Critical Thinking & Reasoning
Short history of Logic
If we take Logic to be the activity of drawing inferences (conclusions) from a
body of information, then no doubt humans have been using logic for as long as
they have been thinking, or at least consciously thinking. The first Neanderthal
to formulate the thought "All members of the Cave-Bear clan are our enemies"
along with "Thag is a member of the Cave-Bear clan" very likely put the 2
together and reached the conclusion "Thag is our enemy". They probably drew
logically correct conclusions from their data about as often as folks do
nowadays (i.e. maybe 62.3% of the time). (Chances are that natural selection
quickly weeded out the Neanderthals who tended to draw the conclusion "Thag is
our friend" from the above data!)
On the other hand, if we take Logic to be the analysis of concepts involved in
making inferences, and the identification of standards and patterns of correct
inference, Logic can be traced only back to the days of Aristotle (350 years
B.C. or so), with some parallel development in early Hindu writings. It's not
clear that this increase in logical self-consciousness improved the accuracy of
reasoning processes for humankind in general, but knowing what Aristotle knew
about logic can definitely help you be a better reasoner.
Symbolic (or Formal) Logic vs Informal Logic (or Critical Thinking).
In a typical symbolic logic course, emphasis is placed on the precise symbolic
representation of logical concepts, the study of the abstract relationships
between these concepts, and the systematization of these relationships.
In an "informal logic" or Critical Thinking course, the focus is instead on the
application of logical concepts to the analysis of everyday reasoning and
problem-solving. Elements of symbolic logic will frequently be involved, but
only to the extent that it contributes to this practical objective.
Notice that neither of these directions of emphasis really concern themselves
much with how people actually think, or what you might call a psychology of
thought. Informal Logic begins with the perception that people don't actually
reason all that well, but jumps from there to the matter of doing something
about it. Symbolic Logic begins with the perception of what constitutes good
reasoning at a rudimentary level, and goes on from there to investigate good
reasoning at higher and higher levels of sophistication.
What is the point of studying Critical Thinking?
Fundamentally, Critical Thinking or Informal Logic deals with the use of reason
in the pursuit of truth. While there is serious doubt about the power of reason
to discover any "new" truth, the "rules" of logic concern the ways truth can be
preserved as we make inferences -- one or more statements to support or justify
another statement. Taken this way, there is no great "mystery" to the concepts
of Logic. At the very core of logic is the idea that certain "patterns of
inference" - i.e. models for combining statements that support with those which
are supposedly supported will, if the supporting statements are true,
guarantee the truth of the statement supported by them.
If we are to be in control of our own beliefs, and to somehow gain an
understanding of the truth, then we must know what good reasoning is, and be
aware of the ways in which our reasoning (and that of others) can go astray.
Introducing logical vocabulary-
Statements or propositions-
A statement is a sentence which "has a truth-value" - i.e., one which is either
true or false. Your English teacher will refer to these as declarative
sentences, which they are called for the obvious reason that they are good for
declaring that things are so or not so. What you declare to be so may really be
so, in which case the "truth value" of the statement will be T (for True). Or it
may not really be so, in which case the truth value of your statement is F (for
False).
The truth value of a given statement may be unknown, but that doesn't keep us
from telling that it HAS a truth value. For example, you don't know whether the
statement "There is a 10.756 kilogram rock on the dark side of the moon" is true
or false, but we all know that either there is such a rock (in which case the
statement has truth-value T) or there's not (and the truth-value would be F).
Some types of sentences which are NOT statements are:
a) Questions, like "Will you still love me tomorrow?"
b) Commands, like "Shut up and go away!"
c) Sheer expressions of emotion, like "Hot Diggity-Dog!"
Statements are one thing, how people go about expressing them is another. In
determining what viewpoint a person is taking, or what they are saying in
defense of that viewpoint, one of the fundamental steps is to determine what
statements their actual words express. There are no rules for this basic
translation process. You just have to rely on what you know about the language,
and the speech customs of its speakers.
Peddlers and Consumers of Statements
In real life, people sometimes make statements just to be speaking the truth.
But frequently they make statements, not primarily (and maybe not even
secondarily) to be speaking the truth, but primarily in order to get other
people to accept them as true. Then we call this peddling the statement, and we
call the those who peddle it the peddlers of it, and those whom they want to
accept it the consumers of the statement. The context of this human interaction
is called a "context of persuasion", or sometimes "the propositional
marketplace."
Being a skilled critical thinker will require, in the long run, knowing a lot
about the propositional marketplace and the various devices a peddler may use
(deliberately or not), which ease the consumer into accepting the statement
being peddled. For now, just remember this key feature of the propositional
marketplace: somebody (the peddler) wants somebody else (the consumer) to
believe something (a statement).
