Violins, violas, and cellos are defined as stringed instruments,
and the composition of a string quartet is known by the definition
of quartet. There is no empirical information in the conclusion which
was not present in the premises.
In valid deductive arguments, if the premises are true, then
the truth of the conclusion follows with certainty.
Worked Example: Distinguishing deduction from
induction sometimes requires analysis. Consider the following
passage by from Hermann Hesse:
“If we hate a person, we hate something in him that
is part of ourselves. What isn't part of ourselves doesn't
disturb us.”[20]
To assess the argument as deductive or inductive, first, we
begin by identifying the conclusion by recognizing that the first
statement is less well known than the second statement, and the
second statement seems to provide a reason for the first statement.
Second, using this information, we can set up the argument
as follows:
What isn't part of ourselves doesn't
disturb us.
∴ If we hate a person, we
hate something in him that is part of ourselves.
Third, if necessary, we can simplify the argument for clarity:
All things disturbing us are things
part of ourselves.
∴ Our hating a person is hating
something in him which is part of ourselves.
Fourth, in order to understand the connection between the premise
and conclusion, we charitably supply obvious implicit assumptions
of the author in order to complete the reasoning:
All [things disturbing us] are
[things part of ourselves].
→ {[Our hating a person] is [a thing
that disturbs us].}
∴ [Our hating a person] is [hating
a thing part of ourselves].
In arranging the things mentioned by generality of scope, we can
see that the conclusion is contained within the scope of the
premises:
[Things part of us] » [things disturbing us]
» [our hating a person]
[Things part of us] » [our hating a person]
All throughout history people repeat
the same mistakes, so we can conclude that similar mistakes will be
made in the future.
Inductive Argument —The conclusion does not follow with absolute
certainty. The reasoning assumes that the future will be in some sense
like the past.
The whale is a mammal, so all killer
whales are mammals.
Deductive Argument — With the implicit premise that killer
whales are whales, the conclusion follows with absolute certainty.
In this example, the reasoning does proceed from general to less
general, but the first general statement can be misleading to some
persons.
All killer whales are mammals, so the
whale is a mammal.
Inductive Argument — As the argument stands, the conclusion is only
probable. Notice that the reasoning is from part to whole even though
the argument “appears” to be reasoned from general to specific.
Even if it is assumed that all persons know whales are necessarily mammals,
the reasoning in this argument is that the reason whales are mammals
is due to one of its subclasses (killer whales) being mammals. This reason,
considered by itself, is insufficient to prove the truth of the conclusion.
“Because of our preoccupation
with the present moment and the latest discovery, we do not read the
great books of the past. Because we do not do this sort of reading,
and do not think it is important, we do not bother about trying to
learn to read difficult books. As a result, we do not learn to read
well at all.” [21]
Inductive Argument and/or Explanation — Depending on the context of
the passage, it is most likely to be an explanation as to why many persons
do not read well rather than an argument proving why we do not read well.
If it is evaluated as an argument, then it would be inductive, since it is
possible for someone who has already learned to read well to be preoccupied
at the present moment and that is why that person does not now read great
or difficult works.
“[M]ost people not only recognize
nothing is good in our life unless it is profitable, but look upon
friends as so much stock, caring most for those by whom they hope to
make most profit. Accordingly they never possess that most beautiful
and most spontaneous friendship which must be sought solely for itself
without any ulterior object.[22]
Deductive Argument — The argument is simplified as follows:
All persons who only look upon friends for profit are people who do not
seek friendship without some ulterior motive.
∴They seek only to profit from friends and don't look solely
for friendship-in-itself (i.e., a friendship without an ulterior
motive.)
“Africans are notoriously religious, and each people has it
own religious system with a set of beliefs and practices. Religion permeates
into all the departments of life so fully, that it is not easy or possible
always to isolate it. A study of these religious systems, is, therefore,
ultimately a study of the peoples themselves in all the complexities of other
traditional and modern
life.”[23]
Inductive Argument — The argument is a strong inductive argument since
a premise indicates it is not always easy or possible to study each
people apart from their religion, suggesting that in some cases studying
some people without considering their religion might be possible. So the
conclusion does not follow with absolute certainty.
