A Simple Lesson in Logic
by Thomas I. Ellis, Ph.D.
Logic is the indispensable foundation of rational communication, critical inquiry, and justice. It begins with what Aristotle calls an enthymemea statement that joins a condition to a consequence, taking the form of "if X is Z, then it is Y" which then can be translated, "X is (or should be) Y because it is Z." Here is an example:
"If George W. Bush was not elected, he is not really President."
This statement asserts that if the condition is shown to be true, the consequence is inescapable. In its positive form, this would be--
"George W. Bush (X) is not really President (Y) because he was not elected. (Z)"
This enthymeme can be unpacked into the following syllogisma formal logical statement
1. All Presidents are elected. (All Y=Z) 2. George W. Bush was not elected. (X not Z) 3. Therefore George W. Bush is not President. (X not Y)
A syllogism is the heart of a logical argument. It consists of
(1) A Major Premisea generalization, that you rely on your reader to accept as self-evident. That is, a major premise must contain the word "All." (2) A Minor Premisea claim of fact that places a specific instance in the category specified by the generalization; and (3) A Conclusion that follows inescapably from the generalization and the claim of fact.
Once we have translated an argument into a syllogism, we are in a good position to evaluate that argument. This can be done by asking the following questions:
(1) Is the generalization valid, and if so, on what grounds? That is, what is your rationale for accepting the validity of the major premise? The rationale can be either factual or value-based, depending on the case. (2) Can the specific claim of fact be demonstrated to be true? What is your evidence? (3) Does the conclusion follow logically from this?
The third question is easiest to answer, because syllogisms are either valid or invalid, depending on their formulation. But a valid syllogism is not necessarily true. For example, the following is a perfectly valid syllogism:
All frogs have six eyes. Kermit is a frog Therefore Kermit has six eyes.
The syllogism is valid, but obviously not true, because we know that the major premise is contrary to fact.
Conversely, a syllogism can have true claims, but still be invalid:
All cats have whiskers John Smith has whiskers Therefore, John Smith is a cat.
This conclusion does not follow because, formally, the conclusion and the second premise are reversed. It is the fallacy of the undistributed middle term. (i.e. because all cats have whiskers, it does not follow that everything that has whiskers is a cat).
To be both valid and true, a syllogism must have both true claims and a valid structure. But how do we know what's true? Here we must draw a careful distinction between claims of fact and value-based claims, both of which may be used in an argument. Claims of fact require supporting evidence; value-based claims require assent. Now, let's look more closely at our syllogism:
1. All presidents are elected. Obviously, this is not a fact everywhere, though we might wish it were. But it is certainly a value- based claim that would be accepted by anyone who believes in democracy. Furthermore, it corresponds to the (value-based) charter the Declaration of Independencethat establishes the foundation for legitimate authority in the United States"Governments...deriv[e] their just power from the consent of the governed." So this proposition forms the legal basis for legitimate political power in the United States.
2. George W. Bush was not elected. This is the claim of fact which we would have to substantiate by evidence. In this case, the evidence is easy to come by: Al Gore won a decisive majority of the nationwide popular vote; the Florida election was marred by massive voter fraud and intimidation of electoral officials (perpetrated by the Bush camp) and accidental irregularities (like the "Butterfly Ballot") that manifestly thwarted voter intent. And finally, Bush was appointednot electedby a partisan majority of the Supreme Court that had a vested interest in the outcome of their decision. In the process, this partisan majority violated the Constitutional separation of powers and simultaneously denied due process to Florida voters by halting their legally binding process for resolving a disputed election.
3. Therefore, George W. Bush is not President. If one accepts, as a value-based premise, the fact that in the United States, Presidential authority derives from an unhindered electoral process that discloses and respects the consent of the governed, and one can establish as factual the multiple violations of this principle perpetrated by Mr. Bush and his allies, then the conclusion is inescapable: Mr. Bush has no legitimate title to the office that he holds, and thus has no claim on our respect, loyalty, or obedience as President of the United States.
Once we have evaluated both the logical validity and the (ethical and factual) truthfulness of the syllogism at the heart of our argument, we are in a good position to seek our reader's assent to the following:
Assumptions"What are you talking about?" The definition of terms and basic value-based propositions we are asking our readers to share as a precondition for their assent. (i.e. What is a "President"? What is the legal basis of political authority in the United States?).
Position"What are you saying about it?" The major point (enthymeme) to which we are seeking our reader's assent: that George W. Bush has no legitimate title to the Presidency because he was not elected by consent of the governed.
Arguments"Why?" The reasons we have for asserting the above claim. (i.e. the voter fraud and irregularities in Florida; the intimidation of electoral officials; and the denial of due process to Florida voters by the partisan Supreme Court.
Evidence"How So?" The facts that can be marshalled in support of each of the above claims. (They are abundant).
Implications"So What?" What all this meanswhat are the policy implications of your claim? Depending on your purpose, implications may be strictly theoretical--(i.e. since we don't have a real President, and the Supreme Court has successfully violated the Constitutional Separation of Powers, the United States of America as envisioned by the Founding Fathers was effectively suspended on December 12, 2000)or policy-based (George W. Bush and the five Supreme Court partisans should be impeached by our legislative branch the only remaining legitimate branch of government) or even personal (We must each do everything we ethically can to withdraw our assent from Bush's illegitimate authority and to subvert his regime, until legitimate government is restored).
The last element to consider, while making any argument, is refutation. That is, for each of the above elements of argument assumptions, position, arguments, evidence, and implications, it is essential that we be ready to anticipate and answer objections from skeptical readers. At the level of assumptions, for example, one could argue that the Constitutionally established Electoral College already violates the strict principle of Consent of the Governed, and that Bush won an electoral majority as had several minority-elected Presidents in the past. One would then answer this objection by pointing out that the Florida electoral college delegation, which gave Bush his putative victory, was itself not legitimately elected, since the vote count was prematurely halted and nobody knows for certain who won the popular vote in Florida, and thus which electoral delegation was entitled to vote.
At the level of implications, one could argue, as many have, that we should simply "move forward" and forget the past, enact electoral reform, and hope to defeat Bush in 2004. But this would imply (one might then respond) that all that happened was "politics as usual" which it manifestly was not. As Dr. Martin Luther King memorably said, "Injustice anywhere is a threat to justice everywhere." As long as we allow an injusticelike the blatant theft of an election by two branches of governmentto stand unchallenged, we are conferring our implicit consent to the abrogation of democracy, and thus making it more likely to happen again.
Thus, as Thomas Jefferson also said, "when a long train of abuses and usurpations, pursuing invariably the same object, evinces a design to reduce them under absolute despotism, it is their right, IT IS THEIR DUTY, to throw off such government, and to establish new guards for their future security."
So be it...