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## Deductive and Inductive Arguments

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.

1. #### The Difference between Deduction and Induction:

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.

1. #### Deductive Arguments Defined:

Deduction: an argument whose premises, if true, provide conclusive evidence for the truth of its conclusion.

1. 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.

2. 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]

The word “claim” 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.

3. 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.

2. #### Some Examples of Types of Deductive Arguments:

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.

1. 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.

2. 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.

3. 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.

4. 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.)

5. 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.

6. 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.)

3. #### Inductive Arguments Defined:

Induction: an argument whose premises, if true, provide some evidence for the truth of its conclusion.

1. 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.)

2. 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.

3. 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.

4. #### Some Examples of Types of Inductive Arguments:

The following brief examples show a few kinds of inductive arguments; note that these inductive categories are neither complete nor exclusive:

1. Probability and modal possibility: 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.

2. Extrapolation: 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.”

3. 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.”

4. 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.

5. 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.

6. 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 that two kinds of things which are similar in some aspects are likely to be similar in other aspects.

2. #### Specificity and Generality of Statements Do Not Always Distinguish Deductive Arguments from Inductive Arguments:

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]

1. 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.)

2. 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.

3. But these definitions are misleading for several reasons. Let us briefly note some of them.

1. 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.

1. 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.

2. 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.

2. 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.

Aristotle was a great Greek philosopher.[17]

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]

3. 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.

4. Consider the difficulty of distinguishing general from specific statements in the following cases:

1. The whale is a mammal. [as in an encyclopedia entry]

2. All novelists of Waverly named Sir Walter Scott are historical writers. [a definite description]

3. All present kings of France are bald. [a non-existent entity]

4. All ideal gases are perfectly elastic. [a theoretical entity or nonobservable entity]

5. 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 to assume that a premise statement is specific or general when the statement's reference is uncertain.

3. #### How to Distinguish Inductive Arguments from Deductive Arguments:

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.

1. Inductive Arguments: Bryan Skyrms provides this example of a strong argument whose conclusion is made more likely by adding additional evidence:

George is a man.

George is 100 years old.

George has arthritis.

George will not run a four-minute mile.[19]

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.

1. 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.

2. 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.

2. 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.

1. 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.

2. In valid deductive arguments, if the premises are true, then the truth of the conclusion follows with certainty.

3. 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]

4. #### Additional Examples Distinguishing Deduction and Induction:

Test yourself on the following examples:

1. 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.

2. 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.

3. 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.

4. “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.

5. “[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.)

6. “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.
For more explanation, see footnote 7 below.

7. “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.

8. “[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.

9. ”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.

10. “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.”

William Whewell, History of the Inductive Sciences vol. I (London: J.W. Parker, 1837), 16.

#### Deduction and Induction Notes

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.

An analogical argument specifies that events or entities alike in several respects are probably alike in other respects as well. See e.g. Yun Xie, “Conductive Argument as a Mode of Strategic Maneuvering,” Informal Logic 37 no. 1 (January, 2017), 2-22. doi: 10.22329/il.v37i1.4696 And Bruce N. Waller, “Classifying and Analyzing AnalogiesInformal Logic 21 no. 3 (Fall 2001), 199-218. 10.22329/il.v21i3.2246

2. Bryan Skyrms, Choice and Chance: An Introduction to Inductive Logic (Dickenson, 1975), 6-7.

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.”

[Trudy Govier, “More on Deductive and Inductive Arguments,” Informal Logic (formerly Informal Logic Newsletter) 2 no. 3 (March, 1979), 8. doi: 10.22329/il.v2i3.2824]

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.

3. “Intentional account” named by Robert Wachbrit, “A Note on the Difference Between Deduction and Induction,” Philosophy & Rhetoric 29 no. 2 (1996), 168.doi: 10.2307/40237896 (doi link not activated 2022.06.28)

4. Bertrand Russell, The Analysis of Mind (London: George Allen & Unwin, 1921), 40.

5. Herbert Spencer, Education: Intellectual, Moral and Physical (New York: D. Appleton, 1860), 45-46.

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.

8. This inductive argument is suggested by this study: Aris P. Agouridis, Moses S. Elisaf, Devaki R. Nair, and Dimitri P. Mikhailidis, “Ear Lobe Crease: A Marker of Coronary Artery Disease?Archives of Medical Science 11 no. 6 (December 10, 2015) 1145-1155. doi: 10.5114/aoms.2015.56340>

9. Friedrich Schlegel, Lectures on the History of Literature: Ancient and Modern trans. Henry G. Bohn (London: George Bell & Sons, 1880), 34.

10. R. Schoeny and W. Farland, “Determination of Relative Rodent-Human Interspecies Sensitivities to Chemical Carcinogens/Mutagens,Research to Improve Health Risk Assessments (Washington, D.C.: U.S. Environmental Protection Agency, 1990), Appendix D, 44.

11.Foreign Agriculture Circular (Washington D.C.: U.S. Department of Agriculture, 5 no. 64 (November, 1964), 4.

12. This type of induction describes the most common variety: it's often called “induction by incomplete enumeration.”

13. John Wesley, “10 Ways to Improve Your Mind by Reading the Classics,” Pick the Brain: Grow Yourself (June 20, 2007).

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.”

P.F. Strawson, “Particular and General,” Proceedings of the Aristotelian Society New Series 54 no. 1 (1953-1954), 260. doi: 10.1093/aristotelian/54.1.233 Also by JStor (free access by registration).

19. Bryan Skyrms, Choice and Chance: An Introduction to Inductive Logic (Dickenson, 1975), 7.

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.

23. John S. Mbiti, African Religions & Philosophy (Oxford: Heinemann, 1969), 1.

24. Ferdinand E. Marcos, The Democratic Revolution in the Philippines (Englewood Cliffs, NJ: Prentice-Hall, 1974), 93. Also, Ferdinand E. Marcos, Toward the New Society: Essays on Aspects of Philippine Development (Philippines: National Media, 1974), 7.

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).

26. Charles Muller, “A Korean Contribution to the Zen Canon; The Oga Hae Seorui (Commentaries of Five Masters on the Diamond Sūtra),” in Zen Classics: Formative Text in the History of Zen Buddhism eds. Steven Heine and Dale S. Wright (Oxford: Oxford University Press, 2006), 54.

27. Barry Hallen, Short History of African Philosophy 2nd.ed. (Bloomington: Indiana University, 2009), 21.

#### Readings on Induction and Deduction

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

George Bowles, “The Deductive/Inductive Distinction,” Informal Logic 16, no. 3 (Fall 1994), 159-184. doi: 10.22329/il.v16i3.2455

Trudy Govier, “More on Deductive and Inductive Arguments,” Informal Logic (formerly Informal Logic Newsletter) 2 no. 3 (March, 1979), 7-8. doi: 10.22329/il.v2i3.2824

David Hitchcock, “Deduction, Induction and Conduction,” 3 no. 2 Informal Logic (formerly Informal Logic Newsletter) (January, 1980), 7-15. doi: 10.22329/il.v3i2.2786

IEP Staff, “Deduction and Induction,” The Internet Encyclopedia of Philosophy

P.F. Strawson, “Particular and General,” Proceedings of the Aristotelian Society New Series 54 no. 1 (1953-1954), 233-260. Also by JStor (free access by registration). doi: 10.1093/aristotelian/54.1.233

Robert Wachbrit, “A Note on the Difference Between Deduction and Induction,” Philosophy & Rhetoric 29 no. 2 (1996), 168-178. doi: 10.2307/40237896 (doi link not activated 2022.06.25) JStor (free with registration)

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