It might be surprising to note that had the conclusion substituted the phrase “almost always” for “ultimately”, the argument would
have been deductive. That is, the argument would be comparable to the following
simplification:
Most African people's religious beliefs are integrated into their lives.
A study of African religions involves studying how most African peoples live.
“Political change is a process that consolidates privilege, which
further entrenches the oligarchic order. Thus the every widening economic
gap — inevitably, a cultural and political gap—between the rich
and the poor.”[24]
Deductive Argument — The conclusion is claimed to follow with
complete certainty as indicated by the adverb “inevitably” in
the conclusion of the argument.
“[A]nxiety sufferers … may respond to their feelings by leaving
nothing to chance. At work, they appear polished and prepared when giving a
presentation because they consider every question that could be posed by
colleagues beforehand and memorize possible answer in the days leading up to a
meeting.”[25]
Inductive Argument — Since the first sentence, the conclusion of this
argument, includes the modal verb “may” the conclusion is not
claimed to follow with certainty. Hence, this argument is inductive since
the conclusion is claimed to follow with some degree of probability.
”The exegete needs to possess not only scholarly training but also the
continual deepening of his own meditative experience, so that he will not
introduce mistaken interpretations into the text. Thus he is required not
only to read the subject deeply enough to penetrate its key themes, but also
to meditate in order to have the necessary mental purity and ‘wisdom
eye&rsqquo; to carry out the
work.”[26]
Deductive Argument —The meaning of the premise phrasing “scholarly
training” and “deepening meditative experience” respectively
imply the meaning of the conclusion phrasings ”reading deeply” and
“meditate in order to have the necessary mental purity …”
So the conclusion follows from the premise by the meaning of the words used.
“One thing upon which Africana scholars and intellectuals largely agree
is that the criteria used to define what is and what is not philosophy in
the world today are unfairly biased by and for ‘philosophy’ as
presently construed by Western culture. There may have to be some
common ground if the work ‘philosophy’ is to continue to have
cross-cultural significance. But Africa, in particular, has not received just
consideration in that regard … In so many respects, it seems, Africa's
cultures have not benefited from the kinds of exhaustive and empathetic
scholarship that are being lavished upon other parts of the world. The oral
literature of the African continent, therefore, has not even begun to receive
the attention it merits.”[27]
Inductive Argument — Since most Africana scholars agree Western culture's
definition of philosophy is biased, this assumed bias is reported to be the
reason the Western definition has little common ground with the oral literature
of Africa and the reason African philosophy is underrepresented in the world.
This argument is inductive as its claim is based on a consensus rather than
universal accord.
Note that this argument is not an ad
populum fallacy (an inappropriate appeal to the people) nor an
ad verecundiam fallacy (an appeal to
an irrrelevant authority) since Africana scholars and intellectuals are
proper authorities as to the nature of African thought.
FIG. 1. Historical Frequency of Use of “deductive argument” and “inductive argument” in Google Books 1700-2008.
postscript
“This process of drawing conclusions from our principles, by
rigorous and unimpeachable trains of demonstration, is termed
Deduction. In its due place, it is a highly important part
of every science; but it has no value when the fundamental principles,
on which the whole of the demonstration rests, have not first been
obtained by the induction of facts, so as to supply the sole materials
of substantial truth. Without such materials, a series of demonstrations
resembles physical science only as a shadow resembles a real object.
To give a real significance to our propositions, Induction must provide
what Deduction itself cannot supply. From a pictured hook we can only
hang a pictured chain.”
1. Richard Whately pointed out in 1831 that
induction can be stated as a syllogism with a suppressed universal major
premise which is substantially “what belongs to the individual or
individuals we have examined, belongs to the whole class under which they
come.” [Richard Whately, Elements
of Logic (London: B. Fellowes, 1831), 230.] This influential
text led many early logicians (e.g., John Stuart Mill) to think
mistakenly that inductive logic can be somehow transformed into demonstrative
reasoning. Following, George Henrik von Wright's A Treatise on Induction
and Probability (1951 Abingdon, Oxon: Routledge, 2003. doi: 10.4324/9781315823157),
logicians have abandoned this program [C.f., 29-30].
