Ship captains are morally obligated to change course once they have been warned of an iceberg ahead.  I sounded such an alarm in my article "Common Core Standards Flunk Logic 101."  Shortly thereafter, I sent e-mails to the addressees below, attaching a link to the article and urging delay in implementing mathematics standards until the problems I raised were corrected.

• Council of Chief State School Officers (CCSSO), Washington DC, which issued the mathematics standards.
• Senator Tom Harkin (D-IA), Chairman, Senate Committee on Health, Education, Labor and Pensions.
• Senator Lamar Alexander (R-TN), Ranking Member, Senate Committee on Health, Education, Labor and Pensions.
• Representative John Kline (R-MN), Chairman, House Committee on Education and the Workforce.
• Mr. Arne Duncan, United States Secretary of Education.
• Departments of Education in all 50 states, the District of Columbia, Puerto Rico, and the Virgin Islands.

The CCSSO and the three members of Congress have yet to reply.  The Department of Education assigned my message "Incident # 28022-24726" and then had its Information Resource Center send me an e-mail, signed by Mr. Julio Torres, stating: "There are no national curriculum requirements or federal regulations concerning curriculum or standards. Each state sets its own curriculum and standards without federal influence.  The U.S. Department of Education was not involved in the development of the standards. Furthermore, individual states choose whether or not to adopt these standards."

I will report in due course if I receive substantive replies from states.  Here I warn of trouble ahead for the other CCSSO document, "Common Core State Standards for English Language Arts and Literacy in History/Social Studies, Science, and Technical Subjects" -- hereafter CE -- owing once again to inadequate treatment of basic concepts of logic.  There is space only to suggest solutions to some of the problems I found.  I urge states to delay implementing logic-related standards until problems have been solved.    

Logic in the CE Document

The CE document consists of a 66-page main text supplemented by three appendices totaling 333 pages.  The document acknowledges (the obvious?) that logical reasoning is key to English language proficiency in reading, writing, speaking, and listening.  Here are examples of logic-related skills that CE Standards expect students to acquire -- some as early as 3^rd grade, most from 6^th grade on.

• Draw inferences from a text.
• Present information logically.
• Organize reasons and evidence logically.
• Support claims with logical reasoning.
• Create an organization that logically sequences claims, counterclaims, reasons, and evidence.
• Describe the logical connection between particular sentences and paragraphs in a text.
• Create an organizational structure in which ideas are logically grouped to support the writer's purpose.
• Provide logically ordered reasons that are supported by facts and details.
• Group related information logically.
• Sequence ideas logically.
• Organize an event sequence that unfolds logically.
• Present information, findings, and supporting evidence logically.
• Provide reasons that support an opinion.
• Distinguishing which claims are supported by facts, reasons, and evidence, and which are not.
• [Present] a balanced, coherent and informed argument.
• Assess whether the reasoning is sound.
• Identify fallacious reasoning.
• Assess the relevance and sufficiency of the evidence and the validity of reasoning.
• Provide a concluding statement that follows from and supports the argument presented.
• Delineate a speaker's argument and specific claims.
• Delineate and evaluate the argument and specific claims in a text.
• Evaluate the validity of the reasoning as well as the relevance and sufficiency of the evidence.
• Evaluate the soundness of reasoning and the relevance and sufficiency of evidence.
• Incorporate narrative elements effectively into arguments.
• Trace and evaluate the argument and specific claims in a text.
• Write arguments to support claims with clear reasons and relevant evidence.

What's the Problem?

The main CE document states (p. 6) that its purpose is to "define what all students are expected to know and be able to do."  So what definitions does CE offer to help teachers make sure lesson plans reflect the list of logic skills they are expected to teach?  Keep in mind that states that have adopted CE are on the hook to prove compliance. 

A definition of "argument" appears on p. 23 of Appendix A in a section titled "Definitions of the Standards' Three Text Types":

An argument is a reasoned, logical way of demonstrating that the writer's position, belief, or conclusion is valid.

What about key evaluative terms applicable to arguments such as "valid," "sound," and "fallacious," and the basic logical skill of "drawing inferences"? 

The term "valid" is neither defined nor illustrated anywhere, despite repeated occurrences in the main CE text (pp. 10, 18, 35, 40, 41, 45, 47, 60, and 63).  CE does avoid (whew!) the non-standard term "viable" used in the mathematics Standards -- though this made me wonder why the CCSSO didn't insist on verbal consistency between the two documents.