Political and Philosophical Peddlers
You are fortunate if you encounter a peddler who is interested in getting you to
agree with a statement by showing you that it is true. We refer to such peddlers
as philosophical, because of their orientation toward the truth (philosophical
means "loving wisdom"). Peddlers who just want to get you to agree, regardless
of truth, we refer to as political, since power and control are their main
concerns.
So we see that a philosophical peddler will try to point out to you facts that
you already accept as true, and show you that in view of these the peddled
statement is true (or at least probably true). When you consider that facts are
expressed by statements, you see that this peddler's essential pitch consists of
a collection of statements:
a) the target statement you're being asked to accept
b) the "supporting" statements which
b1) at least aim to be ones you already accept as true and
b2) supposedly convey their truth to the target statement.
So, to summarize:
a. questions, commands, sentences which refer to a probability of an event,
statements about fictional characters are not statements.
b. a statement is a sentence or a part of a sentence which is true or false (it
has a truth value).
c. Truth of a statement can be established by:
personal experience,
internal consistency, and
consistency with the body of established fact (things we know are true already).
Beyond Simple Statements, we will also have to consider compound statements;
will be of four main types, which correspond to the four main types of logical
connectives-
1. Conjunctions- (A and B) - for statement to be true both A and B must be true,
if either of them is false, statement is false.
2. Disjunctions- (A or B) - for statement to be true only one of the component
simple statements need be true.
3. Negations- (NOT A) - in this type of statement the simple statement is
modified so that the truth value is reversed.
4. Conditionals- (IF A, THEN B) - in this statement, the first part is
identified as the antecedent, and the second part as the consequent. For this
statement to be true, the condition expressed for the truth of B must not be
compromised. The only case when this happens is when A is true and Bis false.
Arguments:
Such a collection of statements is called an ARGUMENT. The supporting statements
are referred to as PREMISES, and the one supposedly being supported is called
the CONCLUSION. In presenting an argument, the peddler is not just stating a
list of separate facts, but rather is seeking to JUSTIFY (show the truth of) one
statement by offering the other statements as support for it.
Based on this concept of an argument, and an understanding of its use in
contexts of persuasion, we can form a broad outline of the main phases of
CRITICAL THINKING:
RECONSTRUCTION- deals with extracting an argument from the surrounding mix of
statements which a peddler may have presented.
ASSESSMENT- deals with the business of determining whether the structure of an
argument really would permit truth to be carried from the premises to the
conclusion.
EVALUATION- deals with the activity of judging whether the premises of an
argument are true or false, clear or vague, and in need of further defense or
not.
FALLACY IDENTIFICATION- deals with the multifarious list of things that may
happen in a persuasion context, leading to the consumers' accepting some
statement without adequate justification.
RECONSTRUCTION
It is sometimes difficult to tell, when examining a peddler's entire
presentation (i.e. everything he or she says, in a context of persuasion).
whether or not we are being given an argument. The business of extracting an
argument from such a presentation is called (Argument) RECONSTRUCTION. We refer
to the unreconstructed presentation as the "raw material" of our analysis.
Inference Indicators
With luck, we will discover in our persuasion raw material certain words or
phrases that provide a clue as to which statements are premises and which
conclusions. These can be premise indicators, such as :
* After all, ...
* Given that...
* Inasmuch as...
* Since.....
* In view of the fact that....
and many others, which signal that an upcoming statement is to serve as a
premise in support of another statement in the immediate vicinity.
Or we might find conclusion indicators, such as:
* Therefore...
* In short,...
* We can conclude that...
* So....
* Thus....
and many others, which signal that an upcoming statement is to be seen as a
conclusion, relative to some premise statement in the immediate vicinity.
Although few inference-indicating phrases are completely unambiguous (and could
therefore lead us to things which are not part of an argument), they remain the
best single clue as to the structure of a latent argument. Accordingly, your
best first move in reconstructing raw material is to scan it for such
indicators, and from them project your initial reconstruction of the argument
therein.
Things become a bit trickier when there are no premise indicators at all. Then
there are two possible strategies. Probably the best strategy is to find a
statement to function as the conclusion of the presentation's as-yet latent
argument. Sometimes such a statement (or rhetorical equivalent thereof) can be
found among the sentences explicitly included in the presentation. If so, use
it. If not, you'll have to construct one of your own (see below). Either way,
here's how to proceed:
*Look over the presentation very thoroughly, to get the general drift.
*If necessary, pick up clues about the author's probable outlook or message from
outside the presented material - from the biographical facts about the author,
for example, or from what you can tell about the context of presentation. (If
your raw material came from a speech given at a Klan rally, for example, the
statement "We need to look beyond superficial differences and find the good in
each individual heart," is probably not a good candidate for its conclusion
statement.)
