The Logic of



The notion of argument

An argument is a connected series of statements or propositions, some of which are intended to provide support, justification, or evidence for the truth of another statement or proposition.

Arguments consist of one or more premises and a conclusion. The premises are those statements that are taken to provide the support or evidence; the conclusion is that which the premises allegedly support. For example, the following is an argument:

Taxes should be increased only if the increase results in better public services. However, public services can improve only if there is a new management, and since the current management will not change until the new elections –which will take place in four years- we must reject the increase in taxes for the coming fiscal year.

The conclusion of this argument is the final statement: "we must reject the increase in taxes". The other statements are the premises; they are offered as reasons or justification for this claim.



Some important elements of an argument might be left implicit or unstated. For example, Dr. Ivan Vlasic is an outstanding scholar. He was appointed Professor Emiritus at McGill University.

In the following example, the author takes it for granted that the reader understands that McGill University only appoints recognized scholars as Professor Emiritus. Therefore, the argument is best understood as an abbreviated form of the full argument: "McGill University has a very rigorous selection process for appointing Professors Emiritus. Only those internationally recognized scholars over 65 years of age, who have significantly contributed to the advancement of their disciplines may be appointed Professor Emeritus. Dr. Ivan Vlasic, who has published numerous books and journal articles, has a Ph.D. from Yale, supervised numerous doctoral and master's theses, and contributed to many International Law debates and pioneered in the development of Space Law, was appointed as McGill University's Professor Emeritus in Law. He is an outstanding scholar."

Argument structure

·            Premise


o          A premise of an argument is something that is put forward as a truth, but which is not proven. It is not proven and hence is assumed to be true (although how universally accepted this truth is may be another matter). If you want to attack another person's argument, you can challenge the truth of their premises. If you are making an argument, you should be ready to defend any of your own premises.


·            Conclusion


o          The conclusion (or claim) is the statement with which you want the other person to agree. It is drawn from the premises of the argument, of which there may be many. A useful way of spotting a conclusion is that may well be a statement of necessity, saying what must or should happen. It may well be framed to persuade the other person to do something or make some decision.


·            Inference


o           Between the conclusion and the premises are further statements which translate the premises into the conclusion. This is the reasoning process, and in a formal argument the author uses careful logic (in informal arguments, emotional reasoning and assumptive leaps may well be used).



Types of reasoning

Formalized arguments can be broadly grouped into two categories: deductive and inductive. The relationship between the premises and conclusion that holds in each case serves to distinguish them:




        I.    If all of the premises are true, the conclusion must be true.

       II.    All of the information or factual content was already contained, at least implicitly, in the premises.

        I.    If all of the premises are true, the conclusion is probably true but not necessarily true.

       II.    The conclusion contains information not present, even implicitly, in the premises.


(P1) All men are human beings.
(P2) Socrates is a man.

\Socrates is a human being.


(P1) Every emerald yet discovered has been green.

\All emeralds are green.


Deductive arguments are assessed in terms of their validity or invalidity. An argument’s validity deals only with the inferential relation between its premises and its conclusion. That is, the premises need not be true for an argument to be valid. For example:

(P1) All Russians are evil.
(P2) My mother is Russian.

(C) My mother is evil.

If we assume that P1 and P2 are true, then the conclusion inexorably follows. (The premises aren't true in this case, though—my mother happens to be perfectly nice). If the premises of a valid deductive argument are indeed true, the conclusion must be true, and the argument is considered sound.


Inductive arguments, in contrast, inhabit a spectrum from weak to strong. Conclusions to arguments of this type go beyond their premises and hence cannot be guaranteed true, regardless of the truth of the premises, and even if its premises are true, an inductive argument’s conclusion is at best probably true. Consider the following example:

(P1) Nearly all deaf persons have little musical ability.
(P2) Beethoven was deaf.

(C) Beethoven had little musical ability.

P1 and P2 are both true, yet the conclusion is certainly false. Hence, though inductive arguments are a primary source of our beliefs, they remain a tentative source of knowledge.


Common Fallacies


Logical fallacies are mistakes in reasoning. They may be intentional or unintentional, but in either case they undermine the strength of an argument. Some common fallacies are defined below.


1.      Hasty Generalization: A generalization based on too little evidence, or on evidence that is biased. Example: All men are testosterone-driven idiots. Or: After being in New York for a week, I can tell you: all New Yorkers are rude.


2.      Either/Or Fallacy: Only two possibilities are presented when in fact several exist. Example: America: love it or leave it. Or: Shut down all nuclear power plants, or watch your children and grandchildren die from radiation poisoning.


3.      Non Sequitur: The conclusion does not follow logically from the premise. Example: My teacher is pretty; I'll learn a lot from her. Or: George Bush was a war hero; he'll be willing to stand tough for America.


4.      Ad Hominem: Arguing against the man instead of against the issue. Example: We can't elect him mayor. He cheats on his wife! Or: He doesn't really believe in the First Amendment. He just wants to defend his right to see porno flicks.


5.      Red Herring: Distracting the audience by drawing attention to an irrelevant issue. Example: How can he be expected to manage the company? Look at how he manages his wife!


6.      Circular Reasoning: Asserting a point that has just been made. Sometimes called "begging the question." Example: She is ignorant because she was never educated. Or: We sin because we're sinners.