The term "sound" first occurs on p. 7 of the main CE text and also on pp. 39, 44, and 49, all in connection with reasoning.  Appendix A (p. 24) mentions "sound" in connection with arguments rather than reasoning.  Neither use is defined; the relationship between "sound" and "valid" is never explained.  I found on p. 49 the phrase "sound valid reasoning"! 

The main CE text commendably wants students to become "sensitive to inconsistencies, ambiguities, and poor reasoning in texts" (p. 3, emphasis mine).  "Poor reasoning" is then inexplicably dropped and replaced with "fallacious reasoning" (pp. 40, 47, and 50).  Neither term is defined or illustrated anywhere.

"Drawing inferences" occurs on pp. 12, 14, 36, 38, 39, and 40, as early as 4^th grade.  Appendix B mentions this skill on pp. 70, 89, and 140.  This term is also not defined or explained anywhere.

The definition of "argument" is such a mess that I'm glad CE compilers did not attempt "definitions" of other terms of logic.

(1) The language comes uncomfortably close to making arguments logically correct by definition.  How can arguments be bad, which they certainly can be, if defined as "reasoned, logical demonstrations of an opinion"? 

(2) "Reasoned," "logical," and "demonstrating" are quite close in meaning, so one or more of these terms is redundant.  Which one(s)?  ("Validity of reasoning" and "sufficiency of evidence," stated on pp. 10, 35, 49, and 60, as if they signified distinct properties, are actually equivalent terms.)

(3) Readers of my previous article know that the term "valid" has a special meaning in logic as a property of arguments, not opinions, as the definition suggests.  The main CE text seems to have this right.  Did Appendix A compilers not read those sections of the main text to ensure consistency?

(4) Imagine trying to explain to a student how to figure out if a text contains an argument using the above definition.  A text is a collection of words, so what words should teachers have students look for to spot arguments?

(5) Suppose that a student correctly concludes (never mind how) that the "validity" of the writer's position is not demonstrated in reasoned, logical way in a text.  Shouldn't the student conclude that a bad (invalid) argument has been presented rather than that no argument has been presented, as the definition implies?

(6) Reference to the writer in the definition is, of course, unnecessary and also a bad idea.  Is the student to conclude that a text does not contain an argument because the author is not identified or because the view at issue is not that of the author?

(7) A definition should make clear what is being defined in terms of what.  Could a teacher easily tell what concepts are used to define "argument"? 

A Solution Outlined

A sound argument is one that is valid and has true premises.  If an argument is sound, its conclusion must be true.  In logic, an argument can be valid even if premises and conclusion are false.  This may seem counterintuitive, but is correct.

For present purpose, only a definition-in-use of "text T contains an argument" is needed.

Text T contains an argument  = df T contains a conclusion sentence, a set of premise sentences, and a claim that the conclusion follows from (is implied by) the premises.

For this definition to be useful, students will need to know what words or phrases they should look for in a text as indicators of argument components, which they can apply when formulating arguments of their own.  A phrase-book of premise and conclusion indicators would be a very useful tool.  Below are some suggestions.

Premise indicators: because, for the reason that, since, inasmuch as, given that, in view of, in light of, on grounds that, on the basis of, justified by, motivated by, proceeds from.

Conclusion indicators: therefore, consequently, thus, as a result, so, and so, implying that, hence, accordingly, entails that, leading to, proving that, for that reason.

"Drawing inferences" can be explained (not defined) in terms of instantiating a valid argument form.  Here are three useful valid argument forms.  replacing the capital letters with sentences will result in a valid argument every time:

1. (If A then B) and A -- infer -- B.

2. (If A then B) and not-B -- infer -- not-A.

3. (Either A or B) and not-A -- infer -- B. 

The following are all fallacious argument forms even though they are very similar to 1-3.  Logic books should be consulted for a list of informal fallacies.

1. (If A then B) and B -- infer -- A.

2. (If A then B) and not-A -- infer -- not-B

3. (Either A or B) and A -- infer -- not-B. 

Arnold Cusmariu is a former logic professor currently making sculpture and playing golf.  He can be reached at aclogic1@yahoo.com.