*Put together a short sentence which seems to summarize the one main message of
the presentation, within the limits of outlook as indicated by the biographical
and circumstantial information at your disposal. Ask yourself what declarative
sentence this peddler would use to state the main point on an expensive
billboard on the Interstate-- one that people have only a few seconds to read,
at 70 mph.
*Look for such a statement, or the equivalent thereof, among the explicit
sentences of the presentation. If you find one, that helps confirm that you're
interpreting the presentation correctly. So call that sentence the conclusion,
and go ahead with the analysis. If you can't find such a sentence, then review
the above procedure in hopes of finding one which is confirmed. If this yields
no better results, then just adopt your own formulation as the conclusion
statement, and go ahead.
*Use that conclusion statement in subsequent steps of reconstruction and
analysis, but remember that your "conclusion" here is a guess or hypothesis, and
could be replaced by a better one if this one doesn't lead to a satisfactory
overall reconstruction. *Once you've picked an overall conclusion, revisit the
raw material in search of statements which could function in a supporting role
for that conclusion-- i.e. ones which the author could be giving in answer to
the question "What makes you think so?" Repeat the process (and the imaginary
question) in your search for further premises in support of those statements,
and so on.
A second strategy is just to leap into the middle of the thing, pick any
statement as a starting point, and keep asking those two very important logical
questions:
a) What makes [the author] think so? This, as you can see, is a request for
statements to function as premises in support of your target statement. So
ransack the raw material until you find something to fill that requirement, then
re-ask.
b) So what? This, for all its apparent insolence, can usefully be seen as a
query as to what conclusion is to be reached, using the starting statement as a
premise. Again, you ransack the material to find a statement which, at least
apparently, was intended to fulfill that relative-conclusion role.
The Principle of Charitable Interpretation (Part I)
In some cases the best approach is to reconstruct as much of the argument as you
can, and then try to determine what is missing by looking at the form (such as
it is) of the argument as it is given, and supply the missing premises (and
occasionally a missing conclusion). Here the core concept will be that of
VALIDITY, and the guiding rule will be the Principle of Charitable
Interpretation. Validity is a key notion in the full formulation of the
Principle, so the whole story will have to wait until the concept of Validity
can be developed. But here are three important aspects of it:
a) Try to interpret a persuasion presentation as containing some argument
structure, if it is at all plausible to do so.
b) Translate a peddler's rhetorical questions, exclamations, idiomatic
expressions and the like, into appropriate and equivalent declarative sentences.
c) Avoid so far as possible a reconstruction that attributes to the peddler
views she wouldn't really hold- that is, that identifies as premise or as
conclusion some statement the author would reject.
When reconstructing an argument which seems to be misordered or incomplete, we
will want to give it the strongest possible interpretation we can. This is
because we are interested in moving closer to the truth, not necessarily in
"winning " an argument. If we interpret an argument in an intentionally weak way
so that we can defeat it, we have not really done anything significant—we risk
committing the fallacy of Straw Man. It is only when we are able to successfully
critique a strong argument that we can claim to have accomplished our aim.
Validity
An argument is said to be valid if (and only if), when the premises are all
true, the conclusion must be true too. To put it another way, an argument is
valid if and only if there's no way the conclusion can be false without at least
one premises being false too.
The term "Valid" refers to arguments, not to statements. Validity concerns the
relationship between the premises and the conclusion, and not the actual truth
values of the component statements at all.
A valid argument is one in which the form is such that:
IF the premises are all true, THEN the conclusion Must be true.
If it is possible for all the premises to be true and the conclusion to still be
false, then you have what is called an Invalid argument. In discussing
arguments, we need to distinguish between deductive arguments- arguments where
the truth of the premises will guarantee the truth of the conclusion and
inductive arguments - those arguments where the truth of the premises will only
make the truth of the conclusion highly probable or likely, but not certain. An
argument could be invalid and still be a good Inductive argument, or it could be
one which commits a Deductive fallacy. Once it is determined that an argument
has a Valid form (it is a Deductive argument), the next step is to determine if
all of the premises are indeed true. This is done in a variety of ways,
depending on the type of premises we are dealing with.
Soundness:
The different types of premises are discussed below, but for now, if all of the
premises of a Valid argument are true, then the argument is said to be Sound as
well as Valid. Only Deductive or Valid arguments can be sound or unsound.
Thus, an argument is sound if and only if :
it is a valid argument, and
all the premises are true.
Valid argument forms:
Modus Ponens-
1. If A then B,
2. A
Therefore, B (conclusion)
Fallacious form: (affirming the consequent)
1. If A then B,
2. B
Therefore, A
Modus Tolens-
1. if A then B,
2. Not B
Therefore, Not A
Fallacious form: (Denying the Antecedent)
1. If A then B,
2. Not A
Therefore, Not B
Disjunctive Syllogism-
1. A or B
2. Not A
Therefore, B
Hypothetical Syllogism-
1. if A then B
2. if B then C
Therefore, if A then C
Filling in Implicit Premises
1. Read what is there carefully to discern what the explicit premises are- (look
at what you have already)
2. See if there is a conclusion that will follow from the premises given.
3. If necessary, provide such a conclusion, or re-word the given conclusion to
make it more reasonable (retaining the meaning)
4. Look at the presuppositions of the premises so far for any additional
implicit premises.
