Arguments. Premises and Conclusions

• Logic

  • The organized body of knowledge, or science, that evaluates arguments.

  • Logic aims to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing our own arguments.

• The benefits that come with the study of logic include an increase in confidence in our ability to make sense when criticizing the arguments of others and our ability to advance arguments of our own.

• Argument

  • A group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion).

  • All arguments may be placed in one of two basic groups, those in which the premises do support the conclusion and those in which they do not, even though they are claimed to. The former stands for a good argument, and the latter is a bad argument.

• The purpose of logic as a science that evaluates arguments is to develop methods and techniques that allow us to be able to distinguish good arguments from bad ones.

• Statement

  • A statement is a sentence that is either true or false, typically a declarative sentence or a sentence component that could stand as a declarative sentence.

  • Example statements include the following:

    • “Chocolate truffles are loaded with calories.” (True)

    • “Political candidates always tell the complete truth.” (True)

    • “No wives ever cheat on their husbands.” (False)

    • “Tiger Woods plays golf and Lindsay Davenport plays tennis.”(False)

• Truth and falsity are called the two possible truth values of a statement.

• Unlike statements, many sentences cannot be said to be either true or false; Questions, proposals, suggestions, commands, and exclamations usually cannot and are not usually classified as statements.

  • The following are NOT statements.

    • “Where is Khartoum?” (question)

    • “Let’s go to a movie tonight.” (proposal)

    • “I suggest you get contact lenses.” (suggestion)

    • “Turn off the TV right now.” (command)

    • “Fantastic!” (exclamation)

• Statements that make up an argument are divided into one or more premises and only one conclusion.

• Premise

  • Premises are the statements that set forth the reasons or evidence.

• Conclusion

  • The statement that the evidence is claimed to support or imply.

• The ability to distinguish the premise from the conclusion is one of the most critical tasks in the analysis of an argument.

• Conclusion Indicators Include the following:

  • Therefore

  • Accordingly

  • Entails that

  • Wherefore

  • we may conclude

• The premises is claimed evidence, and the conclusion is what is claimed to follow from the evidence.

• If an argument does not contain a conclusion indicator, it may include a premise indicator; some typical premise indicators include:

  • Since

  • As indicated by

  • Because

  • For

  • In that

  • Any statement that follows one of these indicators can usually be identified as a premise,

• Sometimes a single indicator can be used to identify more than one premise.

• On occasion, an argument can contain no indicators; when this occurs, it is vital that the reader/listener ask himself or herself such questions as the following:

  • What single statement is claimed (implicitly) to follow from the others?

  • What is the arguer trying to prove?

  • What is the main point in the passage?

  • Asking these questions should point to the conclusion.

• Passages that contain arguments sometimes contain statements that are neither premises nor conclusions.

• Only statements that are actually intended to support the conclusion should be included in the list of premises.

• If a statement serves merely to introduce the general topic or merely makes a passing comment, it should not be taken as part of the argument.

• Inference

  • The reasoning process expressed by an argument.

  • Inferences may be expressed not only through arguments but through conditional statements as well.

  • In the loose sense of the term, “Inference” is used interchangeably with “argument.”

• Proposition

  • The meaning or information content of a statement.

Note on the History of Logic

• Aristotle is generally credited as the father of logic.

  • Aristotle first devised systematic criteria for analyzing and evaluating arguments.

• Aristotle’s chief accomplishment is called “Syllogistic logic.”

• “Syllogistic Logic”

  • A kind of logic in which the fundamental elements are terms, and arguments are evaluated as either good or bad, depending on how the terms are arranged in the argument.

• Aristotle can also be credited with originating “modal logic.”

• Modal Logic

  • A kind of logic that involves such concepts as possibility, necessity, belief, and doubt.

• Throughout Aristotle’s life, he cataloged a number of informal fallacies.

• Greek philosopher and one founder of the Stoic school, Chrysippus, developed logic in which the fundamental elements were whole propositions.

  • Chrysippus treated every proposition as either true or false and developed rules for determining the truth or falsity of compound propositions from the truth or falsity of their components.

  • Following this, Chrysippus laid the foundation for the interpretation of logical connectives and introduced the notion of natural deduction.

• Physician Galen developed the theory of compound categorical syllogism.

