Reasoning: Types-
Inductive, Deductive, Propositional, Syllogistic, Analogical, Categorical
Reasoning is the process of using existing knowledge to draw
conclusions, make predictions, or construct explanations.
Reasoning - a specific type of
thinking
Def: cognitive processes by which
people start with information and transform info to reach conclusions
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Arguments generally are divided into two types:
deductive and inductive.
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Deductive arguments? Valid or invalid?
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Inductive arguments? Strong or weak?
Types of Reasoning
Deductive Reasoning – starting with some pieces of information and
making a logical conclusion
Reasoning
from the general to the specific
ex.
1. to graduate from State University, you have to have at least a C average
(general statement)
2. Stacie is graduating from State
University
a. Therefore, Stacie has at least a C
average. (specific statement)
If premises are true, then the
conclusions will be true (deductive validity)
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Deductive Reasoning – A type of logic in
which one goes from a general statement to a specific instance.
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The classic example
All men are mortal. (major
premise)
Socrates is a man. (minor
premise)
Therefore, Socrates is mortal.
(conclusion)
The above is an example of a syllogism.
Inductive Reasoning – arrive at a conclusion that is probably
true based on evidence
Reasoning from the specific to
the general
Ex. 1. Richard attended State U
for 4 years
2. Richard is now the vice president of a
bank
a. Richard probably graduated from State
U
Do we know that Richard definitely
graduated? No, but he probably did
Conclusions cannot be certain,
there can only be stronger or weaker beliefs in the conclusions (inductive
strength)
Propositional Reasoning
Propositional reasoning is a form of deductive reasoning,
which goes from the general to the specific. Through deductive reasoning one
can state with absolute certainty that a conclusion is either true or false. In
that sense it is similar to syllogistic
reasoning, which involves syllogisms, where a conclusion is drawn or
evaluated based on two or more premises. Propositional reasoning on the other
hand involves propositions,
which are sentences that are either true or false (Galotti, 2008), e.g. “Mark likes football” or “Berlin
is the capital of Germany”. These propositions are abbreviated to letters,
such as p or q.
By using logical connectives single propositions can be combined
into more complicated ones. Logical connectives include: ¬ (‘not’) for negations, & (‘and’) for conjunctions, v (‘or’) fordisjunctions,
and → (‘If…, then…’) for conditionals (Galotti, 2008). For instance, the
sentence “If it is raining,
then I get wet” can be
rephrased as p → q , where p stands for ‘rain’ and q stands for ‘getting wet’.
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Syllogism: An argument composed of two
statements or premises (the major and minor premises), followed by a
conclusion.
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For any given set of premises, if the conclusion
is guaranteed, the arguments is said to be valid.
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If the conclusion is not guaranteed (at least
one instance in which the conclusion does not follow), the argument is said to
be invalid.
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BE CARFEUL, DO NOT CONFUSE TRUTH WITH
VALIDITY!
All math teachers are over 7
feet tall.
Mr. D. is a math teacher.
Therefore, Mr. D is over 7 feet tall.
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The argument is valid, but is certainly not
true.
Analogical Reasoning
Analogical
reasoning is a method of processing information that compares the similarities
between new and understood concepts, then uses those similarities to gain
understanding of the new concept. It is a form of inductive reasoning because
it strives to provide understanding of what is likely to be true, rather than
deductively proving something as fact. This method can be used by both children
and adults as a way to learn new information or as part of a persuasive
argument.
Analogical
reasoning is based on the brain’s ability to form
patterns by association. The brain may be able to understand new concepts more
easily if they are perceived as being part of a pattern. If a new concept is
compared to something the brain already knows, it may be more likely that the
brain will store the new information more readily.
The field of
science also uses this type of reasoning, but it is used for coming up with new
concepts rather than for persuasion. Scientists will often compare a proven
scientific process with an unproven one to form hypotheses to base new research
on. They may reason that because two processes are similar in one way, they may
be more likely to have more things in common.
Psychologists often
focus on the cognitive aspects of reasoning. They may perform research to
determine how and why the brain retains information through analogies.