5. Avoid obviously false or questionable premises (unless they are explicit or a
central presupposition of the argument.)
Writing tips
Make sure that:
1. your conclusion is well stated and clear.
2. subordinate conclusions (if any) support the main conclusion.
3. your premises (reasons) support your conclusions.
4. the examples which illustrate your premises are not contradictory or
questionable.
5. Any unfamiliar or important concepts are defined or explained- i.e. - using a
word or term in a manner different from the usual (write to your audience).
Establishing the truth of premises: Conceptual vs. Empirical Premises
A crucial step in evaluating the soundness of an argument is determining the
truth of the premises. The truth of a statement can be established by:
personal experience,
reference to an established authority,
internal consistency, and
consistency with the body of established fact (things we know are true already).
The most important step in determining the truth value of a given premise is
determining if the premise is making a Conceptual claim or an Empirical claim.
Premises which claim that some state of affairs exists or does not exist are
considered Empirical premises. The truth of these premises will be established
mainly by methods 1,2, and 4. above. On the other hand, the truth of some
premises will depend on the meanings of some central words in the premise. Here,
the statement is taken to present a Conceptual Theory - the author's idea of
what concepts are crucial to the success of the argument. The methods for
establishing the truth of these sorts of premises will be different from those
used to establish the truth of Empirical premises. To illustrate, consider the
following argument:
P1. The "Weekly Enquirer" contains many stories which stretch the credibility of
what is reported.
P2. Putting something in print makes it more likely to be taken as a fact.
P3. Journalism which stretches the credibility of what is reported is deceptive.
P4. Since journalism often involves the printed word, it ought not be deceptive.
Therefore, the "Weekly Enquirer" is bad journalism.
Premise 2 is an example of an empirical premise- it's truth or falsity is
established by empirical means, which will often involve methods which rely on
inductive arguments. (we could conduct a study to determine what people are more
likely to believe or not believe. Premises 3 & 4 are conceptual premises - the
truth or falsity of these premises will involve a discussion of what we
generally mean by words like "deceptive" and what will count as "bad
journalism". To further understand the different methods, we will first consider
the process for evaluating conceptual premises, then look to the process for
evaluating empirical premises.
Understanding more complicated Passages:
(1) Looking at the context- trying to determine the general point of the
argument - may involve several steps:
(a) May require several careful readings
(b) may assume that we know something about the author or their views (or their
opposition) - this will allow us to pick out satirical comments or
tongue-in-cheek comments. (It will be important in this area to realize our own
prejudices so that they do not interfere with our assessment of the argument.
Classic example of the "phantom essay", where the name and title of the author
were changed, but not the content of the essay. This changed the assessment of
the essay by a college audience.)
(c) What seems to be the most important point/conclusion reached? (good place to
look here is the title or at the language use throughout the argument (watch out
for satire)
(d) As always, look for and note the premise and conclusion indicators, keeping
in mind the lessons of the last section.
Keeping these things in mind, we can outline some steps to follow in
reconstructing arguments:
(1) Locate the conclusion-
(a) from here, you can more easily identify what statements will count as
descriptions, explanations, etc. and which will serve as premises (also helps if
you know what is being argued for in general)
(b) will also help in identifying and adding any implicit premises
(presuppositions) or conclusions.
(2) Penetrate the Prose-
(a) define any unknown terms or words, either by using the dictionary or by the
context/use under which they appear (will depend on our experience)
(b) rewrite the premises for clarity (you can oversimplify on the first go in
order to understand the argument better), paraphrase if possible to make the
claims more precise.
(3) Eliminate the Excess-
(a) get rid of anything which may distract us from the actual argument- Change
any prejudicial language to a more neutral wording.
(b) any non-controversial descriptions/explanations can be eliminated if they do
not directly support the conclusion or any premises. (i.e.- eliminate any
appeals to emotion, etc.) Of course, any controversial premises or claims which
do support the argument will have to be defended.
(4) Search out the structure-
(a) Figure out which statements serve as premises, and paraphrase them in order
to reveal the meaning/content of the claim. It may help to oversimplify on the
first re-write and add in the original language on the second go-around. This
step allows us to evaluate the formal structure of the argument- later on we
will see how to attach the argument based on the justification of the individual
premises.
Contributed by: Lauren Miller and Michael Connelly, Longview Community College
Note: This reading is posted online solely for the educational use of the students registered for Angela Yesh's philosophy classes.