There is some controversy in the recent informal
logic movement as to whether conductive, abductive, analogical, plausible,
and other arguments can be classified as either inductive or deductive.
Conductive, abductive and analogical arguments in this course are interpreted
and reconstructed as inductive arguments.
A conductive argument is a complex argument which provides
premises which separately provide evidence for a conclusion —
each is independently relevant to the conclusion. Conductive arguments
can also provide evidence for and against a conclusion (as in
evaluations or decision).
Abductive argument is a process of
selecting hypotheses which best explain a state of affairs very much
like inference to the best explanation.
Some logicians argue that all arguments are exclusively either
deductive or inductive, and there are no other kinds. Also, they claim
deductive arguments can only be evaluated by deductive standards and
inductive arguments can only be evaluated by inductive standards.
[E.g., George Bowles, “The Deductive/Inductive
Distinction,” Informal Logic 16 no. 3 (Fall, 1994),
160. doi:
10.22329/il.v16i3.2455]
Stephen Barker argues:
“Our definition of deduction must refer to what the speaker
is claiming, if it is to allow us to distinguish between invalid
deductions and nondeductions.”
[S.F. Barker, “Must Every Inference be Either Deductive or
Inductive?,” in Philosophy in America ed. Max Black
(1964 London: Routledge, 2013), 62.]
On the one hand, for monotonic reasoning, Barker's definition makes the
tail wag the dog since on this view the distinction between the two kinds
of arguments depends upon the arbitrary psychological factor of what type
of argument someone declares it to be rather than the nature or character
of the argument itself. On Barker's view (and many current textbook views),
the speaker's claim determines whether an argument is deductive or
inductive regardless of the structure of the argument itself.
Barker explains the distinction from a dialogical point of
view:
“Suppose someone argues, ‘All vegetarians are teetotallers,
and he's a teetotaller, so I think he's a vegetarian.’ Is this
inference a definitely illegitimate deduction, or is it an induction
which may possibly be logically legitimate? We cannot decide without
considering whether the speaker is claiming that his conclusion is
strictly guaranteed by the premises (in which case, the inference is
a fallacious deduction) or whether he is merely claiming that the
premises supply real reason for believing the conclusion (in which
case, the inference is an induction which in an appropriate context
might be legitimate).” [Barker, 66.]
On Barker's view, an invalid deduction cannot be considered a weak induction
since, for him, deduction and induction are exclusive forms of argumentation.
This is a popular view, but we do not follow this view in these notes. Trudy
Govier points out:
“If arguers' intentions are to provide the basis for a distinction
between deductive and inductive arguments which will be anything like
the traditional one, those arguers will have to formulate their intentions
with a knowledge of the difference between logical and empirical connection,
and the distinction between considerations of truth and those of validity.”
This point is obvious for monotonic reasoning where arguments
are evaluated independently of claims (1) by the person who espouses them or
when (2) arguments are evaluated in terms of the principle of charity. Even for dialogical
reasoning, a speaker's intention should not determine the distinction between
inductive and inductive arguments, for few speakers are informed of the
epistemological differences to begin with.↩
6. O.B. Goldman, “Heat
Engineering,” The International Steam Engineer
37 no. 2(February 1920), 96.↩
7. Arguments in statistics and probability
theory are mathematical idealizations and are considered
deductive inferences since their probable conclusions are logically
entailed by their probable premises by means of a “rule-based
definitions.”
Consequently, even though the premises and conclusion of
these arguments are only probable, the probabilistic conclusion necessarily
follows from the truth of the probabilistic premises. The inference itself
is claimed to be certain given the truth of the premises.
In a valid deductive argument the conclusion must be true,
if the premises are true. The proper description of the truth value of the
conclusion of a valid statistical argument is that the statistical result
is true, if the premises are true. The truth of the probability value
established in the conclusion is certain given the truth of the data provided
in the premises.↩
14. Adapted from Nikko Schaff, “Letters: Let the
Inventors Speak,” Economist 460 no. 8820 (January 26,
2013), 16.↩
15. James Ramsay, “Dawkins and Religion,”
The Times Literary Supplement 5417 (January 26, 2007),
6.↩
16. Historically, from the time of Aristotle, the distinction
between deduction and induction, more or less, has been described as:
“[I]nduction is a progression from singulars to universals …
and induction is more calculated to persuade, is clearer, and according
to sense more known, and common to many things.” [Aristotle,
Top.
