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Diagram of a two premise 
argument

Introduction to Logic:
How to Diagram Arguments

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

  1. Arguments in logic are composed of premises being offered as reasons in support of a conclusion.

    1. The use of the term "argument" in logic is in accordance with this precising definition; the term is not being used to refer to a dispute or a quarrel.

    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 always be initially presented in declarative sentences.

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

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

      Argument 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.
      Usually, however, the emphasized phrases, “I conclude” and “These are my reason” are omitted omitted in the text for stylistic reasons &mdash leaving the structure of the argument to be inferred from the meanings of the statements used.

    2. The author uses argument indicators signifying the presence of an argument.

      Argument 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.
      In this argument, “since” is being used as a premise indicator and “I conclude” is used as a conclusion indicator.

    3. In order to determine whether or not an argument is present in a passage, it sometimes helps to ask the irreverent question, “What are you trying to prove?” If an answer is directly forthcoming, then the passage is most likely argumentative.

      Despite that, the presence of an argument cannot be always known with certainty; often the purpose of the passage can only be contextually surmised. The intention of the speaker or writer is often a determining factor.

      A charitable, and insofar as possible, a conventional interpretation of the context, content, and purpose of the passage should be sought.

      Argument 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.
      Note that if we ask upon reading this passage, “What are you trying to prove?,” the answer in statement (3) suggests itself.

  3. 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 premises and conclusions.

    1. The conclusion of one argument can become a premise for another argument. Thus, a statement can be the conclusion of one argument and a premise of 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 argument:
        (1) John didn't get much sleep last night. (2) He has dark circles under his eyes. (3) He looks tired.
        Diagram of 
		of argument shows premises (2) and (3) lead to conclusion (1)> The conclusion is the first sentence in the passage. Statements (2) and (3) are observational evidence for statement (4) which is being inferred from those observations.

      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 of an argumentative paragraph, a conclusion indicator is present, or the last sentence is presented as an after-thought with a premise indicator. Frequently used argument indicators are listed below.

        Example Argument:
        (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.
        Argument diagram 
		shows premises (1),(2),and (4)lead to conclusion (3).
      3. The structure of the argument be inferred by attending to the following kinds of
        premise and conclusion indicators.


        1. Premise indicators are terms which often indicate the presence of reasons. Frequently used premise indicators include the following terms:
          for
          since
          as
          because
          for the reason
          follows from
          after all
          in light of the fact
          for the reason [*often mistaken for conclusion indicator]]
          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.
          Diagram shows 
			premise (2) leads to conclusion (1) The term “since” indicates that the second clause of this passage is a premise, the first clause is left as the conclusion. In practice, the second clause can be broken down into two separate premises so that the argument can be set up as follows:
          (2a) Reading the point of intersection of a graph depends on the accuracy with which the lines are drawn.

          (2b) Reading the point of intersection also depends upon the ability to interpret the coordinate of the point.

          (1)Thus, the graphical method for solving a system of equations is an approximation.
          Another Argument with premise indicator:
          (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.
          Diagram shows 
			that premise (2) leads to conclusion (1).
        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
          [*especially note this term] implies that
          for this reason [*term often mistaken for premise indicator]
          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. Equal Status Indicators: Conjunctives (including some conjunctive adverbs) often indicate equal status of premise or conclusion in connecting clauses or sentences. Noticing these conjuncts is especially helpful in argument analysis:
          If one of the clauses has already been identified as a premise or a conclusion then its coordinating clause is of the same type of statement.
          Indicators of clauses of equal status include:
          and
          but
          yet
          however
          moreover
          in addition
          nevertheless
          not only &helip; but also
          (and also the semicolon “;”)
          Example of the Equal Status Indicator “and”:
          Arggument 
			diagram shows statements (2) and (3) lead to statement (1). (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.
          Argument diagram 
		shows premise (1) leads to conclusions (2) and (3).

  4. When analyzing complex arguments, it can be helpful to reconstruct the argument by identifying the conclusion first, and then by working backwards, locate the premises.

    1. 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.
      Note that the following indicators are given in this passage:
      as
      because
      thus
      The argument is complex.

      1. Argument Diagram 
		shows statement (4) leads to statement (3) which in turn leads to 
		statement (2). The premise 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.

      2. 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.

      3. 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 O bjected (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):
        Argument diagram 
		shows statement (1) and (5) lead to statement (6). If A then O
        Not O
        Not A
        (Note that A is the same statement as (6).)

      4. Argument diagram 
    	 shows statement (4) leads to statement (3) which leads to statement (2), 
    	 and statement (2) taken together with statements (1) and (5) lead finally 
    	 to statement (6). Hence the whole argument can now be pieced together as the following complex argument:


    2. In some contexts, the use of indicator words such as those listed above do not typically indicate the presence of an argument.

      1. Literary Implication: For example, in following book review, two example passages drawn from the work of the poet Stevie Smith illustrate a literary insight into her writing.

        In the passage excerpted below, the emphasized phrase “The implication … is” does not function as an argumentative conclusion indicator. Instead, these examples are intended to suggest a meaning beyond the literal interpretation of the events described:
        “In The Voyage of the Dawn Treader, the ship's prow is ‘gilded and shaped like the head of a dragon with wide open mouth’ so when, a moment later, the children stare at the picture ‘with open mouths’, they are being remade in its image … The painted ocean to which Joan is drawn is ‘like a mighty animal’, a ‘wicked virile thing’. The implication [emphasis mine] in both cases is that art is not safe, and that this is why it's needed.”

        [Matthew Bevis, “What Most I Love I Bite,” in the &ldquopReview of The Collected Poems and Drawings of Stevie Smith,” London Review of Books 38 No. 15 (28 July 2016), 19.]
        From a logical point of view, literary implication is a type of literary generalization meant to enlighten.

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