• Peter Abelard was the first significant logician of the middle ages.

  • Abelard reconstructed and refined the logic of Aristotle and Chrysippus as communicated by Boethius. He originated a theory of universals that traced the universal character of general terms to concepts in the mind rather than to “natures” existing outside the mind, as Aristotle had held.

  • Abelard also distinguished arguments that are valid because of their form from those that are valid because of their content, but he held that only formal validity is the “perfect” or conclusive variety.

• William Sherwood is credited with developing logical treatise.

• Summulae Logicales was developed by Peter of spain and became the standard textbook in logic for three hundred years.

• During the middle ages, William of Ockham made significant contributions. Including extending the theory of modal logic, conducting an exhaustive study of the forms of valid and invalid syllogisms, and further developing the idea of a metalanguage; used to discuss linguistic entities such as words, terms, and propositions.

• During the middle of the fifteenth-century rhetoric largely displaced logic as a primary focus.

  • The reawakening didn’t occur till two hundred years later, in the works of Gottfried Wilhelm Leibniz.

• Leibniz attempts to develop a symbolic language that could be used to settle all forms of disputes led him to be credited with being the father of symbolic logic.

• People who helped with the rapid development of symbolic logic during the middle of the nineteenth century include:

  • Augustus DeMorgan

  • George Boole

  • William Stanley Jevons

  • John Venn

• British philosopher John Stuart initiated a revival in inductive logic.

• American philosopher Charles Sanders Peirce developed a logic of relations, invented symbolic quantifiers, and suggested the truthtable method for formulas in propositional logic.

• During the twentieth century, much of the work in logic has focused on the formalization of logical systems and on questions dealing with the completeness and consistency of such systems.

• Now famous theorem proved by Kurt Goedel states that in any formal system adequate for number theory, there exists an undecidable formula, that is, a formula such that neither it nor its negation is derivable from the axioms of the system.

• Logic has made a significant contribution to technology by providing the conceptual foundation for the electronic circuitry of digital computers.

Recognizing Arguments

• A passage contains an argument if it purports to prove something; if it does not do so, it does not contain an argument.

• The following two conditions must be fulfilled for a passage to purport to prove something

  • At least one of the statements must claim to present evidence or reasons.

  • There must be a claim that the alleged evidence or reasons supports or implies something—that is, a claim that something follows from the alleged evidence.

    • It is not necessary that the premises present actual evidence or true reasons nor that the premises actually support the conclusion; But at least the premises must claim to present evidence or reasons, and there must be a claim that the evidence or reasons support or imply something.

• Deciding whether an argument has fulfilled the parameter of expressing a factual claim often falls outside the domain of logic.

• Inferential claim

  • The claim that the passage expresses a certain kind of reasoning process—that something supports or implies something or that something follows from something; it can be either explicit or implicit.

• An explicit inferential claim is usually asserted by premise or conclusion indicator such as the following words

  • Thus

  • Since

  • Because

  • Hence

  • Therefore

• An implicit inferential claim exists if there is an inferential relationship between the statements in a passage, but the passage contains no indicator words.

  • Example: “The genetic modification of food is risky business. Genetic engineering can introduce unintended changes into the DNA of the food-producing organism, and these changes can be toxic to the consumer.”

Simple Noninferential Passages

• Simple non-inferential passages are unproblematic passages that lack a claim that anything is being proved.

  • These passages contain statements that could serve as premises or conclusions (or both) but do not contain a claim that any potential premise supports a conclusion or that any potential conclusion is supported by premises.

  • These passages typically contain warnings, pieces of advice, statements of belief or opinion, loosely associated statements, and reports.

• Warning

  • A form of expression that is intended to put someone on guard against a dangerous or detrimental situations.

    • Example: “Whatever you do, never confide personal secrets to Blabbermouth Bob.”

      • If no evidence is given to prove that such statements are true, then there is no argument.

• Piece of advice

  • A form of expression that makes a recommendation about some future decision or course of conduct.

    • Example “You should keep a few things in mind before buying a used car.Test drive the car at varying speeds and conditions, examine the oil in the crankcase, ask to see service records, and, if possible, have the engine and power train checked by a mechanic.”

      • As with warnings, if there is no evidence that is intended to prove anything, then there is no argument.

