In logic courses, deductive reasoning is defined as a type of inference in which the premises are intended to guarantee the truth of the conclusion, whereas inductive reasoning gives premises that are intended only to provide evidence for the truth of the conclusion (I discussed this definition in more depth in an earlier post on
However, it is possible that you have heard someone define induction as reasoning from the specific to the general and deductive inference as going from the general to the specific (I will call this the "old definition"). The purpose of this post is to give the reasoning for why the distinction is not defined that way in the field of logic today.
Definitions are tricky things to argue about because different people can define the same word differently and because different definitions can serve different purposes (I got involved in an argument recently, for example, about whether Pop-Tarts are "sandwiches").
However, there are several ways that we can argue about which definitions are best, which I will outline below. If you are interested in this question, you are welcome to read the below. However, do not feel obligated at all, as this goes well beyond what is required for an intro logic course.
Since this is a semantic issue, there may not be an objective ‘fact’ about what definition (of any term) is ‘right.’ However, some
semantic decisions can be better than others for reasons including the
following:
1. Historical definitions of the term.
2. How authorities in the field define the term.
3. How it is most useful to define the term.
4. What definition best captures pre-theoretic intuitions
about what the term means (the ‘concept’).
5. How people commonly use the term.
The rest of this entry will attempt to show that all five
of these support the new definition, at least within the field of logic.
Part 1: Historical Definitions
It has been said that Aristotle defined inductive
reasoning as reasoning that goes from the specific to general (Groarke, n.d.;
Kneale & Kneale, 1962). However, Aristotle’s word for this was epagōgē (ἐπαγωγή), which was translated as
“induction” in the work of Cicero (etymonline, n.d.). It is not clear, therefore,
that the “old definition” (especially not Aristotle’s version) was a definition
of the same term at all. Cicero defined "induction" as having to do with reasoning based on similar cases (Fortenbaugh, 1996, p. 2), which is not synonymous with generalization.
Philosophers by the nineteenth century were using the modern definition
(that inductive inferences are based on probabilistic reasoning). However, in
1865, logician Charles Sanders Peirce came up with a different way of
categorizing the terms “deductive,” “inductive,” and “abductive” according to
their forms (Burch, 2018). He interprets induction as generalization. His
distinctions are fascinating, but they did not become the dominant ones used in
logic today (Burch, 2018).
In the early 20th century, the successes formal
developments within deductive logic inspired many to attempt to create formal
principles of inductive reasoning, understood as probabilistic inference
(Hawthorne, 2018). Induction defined as probabilistic
inference generally, not limited to generalization, has become the dominant usage
of the term, as verified in the next section.
Part 2: How Authorities in the Field Define the Term
In my house, I have a pile of 18 logic books. I have
looked through how each of them makes the deductive/inductive distinction. Here
is how they sort out:
The books on the left define it in the new way (deductive
arguments attempt to give conclusive support for their conclusions, while
inductive arguments try to give probabilistic evidence for their conclusions).
The two on the (far) right do not define the distinction at all. The one in the
middle is the only one that does not define it this way. It defines inductive
arguments as asserting that the future will resemble the past, learning from
experience. However, it then gives typical examples of the new definition of inductive
reasoning (induction by enumeration, analogy, statistical reasoning, etc.) and
goes on to explicitly reject the old definition, calling it a “misconception”
and giving counter-examples (Kahane & Cavender, 2006). So this jury of
scholars voted 16 to 0 (with two abstentions).
The next section outlines reasons this logical terminology
may have come to be preferred.
Part 3: The Most Useful Way to Define the Term
Perhaps the reason that most philosophers have resolved
upon the new version of the distinction is because it is more useful. Here is a
visual of how the two ways carve up the taxonomy of common argument forms:
Old Way:
Deductive:
Statistical syllogism
Universal instantiation
|
Inductive:
Enumerative Induction (aka inductive generalization)*
Mathematical Induction**
|
Neither:
Propositional Logic
Most Predicate Logic (including Aristotelian
syllogisms)
Argument from Analogy
Appeals to Authority
Inference to the Best Explanation
|
*One could argue for
including the universal generalization rule
(from predicate logic) as a second type of “inductive” argument in this column.
However, that rule is not really an argument but an inference rule that requires the use
of a special arbitrary constant (sometimes indicated with a dot over it) and
does not typically occur as an argument in daily life.
The principle of mathematical induction is a form of inference that occurs within mathematical proofs and not much in daily life.
New Way:
Deductive:
Propositional Logic
Predicate Logic (Including Aristotelian Syllogisms)
Mathematical Inference
|
Inductive:
Inductive Generalizations
Argument from Analogy
Appeal to Authority
Inference to the Best Explanation
Statistical Syllogism
|
|
This chart may help to clarify why the new
way is more useful than the old way within the field of logic. Since universal generalizations and mathematical induction are generally used only in formal proofs, and rarely in daily life, in typical reasoning contexts, the old classification does not make a distinction that we
did not have available simply by talking about inductive generalizations. Furthermore, the new version divides all of logic into two important categories, which strikes me as the
real intention behind the deductive/inductive distinction within the field of logic.