Psychologists may also study the differences between how children and adults
use them.
CATEGORICAL REASONING
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A form of deductive argument.
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Also called syllogism.
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Consists of two or more premises that precede
the conclusion.
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Reasoning conclusions about the properties of
individuals from more general premises that concern all the members of the
relevant categories.
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Example:
All
whales live in water (Premise)
All
fish live in water, too (Premise)
All
fish must be whales. (Conclusion)
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If the conclusion of an argument is not
guaranteed by the truth of the premises then the syllogism is not valid.
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An invalid argument involving categories is
called a categorical fallacy.
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In a categorical syllogism, each of the premises
states a relationship between the middle term and one of the others.
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Categorical
syllogism features:
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Every proposition is in standard categorical
form
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There are three terms.
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The major premise is listed first, the minor is
listed second.
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Each term is used in the same sense throughout
the argument.
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Example:
All German cars are reliable (major
premise)
All BMW are German cars (minor
premise)
All BMW will be reliable (conclusion
– derived from relationship between minor premise and major premise)
Approaches- The componential, Rules/ Heuristics,
Mental models
Major
programmatic approaches to the study of reasoning are classified into three
types: the componential approach, the rules/heuristics approach, and the mental
models/search approach.
The Componential Approach
The
componential approach studies reasoning by analyzing a task into its component
cognitive processes. A computer metaphor may be useful here. Those of you who
have done computer programming know that programs can be built from
subroutines, each of which performs a very specific function (such as sorting a
list of numbers or adding a list of numbers). To understand how reasoning
works, we need to figure out if analogous mental subroutines of reasoning exist
and, if so, what they are, when and for how long each is executed, and the
chances of each one’s running without error.
To
illustrate, let’s return to the sample analogy given at the beginning of the chapter:
Washington is to one as Jefferson is to what? Sternberg (1977a, 1977b, 1986a,
1986b) studied people’s performance on such problems extensively. He argued
that to fill in the blank, we must perform several mental subroutines or, to
put it more formally, execute a number of component cognitive processes. First
we must encode each of the terms; that is, we must read the words Washington,
one, and Jefferson.
We then must
recognize these terms, retrieving from memory the meaning of each term and
mentally representing these meanings. Next we must infer the relationship
between the first two terms (often called the A and the B terms)—in this case, Washington
and one.
One
relationship that comes immediately to mind is that Washington was the first
president of the United States. The next step is to map the A term and the C
term (here, Jefferson)—that is, find a relationship between them. Jefferson was
also a president of the United States. In the next step, we apply the
relationship previously found between the A and the B terms onto the C term, remembering
(if we recall our U.S. history) that Jefferson was the third president. Thus
our answer to the analogy would be three. Sometimes analogies are provided in
multiple-choice format, and in those cases the answers don’t always fit.
In
Sternberg’s theory, each component has associated with it several parameters that
determine, for instance, the probability that it will be used, the amount of
time it will take to execute, and the difficulty of executing it.
Sternberg’s
method of estimating these parameters was quite clever. He presented
participants with a number of different verbal and pictorial analogies
(Sternberg, 1977a) on a tachistoscope, and each trial consisted of two parts:
(a) precueing and (b) presentation of the full analogy. Figure 12-7 presents
examples.
During precueing, participants saw either a blank field (no
cues), the A term of the analogy only, the A and the B terms of the analogy
only, or the A, B, and C terms of the analogy. Sternberg (1977a) compared the
amounts of time it took participants to decide if the full analogy was true or
false on trials with no cues to the amounts of time on trials in which cues had
first appeared. For example, when participants had been precued with the A
term, Sternberg reasoned that they had been able to encode this term; thus they
should be (and were) faster to respond to the full analogy. Let’s say it took
participants, on average, 2 seconds to respond to the full analogy, but only
1.8 seconds when the A term was precued. That 0.2-second difference presumably
reflects the time it takes to encode the A term. Similarly, if participants
were precued with the A and B terms and then took only 1 second to respond to
the full analogy, we could infer that the other 1 second was the time it took
to encode the A term, encode the B term, and infer a relationship between them.