• Statement of belief or opinion

  • An expression about what someone happens to believe or think about something.

    • Example: “We believe that our company must develop and produce outstanding products that will perform a great service or fulfill a need for our customers.We believe that our business must be run at an adequate profit and that the services and products we offer must be better than those offered by competitors.”

      • Because the author does not make any claim that his or her belief or opinion is supported by evidence, or that it supports some conclusion, there is no argument.

• Loosely associated statements

  • Loosely associated statements may be about the same general subject, but they lack a claim that one of them is proved by the others.

    • Example: *“Not to honor men of worth will keep the people from contention; not to value goods that are hard to come by will keep them from theft; not to display what is desirable will keep them from being unsettled of mind.”*

      • Because there is no claim that any of these statements provides evidence or reasons for believing another, there is no argument.

• Report

  • A group of statements that convey information about some topic or event.

    • Example: “Even though more of the world is immunized than ever before, many old diseases have proven quite resilient in the face of changing population and environmental conditions, especially in the developing world. New diseases, such as AIDS, have taken their toll in both the North and the South.

      • These statements could serve as the premises of an argument; but because the author makes no claim that they support or imply anything, there is no argument.

Expository Passages

• Expository passage

  • A kind of discourse that begins with a topic sentence followed by one or more sentences that develop the topic sentence.

    • If the objective is not to prove the topic sentence but only to expand it or elaborate it, then there is no argument.

• Expository passages differ from simple noninferential passages (such as warnings and pieces of advice) in that many of them can also be taken as arguments.

  • If the purpose of the subsequent sentences in the passage is not only to flesh out the topic sentence but also to prove it, then the passage is an argument.

• In deciding whether an expository passage should be interpreted as an argument, try to determine whether the purpose of the subsequent sentences in the passage is merely to develop the topic sentence or also to prove it.

Illustrations

• Illustration

  • A statement about a certain subject combined with a reference to one or more specific instances intended to show what something means or how it is done.

    • Illustrations are often confused with arguments because many of them contain indicator words such as “thus.”

• Arguments from example

  • illustrations taken as arguments.

• To determine whether an illustration should be interpreted as an argument, one must determine whether the passage merely shows how something is done or what something means, or whether it also purports to prove something.

Explanations

• One of the most important kinds of nonarguments is the explanation.

• Explanation

  • A group of statements that purports to shed light on some event or phenomenon.

    • The event or phenomenon in question is usually accepted as a matter of fact.

• Every explanation is composed of two distinct components those being the following:

  • Explanandum

    • The statement that describes the event or phenomenon to be explained

  • Explanans

    • The statement or group of statements that purports to do the explaining.

• Explanations are sometimes mistaken for arguments because they often contain the indicator word “because.”

  • Explanations are not arguments because in an explanation, the purpose of the explanans is to shed light on, or to make sense of, the explanandum event—not to prove that it occurred.

• to distinguish explanations from arguments, identify the statement that is either the explanandum or the conclusion.

  • Usually this is the statement that precedes the word “because”.

• The greatest problem confronting the effort to distinguish explanations from arguments lies in determining whether something is an accepted matter of fact.

Conditional Statements

• Conditional statement

  • An “if . . . then . . .” statement

    • Example: “If professional football games incite violence in the home, then the widespread approval given to this sport should be reconsidered.”

• Every conditional statement is made up of two component statements, those being the following:

  • Antecedent

    • The component statement immediately following the “if ”.

  • Consequent

    • the one component statement immediately following the “then”.

• Conditional statements are not arguments.

  • In an argument, at least one statement must claim to present evidence, and there must be a claim that this evidence implies something.

  • In a conditional statement, there is no claim that either the antecedent or the consequent presents evidence.

• A conditional statement as a whole may present evidence because it asserts a relationship between statements'; Still, when conditional statements are taken in this sense, there is still no argument because there is then no separate claim that this evidence implies anything.

• Some conditional statements are similar to arguments, however, in that they express the outcome of a reasoning process.

• While no single conditional statement is an argument, a conditional statement may serve as either the premise or the conclusion (or both) of an argument.

  • Example:

    • If Iran is developing nuclear weapons, then Iran is a threat to world peace.

    • Iran is developing nuclear weapons.

