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Philosophy 103: Introduction to Logic
Diagramming Arguments

Abstract: Analyzing the structure of arguments is clarified by representing the logical relations in diagram form.

  1. Arguments in logic are composed  reasons being offered for a conclusion. (The use of the term "argument" in logic does not carry the everyday connotation of a quarrel in everyday discourse.

  2. The presence of an argument in a passage is discovered by understanding the author's intention of proving a statement by offering reasons or evidence. Generally speaking, these reasons are presented as verbal reports although they might not be initially presented  in declarative sentences.

  3. There are three main ways of judging the presence of an argument:

    1. The author or writer explicitly states explicitly lists the reasons, evidence, justification, rationale, or proof of a statement.

      Example:

      (1) I conclude the dinosaurs probably had to cope with cancer. These are my reasons: (2) a beautiful bone found in Colorado filled with agate has a hole in its center, (3) the outer layer was eroded all the way through, and (4) this appearance closely matches metastatic bone tumors in humans.

    2. The author uses argument indicators signifying the presence of an argument. (Common premiss and conclusion indicators are listed below in Section IV).

      Example:

      (1) Since the solution turned red when the indicator was added, (2) I conclude it is acidic, inasmuch as acidic substances react with this indicator to form a red color.

    3. The passage under question implicitly provides an answer to the sometimes irreverent question of "What are you trying to prove?" The presence of an argument cannot be always known with certainty. A charitable, conventional interpretation of the content and context of the passage is assumed.

      Example:

      (1) The types of sentences you use are quite varied. (2) I've noticed that your essays are quite sophisticated. (3) You have been learning much more about sentence structure.

      [The conclusion is statement (3)].

  4. In order to analyze simple and complex arguments, we will find it useful to construct a diagram of the structure of the argument that details the relations among the various premisses and conclusions.

    1. A conclusion of one argument can become a premiss for another argument. Thus, a statement can be the conclusion of one argument and a premiss for another argument just as a daughter in one family can become a mother in another family.

    2. The number of arguments in a passage is conventionally established by the number of conclusions in that passage.

    3. In analyzing the structure of an argument, whether simple or complex, the all-important first step is to find the conclusion. Here are some specific suggestions as to how to find the conclusion.

      1. The conclusion might be evident from the content and context of the paragraph structure. The sequence of sentences is often an indication of the conclusion. Arrangement of sentences from most general to specific is a common form of paragraph or passage; the arrangement of sentences from specific to general is a bit less common. Considering both cases, the conclusion is often the first and sometimes the last sentence in a passage.

        Example:

        (1) John didn't get much sleep last night. (2) He has dark circles under his eyes. (3) He looks tired.

        The conclusion is the first sentence in the passage.

      2. Nevertheless, the conclusion can occur anywhere in the paragraph, especially if the passage has not been revised for clarity. Usually, if a conclusion is not the first or last sentence, a conclusion indicator is present, or the last sentence is presented as an after thought with a premiss indicator. See below for lists of premiss and conclusion indicators.

        Example:

        (1) Studies from rats indicate that neuropeptide Y in the brain causes carbohydrate craving, and (2) galanin causes fat craving. (3) Hence, I conclude that food cravings are tied to brain chemicals (4) because neuropeptide Y and galanin are brain chemicals.

      3. The structure of the argument (and, of course, the conclusion, as well) might be inferred by the following kinds of indicators.

        1. Premiss indicators are words which often indicate the presence of reasons. Common premiss indicators include the following:

          for
          since
          as
          because
          for the reason
          follows from
          after all
          in light of the fact
          *for the reason

          Example Argument:

          (1)The graphical method for solving a system of equations is an approximation, (2) since reading the point of intersection depends on the accuracy with which the lines are drawn and on the ability to interpret the coordinates of the point.

          Another example argument:

          (1) Questionable research practices are far more common than previously believed, (2) after all, the Acadia Institute found that 44 percent of students and 50 percent of faculty from universities were aware of cases of plagiarism, falsifying data, or racial discrimination.
        2. Conclusion indicators are words which often indicate the statement which logically follows from the reasons given. Common conclusion indicators include the following:

          thus
          therefore
          consequently
          hence
          so
          it follows that
          proves that
          indicates that
          *accordingly
          implies that
          *for this reason

          Examples of their use in arguments:

          (1) No one has directly observed a chemical bond, (2) so scientists who try to envision such bonds must rely on experimental clues and their own imaginations.

          (1) Math grades for teens with bipolar disorder usually drop noticeably about one year before their condition is diagnosed, thus (2) probably bipolar disorder involves a deterioration of mathematical reasoning.


          (1) Coal seams have been discovered in Antarctica. (2) This means that the climate there was once warmer than it is now. (3) Thus, either the geographical location of the continent has shifted or the whole Earth was once warmer than it is now.

        3. Conjunctives (including conjunctive adverbs) often indicate equal status for clauses or sentences. Noticing these conjuncts is especially helpful for argument analysis if one of the elements has already been identified.

          Indicators of clauses of equal status include:

          and
          but
          yet
          however
          moreover
          in addition
          nevertheless
          (and also the semicolon ";")

          Examples:

          (1) Some students absent today are unprepared for this test, since (2) the law of averages dictates that only 10% of students are absent due to illness, and (3) more than 10% are absent.

          (1) Lenses function by refracting light at their surfaces. (2) Consequently, not only does their action depends on the shape of the lens surfaces but also (3) it depends on the indices of refraction of the lens material and the surrounding medium.

  5. When working with complex arguments, it is often helpful to reconstruct the argument backwards from the conclusion. Consider the following argument.

    (1) If students were environmentally aware, they would object to the endangering of any species of animal. (2) The well-known Greenwood white squirrel has become endangered (3)as it has disappeared from the Lander Campus (4) because the building of the library destroyed its native habitat. (5) No Lander students objected. (6) Thus, Lander students are not environmentally aware.

    • The premiss indicators suggest that (2) is a subconclusion of (3) since the indicator "as" connects them, and (3), in turn, is a subconclusion of (4) since the indicator "because" connects those two statements.

    • Statement (6) is the final conclusion since it has the conclusion indicator "thus" and the import of the paragraph indicates that this statement is the main point of the argument.

    • Intuitively, the structure of the first statement (1) together with statement (5) is a common argument form:

      If students were environmentally Aware, they would Object to the endangering of any species of animal.
      No student Objected (to the endangering of the Greenwood white squirrel).

      which can be abbreviated as follows:

      If A then O
      Not O

      and the negation of clause O is logically equivalent to conclusion (6).
      (Later in the course we will see that this argument structure is termed modus tollens):

      If A then O
      Not O
      _____________
      Not A which is the same statement as (6).

    • Hence the whole argument can now be pieced together as:


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