Sternberg
and his colleagues have studied other inductive reasoning tasks and have
presented componential models of each. Each componential model identifies the
mental processes (such as encoding or comparing) that are used in each task.
From these studies, Sternberg has argued that the componential approach to the
study of reasoning will reveal important insights into what reasoning is and
how it can be improved (Sternberg, 1986a).
In
later work, Sternberg (1983, 1984) distinguished among three kinds of
components used in reasoning. Components that consist of individual cognitive
processes are called performance components and include those given
earlier. Metacomponents are “executive” processes used in the planning
and monitoring of a task. For example, metacomponents select which performance
components will be used and in what order. Knowledge acquisition components are
used whenever we acquire new information. These include things such as
selective encoding (sifting relevant from irrelevant information), selective
combination of previously encoded information, and selective comparison.
Knowledge
acquisition components have to do with how we learn or pick up new information.
Sternberg (1986a) argued that people differ in the ways in which they learn:
Given the same exposure to the same
novel situation, two people may acquire different kinds and amounts of
information from it. The mental processes we use in learning are knowledge
acquisition components.
Sternberg’s (1986a) book gives advice and examples to
provide practice with performance components, metacomponents, and knowledge
acquisition components. Many errors in reasoning tasks appear to stem from
problems in encoding (a performance component). Many of the problems in
reasoning noted earlier (such as problems with premise interpretations,
alteration of premise meanings, or failure to consider all possibilities) arise
because reasoners fail to encode enough relevant information. Moreover,
complicated syntactic expressions (those with many terms, those with negatives)
presumably take more processing resources to encode, leaving fewer resources
available for other components of reasoning. Other problems in reasoning could
be described in terms of differences in using metacomponents. A reasoner who
plans her approach to a problem and monitors his or her performance is less
likely to be biased or to make other kinds of errors.
The Rules/Heuristics Approach
One idea is that the rules of logic are the same rules we
use to draw conclusions Most modern psychologists reject the strong version of
this idea but agree that people use “mental logics” or systems of inference
rules to draw conclusions. Using this rules/heuristics approach, these
researchers make an analogy between mental logics and grammars: Both are
systems of rules to which we have only implicit access.
Different researchers describe slightly different sets of
inference rules. Generally, rules take the form “(premises) → (conclusion).”
Here’s a specific example (from Braine, 1978): “p ∨ q; ￢p therefore q.” The idea is that when given
information, people try to match it to one of these rules and use the rules to
draw appropriate conclusions.
These proposals are not the only ones that view reasoning in
terms of mental rules. Work by philosophers on practical logic also follows a
rules approach. The goal of practical logic is to teach people to avoid
fallacies or errors that occur in real-life arguments. Box 12-4 presents some
common fallacies.
The key issue for the rules explanation of reasoning is how
people figure out when and what rules apply. Braine (1990) proposed the
existence of abstract rules that we use in all situations. Patricia Cheng and
her colleagues rejected the idea of abstract rules, instead proposing sets of
rules that are sensitive to the context. The idea here is that different rules
are called to mind in different situations.
One example is the permission schema, made up of four rules:
Rule 1. If the action is to be taken, then the precondition
must be satisfied.
Rule 2. If the action is not to be taken, then the
precondition need not be satisfied.
Rule 3. If the precondition is satisfied, then the action
may be taken.
Rule 4. If the precondition is not satisfied, then the
action must not be taken.
The rules approach to reasoning is particularly effective at
explaining content effects in reasoning.
The explanation goes as follows:
Presumably, different contents “cue” different sets of
rules, although exactly how this process works is not well understood. It may
be that personal experience facilitates this cueing, so that people are more
likely to reason correctly with premises about drinking ages simply because
their own experiences cause them to interpret the situation in terms of a
permission rule.