7.      False Analogy: Wrongly assuming that because two things are alike in some ways, they must be alike in all ways. Example: An old grandmother's advice to her granddaughter, who is contemplating living with her boyfriend: "Why should he buy the cow when he can get the milk for free?"


8.      Post Hoc, Ergo Propter Hoc: The mistake of assuming that, because event a is followed by event b, event a caused event b. Example: It rained today because I washed my car. Or: The stock market fell because the Japanese are considering implementing an import tax.


9.      Equivocation: Equates two meanings of the same word falsely. Example: Christianity teaches that faith is necessary for salvation. Faith is irrational, it is belief in the absence of or contrary to evidence. Therefore: Christianity teaches that irrationality is rewarded.


10.                                  Middle Ground: The fallacy of the middle ground is based on the assertion that a proposition is true simply because it falls between two more extreme propositions. The principle of moderation is however not necessarily fallacious. Example: Some people claim that God is all powerful, all knowing, and all good. Other people claim that God does not exist at all. Now, it seems reasonable to accept a position somewhere in the middle. So, it is likely that God exists, but that he is only very powerful, very knowing, and very good. That seems right to me



These are only common non-arguments. That is not to say that some instances of them will not be arguments. Remember, if an inferential claim is being made between the evidence and conclusion, then there is an argument. In order to establish this, the reader must make a subjective deduction about the author's intentions. 

Non-inferential passages: passages in which there is no inference being made that the premises support or entail a conclusion. 


Ex: “Stop!” or “Duck so you do not hit your head on the pipe”

* For one, these are not statements as they have no truth value. Further, there are no premises which support the conclusions in these examples. 

Piece of advice: 

Ex: “I suggest you slow down while driving.

* Again, no truth vale for the statement and no evidence (premises). 


Ex: “I think you should buy a bullet proof vest to ensure your safety.”

*No evidence is used to support opinion; therefore, it is not an argument. 

Loosely associated statements: These are statements that are perhaps loosely related but there is no inferential claim being made between the statements. Therefore, there is nothing being proved in such a passage. 

Ex: Water is wet. Swimming pools are filled with water. Many colleges and universities have collegiate water sports. Water is fun to play in. 

Report: A passage which conveys information about a subject (topic). Reports are not used to prove anything. The facts are simply reported without any inferences being made. 

Ex: See report example on the previous page of the notes. 

Expository passages: These are passages of which one offers a topic sentence and then expounds upon the topic. The key to these passages is deciding if the author provides proof for his topic sentence or just expounds upon it in more detail. If the author only intends his exposition to expound upon the topic sentence then there is no argument because he is offering no proof for the conclusion (the topic sentence). However, if the author provides reason for the reader to believe his exposition proves that the topic sentence is true, then the exposition is an argument. 

Illustrations: These are passages in which a statement is made about a certain subject and then specific instances are used to illustrate this statement. 

Ex: Elements can be represented by atomic symbols. Thus, oxygen is represented by O and potassium is represented by K.

* This is not an argument because the author makes no claim that he is proving that Elements can be represented. All he is doing is illustrating how it is done. At best, all he can say is “If elements can be represented by atomic symbols, this is how it would be done. 


It is important to remember that the author has to make a claim that her premises entail her conclusion. Illustrating her conclusion, or showing how it is done, is usually not enough to establish entailment. However, again, there is a large amount of subjectivity in just what the author is trying to prove. 

Explanations: These are passages which intend to shed light on a specific fact. 

In an explanation the author usually relates an excepted fact and then tries to make sense of it. That is, he tries to explain why it might have happed or some of the causes for the fact. However, the author is not intending for his explanations to prove that the fact is in fact true. All he is trying to do is make sense of it or explain it. These types of passages are easily mistaken for arguments. One has to ask, though, is the author trying to prove the conclusion or is he trying to explain what happed (make sense of it). 

Conditional Statements: The statements are if/then statements. 


If I go to the store then I will buy chocolate.

I will buy chocolate if I go to the store.

If I win my match then I will go on to regional. 

These seem to be arguments; however, at best they can only be parts of an argument. Again, to be an argument, there must be at least one statement which gives us reason (evidence) to believe the conclusion (another statement). However, conditional statements are only one statement. 


If these statements are broken up into antecedent (taken as evidence) and consequent (conclusion) there is still no argument because there is no truth value to the resulting claims.


Remember, conditional statements alone are not arguments. 

Example of an argument: 

If I go to the store then I will buy chocolate.

I will go to the store.

Therefore, I will buy chocolate. 


The basic elements of the argument


Stephen Toulmin identified the following elements of an argument:


1.      Claim (assertion, proposition): A statement affirming or denying something.


2.      Evidence: Material which will convince audience


3.      Warrant: what links support evidence to claim, e.g., a principle of logic or reasoning, a recipe or license, a formal rule, generally unstated, an assumption that both rhetor and audience implicitly accept.





·            Claim:  Joe Smith is a good choice for the position of Appellate Court Judge


·            Grounds:  The American Bar Association recommended Smith as well qualified.


·            Warrant:  (usually unspoken) The ABA is an authority source known as competent to determine who is a good choice for appellate judge positions.