Furthermore, the distinction made by the new version is
more important. The new version makes a distinction that is crucial since the
two types of reasoning have different standards for evaluating the quality of
the inference (validity versus strength). The distinction of whether one is generalizing
is less important in terms of the concept used to evaluate the strength of the
reasoning (which is the more important skill within the field of logic).
Finally, in the old version, the majority of inferences
would be classified as neither deductive nor inductive. Contrast this with the
new definition, which divides reasoning into two roughly equal categories based
on an important commonality (allowing us to evaluate them based on unified
standards). Because the newer version provides a more valuable way of dividing
up two important types of logical inferences, one can perhaps see why the old
definition has been replaced overwhelmingly in the study of logic.
Part Four: The Pre-Theoretic Notion and Common Usage
I cannot speak for others in terms of what they
feel is the “true” meaning of the concept, many people who give the old
definition may have something like the following types of arguments in mind:
Deductive:
All dolphins are mammals.
Flipper is a dolphin.
Therefore, Flipper is a mammal.
Inductive:
Every crow I have seen has been
black.
Therefore, all crows are black.
They may feel that the first type of inference is
deductive because the information in the conclusion is ‘contained’ in some
sense, within the premises. They may feel that the second one is inductive
because the information in the conclusion goes beyond what is contained in the
premises. In this sense, inductive inference is ampliative (Haack, 1992).
However, this intuition is not what is captured by the
old definition. Here are some counterexamples to the idea that a non-ampliative
argument must go from general to specific and that an ampliative one must go
from the specific to the general.
Is this argument deductive or inductive?
All dogs are mammals.
All mammals are animals.
Therefore, all dogs are animals.
According to the new definition, this argument is
stereotypically deductive, but it does not go from the general to the specific.
It does not go from the specific to general either, so according to the old
definition, it is neither deductive nor inductive.
Here’s another example: Is this inductive or deductive?
97% of all people enjoy ice
cream.
Therefore, Mike probably enjoys
ice cream.
According to the old definition, this would qualify as
deductive (since the premises are general and the conclusion is specific),
though few in logic would call this argument deductive. Rather this
argument strikes many as paradigmatically inductive since the conclusion is
intended only to be supported with evidence rather than proven. This
probabilistic inference is what is captured by the new definition.
In fact, according to the old definition, nearly the
entire field of formal logic would not qualify as deductive, including propositional
logic (which is frequently called “deductive logic” in university courses).
Take, for example, one of the paradigm instances of a deductively valid argument
form, modus ponens:
If P then Q
P
Therefore, Q
Though this form is valid, according to the old definition
it would not use deductive logic, since its premises and conclusion have the
same level of generality. This again violates standard intuitions about the
distinction today. Furthermore, to call this argument non-deductive would also
require divorcing the concept of validity from deduction.
Aside: Some supporters of the old definition will defend modus ponens as deductive by saying that
the inference from the general form to each of its instances is from the general to the specific. However, to say that
the inference from the form to each of its instances is deductive that is not
to say that the form is deductive nor
that its instances are deductive. It
would be to say that the real argument
is the second order inference. Such a response presupposes we have to see propositional
logic, as well as most Aristotelian syllogisms, as really second-order logic;
which would be a very controversial
move (many philosophers of logic do not accept second order logic as logic at
all).
To call Aristotelian syllogisms, the whole field of
truth-functional logic and much of predicate logic not deductive is, in light
of the hundreds of the content of hundreds of courses called “deductive logic”
that cover all of those topics, would be in plain contradiction to standard
professional use within the field of logic.
I bring these examples up not just to show the
implications of the old definition, but to show how this usage is in violation
of how we use the terms ‘deductive’ and ‘inductive’ routinely in logic today.
There are many in the fields of rhetoric and science, I am told, that define induction as generalization (DeLaplante, 2009). If this definition better satisfies the purposes of those disciplines, then it makes sense for them to use it that way. This can create an ambiguity within a word, with different fields meaning different things by the same word. This can be confusing, but it allows disciplines the freedom to define things in ways that are most useful within their own field (I have learned recently that scientists have defined the word "berry" in a way that included cucumbers and eggplants but excludes strawberries and blackberries. One could argue that this word is used ambiguously as well). The purpose of this post is to explain why we defined the term the way we do within the field of logic.
In summary, I have attempted to make a case that defining
the deductive/inductive distinction in terms of the argument’s attempt to be
valid versus strong (those terms are defined in
another post) is a more useful
distinction than the “old definition” and that perhaps this explains why it is
the distinction overwhelmingly used by scholars in the field of logic today.
References:
Haack, S.
(1992). Philosophy of Logics. New
York, NY: Cambridge University Press, 12.
Kahane, H. & Cavender, N. (2006). Logic and Contemporary Rhetoric: The Use of
Reason in Everyday Life. Belmont, CA: Thomson Higher Education, 42.
Kneale, W. & Kneale, M. (1962). The Development of Logic. New York, NY: Oxford University Press, 36.