Cheng et al. (1986) have reported success in teaching people
to recognize and use pragmatic reasoning rules correctly after only brief
periods of practice. This suggests that people quickly learn to use inference
rules as a guide to processing information on certain tasks. Similarly, the
existence of logic courses in colleges and universities suggests that rules of
logic can be taught. The hope is, of course, that people who learn to use a set
of inferencerules in one situation will transfer their understanding of the
rules to new circumstances.
The Mental Models Approach
Proponents of the mental
models approach deny that reasoning consists of using special-purpose rules
of inference and that reasoning involves specialpurpose cognitive processes.
Philip Johnson-Laird (1982, 1983), a major spokesperson for the models
approach, argued that the processes we use to draw conclusions are also the
ones we use to comprehend language.
Reasoning, for Johnson-Laird, consists of constructing
mental models to depict the premises. Effective reasoning occurs when the
reasoner checks to be sure his or her first idea of what the conclusion might
be is assessed by an attempt to construct alternative models consistent with
the premises but inconsistent with the hypothesized conclusion.
To explore Johnson-Laird’s approach, consider the following
syllogism:
Some of the scientists are parents. All of the parents are
drivers.” Figure 12-8 offers one interpretation of how these premises might be
mentally modeled for this relatively easy-to-solve reasoning problem.
Scientists are depicted as people holding a flask; drivers, as people standing
next to a car; and parents, as people holding a child. The diagram indicates
that some scientists are drivers but (possibly) some other scientists aren’t
drivers (those shown in faded lines) and, also possibly, some drivers aren’t
parents (also rendered in faded lines). Notice that the two scientists in the
middle of the diagram (the ones who aren’t “optional”) are drivers, leading to
the necessarily true conclusion, “Some of the scientists are drivers.”
Consider another of Johnson-Laird’s syllogisms, this one
more difficult to work with: “All of the beekeepers are artists. None of the
chemists are beekeepers.” You might try this one yourself before reading on.
Figure 12-9(A) depicts the model most people generate first. Notice that no
individual is both a chemist and a beekeeper nor both a chemist and an artist.
This depiction would lead one to conclude, “None of the chemists are artists.”
However, if they keep at it, people may discover other possible depictions,
such as the one shown in Figure 12-9(B), where one artist is a chemist. This
depiction means the preceding conclusion cannot be true. At this point, a
reasoner who had constructed both models might conclude, “Some of the chemists
are not artists.” Again, however, another possibility exists, the one depicted
in Figure 12-9(C). Here, all the chemists are artists, so the last conclusion
cannot be valid, either.
Is there no valid conclusion, then? In fact, there is. The
one statement true of all three models is “Some of the artists are not
chemists.” In particular, the beekeeper/artists, necessarily depicted in each
model, are not chemists. One problem with the mental models framework is
specifying what information models contain and what information is omitted.
Notice, for instance, that in Figures 12-8 and 12-9 we did not specify any
physical, ethnic, or philosophical
information about the people depicted. How much information
the reasoner chooses to represent and how this decision affects performance are
issues that remain to be investigated.
The construction of a mental model can be considered a
creative act. Perkins (1985) argued that—contrary to stereotype—model building
(and therefore good reasoning) relies on imagination. The more imaginative the
process, the more likely a reasoner is to generate potential counterexamples
and avoid drawing hasty conclusions. Interestingly, this view links reasoning
with other kinds of thinking, helping to explain the apparent links among
reasoning, problem solving, and decision making. In the mental models approach,
errors in reasoning derive from several possible sources. One is the failure to
construct relevant models. If the premises are not presented in an optimal
order (for example, in a syllogism, in the order A-B, B-C), it is harder to
construct an integrated representation of both premises that accurately depicts
all the relevant information. If there is a great deal of extraneous
information in the premises, mental resources may be diverted from the
processes needed to selectively represent the essential information. A second
source of error is the failure to assess the implications of all the models
found. For instance, in the previous example, someone might have decided
that no conclusion relating artists and chemists was
valid, overlooking the one relation shown in all three models. A final and
important source of error is the failure to search for and construct enough
models. This accounts for the findings described earlier—namely, that people
often fail to consider enough of the possibilities allowed by any set of
premises.
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