    • Therefore, Iran is a threat to world peace.

Deductive and Inductive

• Arguments can be divided into two groups, those being the folowing

  • Deductive arguments

    • An argument, in which the arguer claims that it is impossible for the conclusion to be false given that the premises are true.

      • deductive arguments are tthose that involves necessary reasoning.

  • Inductive arguments

    • An argument in which the arguer claims that it is improbable that the conclusion be false given that the premises are true.

      • Inductive arguments are those that involve pprobabilistic reasoning.

• The three criteria that influence our decision on a claim in a passage includes the following:

  • The occurrence of special indicator words.

  • The actual strength of the inferential link between premises and conclusion.

  • The form or style of argumentation the arguer uses.

• Deductive indicator works include the following:

  • Certainly

  • Absolutely

  • definitely

• Inductuve indicator words include the following:

  • Improbable

  • Plausible

  • Implausible

  • Likely

  • unlikely

  • Reasonable to conclude

• Inductive and deductive indicator words often suggest the correct interpretation; however, if you find them to contradict, they should be ignored.

Deductive Argument Forms

• Five kinds of arguments with distinctive characters or form that indicate the premises are supposed to provide absolute support for the conclusion, including the following:

  • Arguments based on mathematics

    • An argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement.

  • Argument from definition

    • An argument in which the conclusion is claimed to depend merely upon the definition of some word or phrase used in the premise or conclusion.

  • Categorical syllogism

    • A syllogism in which each statement begins with one of the words “all,” “no,” or “some.”

  • Hypothetical syllogism

    • A syllogism having a conditional statement for one or both of its premises.

  • Disjunctive syllogism

    • A syllogism having a disjunctive statement (i.e., an “either . . . or . . .” statement) for one of its premises.

Inductive Argument Forms

• inductive arguments are such that the content of the conclusion is in some way intended to “go beyond” the content of the premises.

  • The premises of such an argument typically deal with some subject that is relatively familiar, and the conclusion then moves beyond this to a subject that is less familiar or that little is known about.

• Six kinds of arguments that the premises of such an argument typically deal with some subject that is relatively familiar, and the conclusion then moves beyond this to a subject that is less familiar, or that little is known about, include the following:

  • Prediction

    • An argument that proceeds from our knowledge of the past to a claim about the future.

  • Argument from analogy

    • An argument that depends on the existence of an analogy, or similarity, between two things or states of affairs.

  • Generalization

    • An argument that proceeds from the knowledge of a selected sample to some claim about the whole group.

  • Arargument from authority

    • An argument that concludes something is true because a presumed expert or witness has said that it is.

• Argument based on signs

  • An argument that proceeds from the knowledge of a sign to a claim about the thing or situation that the sign symbolizes.

• Causal inference

  • An argument that proceeds from knowledge of a cause to a claim about an effect, or, conversely, from knowledge of an effect to a claim about a cause.

• Inductive arguments are those that proceed from the particular to the general, while deductive arguments are those that proceed from the general to the particular.

  • Particular statement

    • One that makes a claim about one or more particular members of a class

  • General statement

    • A claim about all the members of a class.

The Validity, Truth, Soundness, Strength, and Cogency

• There are two kinds of claims, the first being a factual claim and the second an inferential claim, and the evaluation of an argument centers around them, with the more important of the two being the inferential claim because if the premises fail to support the conclusion (that is, if the reasoning is bad), an argument is worthless.

  • It is because of this we should always test the inferential claim first, and only if the premises do support the conclusion will we test the factual claim.

Deductive Arguments

• As previously stated, a deductive argument is one in which the arguer claims that it is impossible for the conclusion to be false given that the premises are true;

  If this claim is true, the argument is said to be valid.

• Valid deductive argument

  • An argument in which it is impossible for the conclusion to be false given that the premises are true.

  • In these arguments, the conclusion follows with strict necessity from the premises.

• Invalid deductive argument

  • A deductive argument in which it is possible for the conclusion to be false given that the premises are true.

  • In these arguments, the conclusion does not follow strict necessity from the premises, even though it is claimed to.

• There is no middle ground between an argument being valid or invalid for these given definitions; there is no such thing as “almost” valid, and there also isn’t such a thing as “almost” invalid.