I.xii 105a12-13;16-19 (trans. Owen)
“Induction, then, is that operation of the mind, by which we
infer that what we know to be true in a particular case or cases,
will be true in all cases which resemble the former in certain
assignable respects. In other words, Induction is the process by
which we conclude that what is true of certain individuals of a
class is true of the whole class, or that what is true at certain
times will be true in similar circumstances at all times.”
[John Stuart Mill, A
System of Logic 2 vols.(London: Longmans, Green, Reader, and
Dyer,) I:333.]
“[D]eduction consists in passing from more general to less
general truths; induction is the contrary process from less to
more general truths.” [W. Stanley Jevons, The
Principles of Science 2nd ed. rev. (1887 London: Macmillan,
1913), 11.]
This view remains a popular view and does distinguish
many arguments correctly. However, since this characterization is not
true in all instances of these arguments, this distinction is no longer
considered correct in the discipline of logic.
William Whewell was perhaps the earliest philosopher to
register a correction to the view that induction can be defined as a process
of reasoning from specific statements to a generalization. Throughout his
writings he explains that induction requires more than simply generalizing
from an enumeration of facts. He suggests as early as 1831 that the facts
must be brought together by the recognition of a new generality of the
relationship among the facts by applying that general relation to each of
the facts. See. esp. William Whewell, The
Mechanical Euclid (Cambridge: J. and J.J. Deighton, 1837), 173-175;
The Philosophy of the Inductive Sciences, vol. 2 (London: J.W. Parker and Sons,
1840), 214; On the Philosophy of Discovery (London: John
W. Parker and Son, 1860), 254.↩
17. Notice that if this argument were
to be taken as a syllogism (which will be studied later in the course), it
would be considered an invalid deductive argument. A valid deductive
argument has its conclusion follow with necessity; when the conclusion does
not logically follow as in the “great Greek philosophers” example,
there still is some small bit of evidence for the truth of the conclusion,
so the argument could be evaluated as an extremely weak inductive argument.
No matter what class names (i.e. no matter what
subjects and predicates) are substituted into the form or grammatical
structure of this argument (assuming the statements themselves are not
tautological in some sense), it could never be a valid deductive argument
— even when all the statements in it happen to be true.↩
18. P.F. Strawson distinguishes the
particular and the general in this manner:
“[W]hen we refer to general things, we abstract
from their actual distribution and limits, if they have any, as we
cannot do when we refer to particulars. Hence, with general things,
meaning suffices to determine reference. And with this is connected the
tendency, on the whole dominant, to ascribe superior reality to particular
things. Meaning is not enough, in their case, to determine the reference
of their designations; the extra, contextual element is essential. …
So general things may have instances, while particular
things may not.”
20. Adapted from Hermann Hesse, Demian (Berlin:
S. Fischer, 1925), 157.↩
21. Mortimer J. Adler, How to Read a Book
(New York: Simon and Schuster: 1940), 89.↩
22. Marcus Tullius Cicero, Old
Age in Letters of Marcus Tullius Cicero with his Treatises
on Friendship and Old Age and Letters of Gaius Plinius Caecilius Secundus,
trans. E.E. Shuckburgh and William Melmoth, Harvard Classics, vol. 9 (P.F.
Collier & Son, 1909), 35.↩
25. Francine Russo, “The Personality Trait
‘Intolerance of Uncertainty’ Causes Anguish During COVID,”
Scientific American Mind 33 no. 3 (May-June 2022),
14. Also, here: Francine Russo, “The
Personality Trait ‘Intolerance of Uncertainty’ …”
Scientific American (accessed June 25,
2022).↩
S.F. Barker, “Must Every Inference be Either Deductive or
Inductive?,” in Philosophy in America ed. Max Black
(1964 London: Routledge, 2013), 62. doi: 10.4324/9781315830636
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