LOGIC AND

Jonathan Dolhenty, Ph.D. Logic and Critical Thinking.
Available at
   Truth is the object of thinking.
   Some truths are obvious; others are difficult to
   Some judgments we make are simple; some
    judgments are complicated.
   Some arguments, whether made by us or others,
    may be straightforward and easily understood;
    other arguments may be complex and consist of a
    series of smaller arguments, each needing to be
    critically examined and evaluated.
   Every object of knowledge has a branch of knowledge which studies it.
      Planets, stars, and galaxies are studied by astronomy.
      Chemistry studies the structure, composition, and properties of material
        substances and the transformations they undergo.
      The origin, evolution, and development of human society is the object studied by
      Economics, biology, geography, and grammar all have objects of knowledge
        which they investigate, describe, and try to explain.
      Critical thinking involves knowledge of the science of logic, including the skills of
        logical analysis, correct reasoning, and understanding statistical methods.
      Critical thinking, however, involves more than just an understanding of logical
   A good critical thinker must also understand the sources of knowledge, the nature of
    knowledge, and the nature of truth.
   The object of knowledge involved in the science
    of logic is "thinking," but it is "thinking"
    approached in a special way.
   Generally speaking, logic is that branch of
    knowledge which reflects upon the nature of
    "thinking" itself.
   But this may confuse logic with other branches of
    knowledge which also have the nature of
    "thinking" as a part of their specific object of
   Logic doesn't just deal with "thinking" in general. Logic
    deals with "correct thinking."
       Training in logic should enable us to develop the skills
        necessary to think correctly, that is, logically.
   A very simple definition would be:
   Logic is the subject which teaches you the rules for
    correct and proper reasoning.
   A more complete and "sophisticated" definition of logic, you
    can define it this way:
   Logic is the science of those principles, laws, and
    methods, which the mind of man in its thinking must
    follow for the accurate and secure attainment of truth.
   “Natural Logic" or Common Sense
   We all have an internal sense of what is
    logical and what is not, which we generally
    refer to as "common sense."
   This "natural" logic we have learned from
    the moment of birth, through our personal
    experiences in the world and through our
    acquisition of language.
   Scientific logic is simply our natural
    logic trained and developed to
    expertness by means of well-
    established knowledge of the principles,
    laws, and methods which underlie the
    various operations of the mind in the
    pursuit of and attainment of truth.
   Logic as a science:
        The science part is the knowledge of the principles, laws, and methods of
         logic itself.
   Logic as an art:
        Logic must be put into action or else the knowledge provided within the
         science of logic is of little use.
        We can speak of the "art" of logic, that is, the practical application of the
         science of logic to our everyday affairs.
   Logic as a science and an art
        Logic is not intended merely to inform or instruct.
        It is also a directive and aims at assisting us in the proper use of our power
         of reasoning.
        In this sense, we can speak of logic as both a science and an art, a
         practical art meant to be applied in our ordinary affairs.
Why Study Logic?
   Aim: To develop a system of methods and
    principles that we may use as criteria for
    evaluating the arguments of others and as
    guides in constructing arguments of our
   Benefits: an increase in confidence that we
    are making sense when we criticize the
    arguments of others and when we advance
    arguments of our own.
 OF THE MIND                          SIGNS
Simple          Concept / Idea   Oral / written
   Apprehension                  terms
Judgment         Mental          Oral / Written
                 Proposition     Proposition or
Reasoning        Mental          Oral / written
                 agreement /     argument
Simple Apprehension, Judgment,
   Simple Apprehension: an operation of the mind
    whereby we abstract from the non-essential elements
    of a thing and recognize those essential elements
    which make it to be precisely that particular thing.
   Judgment: an operation of the mind which unites two
    ideas by affirmation or separates by negation.
   Reasoning / Mediate Inference: an operation of the
    mind that involves a process whereby from certain
    truths already known, we proceed to another which is
    different from those that are given but necessarily
    following from them.
    Basic Concept: ARGUMENTS
   Argument: a group of statements, one of
    which (the conclusion) is claimed to follow
    from the other or others (the premises).
   Good arguments: those in which the
    conclusion really does follow from the
   Bad arguments: those in which does not,
    even though it is claimed to
Basic Concept: Statement
    Basis: Argument as a group of statement
    Statement: a sentence that is either true or
     false; typically a declarative sentence.
    Examples:
1.   Hydrogen is combustible.
2.   World War II began in 1939.
3.   Some ducks are fish.
4.   Abraham Lincoln was beheaded.
Basic Concept: Truth - Value
   Truth value of the statement: the attribute
    by which a statement is either true or false.
        Examples:
    1.   Hydrogen is combustible. (true)
    2.   World War II began in 1939. (true)
    3.   Some ducks are fish. (false)
    4.   Abraham Lincoln was beheaded. (false)
Basic Concept: Non-Statements
    Sentences which cannot be said to be either
     true or false.
1.   What is the atomic weight of carbon? (question)
2.   Let’s go to the park today. (proposal)
3.   We suggest that you travel by bus. (suggestion)
4.   Turn to the left at the next corner. (command)
5.   Ouch! (exclamation)
Components of an Argument:
Premise(s) and conclusion
   Premises: the statement that set forth the evidence.
   Conclusion: the statement that is claimed to follow from
    the evidence.
   Example:
      All cats are animals.