• The relationship between premises and conclusion determines validity.

• The idea that any deductive argument having actually true premises and a false conclusion is invalid may be the most important point in all of the deductive logic.

• Sound argument

  • A deductive argument is valid and has all true premises.

  • Both conditions must be met for an argument to be sound, and if either is missing, the argument is unsound.

  • By definition, all sound arguments will have a true conclusion.

• Unsound Argument

  • A deductive argument that is invalid; has one or more false premises or both.

Inductive Arguments

• An inductive argument was previously defined as “one in which the arguer claims that it is improbable that the conclusion be false given that the premises are true.”

  • If the arguer’s claim is true then it is said to be a strong argument.

• Strong inductive argument

  • an inductive argument in which it is improbable that the conclusion be false given that the premises are true.

• Weak inductive argument

  • An argument in which the conclusion does not follow probably from the premises, even though it is claimed to.

• In order to test the strength of an inductive argument we first need to assume the premises are true and then we determine whether, based on that assumption, the conclusion is probably true.

• To be considered strong, an inductive argument must have a conclusion that is more probable than improbable. In other words, the likelihood that the conclusion is true must be more than 50 percent, and as

  the probability increases, the argument becomes stronger.

• Cogent argument

  • an inductive argument that is strong and has all true premises; if either condition is missing, the argument is uncogent.

  • A cogent argument is the inductive analogue of a sound deductive argument and is what is meant by a “good” inductive argument without qualification.

  • Because the conclusion of a cogent argument is genuinely supported by true premises, it follows that the conclusion of every cogent argument is probably true.

• Uncogent

  • An argument that is an inductive argument that is weak, has one or more false premises, or both.

• There is a difference, however, between sound and cogent arguments in regard to the true premise requirement.

  • In a sound argument, it is necessary only that the premises be true and nothing more.

  • In a cogent argument, on the other hand, the premises must not only be true, but they must also not ignore some important piece of evidence that entails a quite different conclusion.

    • This is called the total evidence requirement.

Argument Forms: Proving Invalidity

• Substitution instance

  • Any argument that is produced by uniformly substituting terms or statements in place of the letters in an argument form.

• Every substitution instance of a valid form is a valid argument, but it is not the case that every substitution instance of an invalid form is an invalid argument.

Counterexample Method

• Counterexample

  • A substitution instance having true premises and a false conclusion.

• Counterexample method

  • isolating the form of an argument and then constructing a substitution instance having true premises and a false conclusion.

  • This proves the form invalid, which in turn, proves the argument invalid.

  • Before the method is applied to an argument, the argument must be known or suspected to be invalid in the first place.

• The counterexample method can be used to prove the invalidity of any invalid argument, but it cannot prove the validity of any valid argument.

• In applying the counterexample method to categorical syllogisms, it is useful to keep in mind the following set of terms:

  • Cats

  • Dogs

  • Mammals

  • Fish

  • Animals

    • Most invalid syllogisms can be proven invalid by strategically selecting three of these terms and using them to construct a counterexample; this is because everyone agrees about these terms, and everyone will agree about the truth or falsity of the premises and conclusion of the counterexample.

• In constructing the counterexample, it often helps to begin with the conclusion.

• Keep in mind that the word “some” in logic always means “at least one.”

• Identifying an argument's form with ease requires familiarity with the primary deductive argument forms.

  • The first task consists in distinguishing the premises from the conclusion.

  • The second task involves distinguishing what we may call “form words” from “content words.”

• The following words are not forme words for categorical syllogisms.

  • All

  • No

  • Some

  • Are

  • Not

• For hypothetical syllogisms, the following words are form words.

  • If

  • Then

  • Not

• Additional form words for other types of arguments include:

  • Either

  • Or

  • Both

  • And

• Using the counterexample method to prove arguments invalid requires a little ingenuity because there is no rule that will automatically produce the required term or statement to be substituted into the form.

  • Ideally, the truth value of these statements should be known to the average individual; otherwise, the substitution instance cannot be depended upon to prove anything.

  • The method is useful only for deductive arguments because the strength and weaknesses of inductive arguments are only partially dependent on the form of the argument.

• If a substitution instance is produced having true premises and a true conclusion, it does not prove that the argument is valid.