      Felix is a cat.

      Therefore, Felix is an animal.

   N.B. the first two statements are the premises; the third
    is the conclusion.
   The claim that the conclusion follows from the premises
    is indicated by the word “therefore”.
Schema of an Argument:
Premises     Statement   Evidence

Conclusion   Statement      What is
                           claimed to
                          follow from
                         the evidence
          Recognizing Arguments
   One of the most important tasks in the
    analysis of arguments is being able to
    distinguish premises from conclusion.
       If what is thought to be a conclusion is really a
        premise, and vice versa, the subsequent analysis
        cannot possibly be correct.
       Frequently, arguments contain certain indicator
        words that provide clues in identifying premises
        and conclusion.
Conclusion Indicator
   A word that provides a clue to identifying a conclusion.
   Examples
       Therefore      hence                  whence
       Wherefore      thus                   consequently
       Accordingly    so                     it follows that
       Entails that   as a result            We may conclude
       Implies that   it must be that        We may infer
   Whenever a statement follows one of these indicators, it can
    usually be identified as the conclusion.
   By process of elimination the other statements in the
    argument are the premises.
   Example: This is pen is out of ink. Consequently, it will not
Premise Indicator
   A word that provides a clue to identifying a premise.
   If an argument does not contain a conclusion indicator, it may
    contain a premise indicator.
   Examples:
       for the reason that    in that        seeing that
       As indicate by         for            since
       Because           as           inasmuch as
       may be inferred from   given that     owing to
   Any statement following one of these indicators can usually
    be identified as a premise.
   Example: This locket is worth a lot of money, since it is made
    of platinum.
Basic Concept: Inference &
   An inference, in the technical sense of the
    term, is the reasoning process used to
    produce an argument.
   A proposition, in the technical sense, is the
    meaning or information content of a
Passages lacking an inferential claim
   Passages lacking an inferential claim contain statements that could
    be premises or conclusions (or both) but what is missing is a claim
    that a reasoning process is being expressed.
   Warnings/ pieces of advice: kinds of discourse aimed at
    modifying someone’s behavior.
        Ex. “Watch out that you don’t slip on the floor.”
        Ex. “I suggest you take philosophy in the first semester.”
             Each of these could serve as the conclusion of an argument; but in their
              present context, there is no claim that they supported or implied by reasons
              of evidence.
   Statements of beliefs or opinion: expressions of what someone
    happen to believe or think at a certain time.
        Ex. I think a nation such as ours, with its high moral traditions and
         commitments, has a further responsibility to know how to became drawn
         into this conflict, and to learn the lessons it has to teach us for the future.
                        Alfred Hassler, Saigon, U.S,A.
Passages lacking an inferential claim
   Loosely associated statements: may be about the same general subject,
    but they lack a claim that one of them is proved by the others.
       Ex. Not to honor men of worth will keep the people from contention; not
         to value goods that are hard to come by will keep them from theft; not
         to display what is desirable will keep them from being unsettled of
                     Lao-Tzu, Thoughts from the Tao Te Ching
   Report: consists of a group of statements that convey information about
    some situation or event. Ex. News Report
   Expository passage: a kind of discourse that begins with a topic sentence
    followed by one or more sentences that develop the topic sentence.
   Illustration: consists of a statement about certain subject combined with a
    reference to one or more specific instances intended to exemplify that
       Ex. Chemical elements, as well as compounds, can be represented by
         molecular formulas. Thus, oxygen is represented by “O 2”, sodium
         chloride by “NaCl”, and sulfuric acid by “H 2SO4”.
Conditional Statements
   A conditional statement is an “if… then…” statement.
       Ex. If it rains, the soil is wet.
   It is made up of two component statements: if = antecedent;
    then = consequent
       Occasionally, “then” is left out
       Conditional statements are not arguments because there is no
        claim that either the antecedent or the consequent presents
            In other words, there is no assertion that either the antecedent or
             the consequent is true. Rather, there is only the assertion that if the
             antecedent is true, then so is the consequent.
   A conditional statement may serve as premise or the
    conclusion of an argument.
   An explanation consists of a statement or a group of statements
    intended to shed light on some phenomenon that is usually
    accepted as a matter of fact.
      Ex. Cows can digest grass, while humans cannot, because their
         digestive systems contain enzymes not found in humans.
   2 parts:
      Explanandum: the statement that describes the event or
         phenomenon to be explained.
      Explanans: the statement or group of statements that purports
         to do the explaining.
   Explanations are sometimes mistaken for arguments because they
    often contain the indicator word “because”. Yet explanations are not
    arguments for the following reason: In an explanation, the
    explanans is intended to show why something is the case, whereas
    in an argument the premises are intended to prove that something
    is the case.
Argument                  Explanation
  Premises     facts        Explanans

                                          Claimed to
               To prove
                                          shed light on
                            Explanandum   Accepted

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