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PHIL 201 Chapter 1 What logic Studies
Chapter 1: What Logic Studies � Logic: the study of reasoning and its evaluation. ◦ Reasoning: thinking (mental activity) that aims at a conclusion. � When we present our reasoning, we do so in the form of arguments. ◦ Argument: a group of statements in which a conclusion is claimed to follow from premise(s). � If the premises actually do support the conclusion the argument is a good one, if not the argument is a bad one. � One of the primary tasks of logic is to provide us with techniques that allow us to distinguish good arguments from bad arguments. � The premises and conclusions of arguments are what we call statements. ◦ Statement: a sentence or sentence part that is either true or false. ◦ This feature of statements (they’re being true or false) is what we call Truth Value.
Arguments and Statements �The element that makes a group of statements an argument is the presence of an inference. ◦ Inference: the reasoning process expressed by an argument �In addition to truth value, statements have propositional content. ◦ Proposition: the information content or meaning of a statement. �A door is closed. ≡ Une porte est fermée.
Statements and Non-Statements �Sentence with truth value (it is either true or false): ◦ The door is open. �Sentences without truth values (they are neither true nor false): ◦ Questions. Is the door open? ◦ Commands. Close the door now. ◦ Requests. Please close the door. ◦ Proposals. Let’s close the door. ◦ Exclamations. Great door!
Recognizing Arguments �The inferential content of an argument is the support provided by the premise(s) to the conclusion. ◦ We should boycott that company. They have been found guilty of producing widgets that they knew were faulty, and that caused numerous injuries. �Identifying groups of statements as arguments is a matter of identifying this inferential content. ◦ This amounts to identifying which of the statements (if any) is serving as the conclusion of the argument. �Conclusion arguments and premise indicators help us identify ◦ Since they have been found guilty of producing widgets that they knew were faulty, and that caused numerous injuries, we should therefore boycott that company.
Premise and Conclusion Indicators � Conclusion Indicators ◦ Therefore ◦ Consequently ◦ It proves that ◦ Thus ◦ In conclusion ◦ Suggests that ◦ So ◦ It follows that ◦ Implies that ◦ Hence ◦ We can infer that ◦ We can conclude that � Premise Indicators ◦ Because ◦ Assuming that ◦ As indicated by ◦ Since ◦ As shown by ◦ The fact that ◦ Given that ◦ For the reason(s) that ◦ It follows from
Factual Claims and Inferential Claims �All arguments make two sorts of claims. ◦ The first sort is called a factual claim. This is a claim to the truth of the propositional content of the statements in the argument. ◦ The second sort is the inferential claim. This is the claim that the premise(s) of the argument provide support for, justification of, reasons to accept the propositional truth of the conclusion. �Compare: Unauthorized cars will be towed at owner’s expense. (a warning, not an argument) Given that your car is unauthorized and unauthorized cars will be towed at the owner’s expense, your car will be towed. (an inferential claim is present, thus there is an argument)
Exercises 1 B Example Buy an Apple instead of a Windows computer, because Apple computers have more features for graphic artists and you are a graphic artist. Answer Premises: (a) Apple computers have more features for graphic artists. (b) You are a graphic artist. Conclusion: Buy an Apple instead of a Windows computer. Example You should buy an i. Pad instead of a Notebook. You should also buy a Honda instead of a Toyota, and a Vizio television instead of a Sony. Answer Not an argument. These statements do not offer support for the truth of any particular claim.
Arguments and Non-Arguments Groups of statements that lack either factual claims or inferential claims aren’t arguments. � There are many types of statement groups that are sometimes taken as arguments but which are not, because they lack an inferential claim. � ◦ ◦ ◦ ◦ � Warnings Advice Statement(s) of opinion Series of related observations Reports Expository passages Illustrations Conditional statements are a special case. There is a clear inferential claim operating within the statement, and by definition, the statement as a whole is true or false, but the inferential movement in the statement is not grounded in a claimed fact, but rather in a possible condition. ◦ Example: If it is raining, then Julie has her umbrella.
A Special Case: Explanations �An Explanation is a statement or set of statements that accounts for or makes sense of an event or phenomenon. ◦ Explanandum: what is being explained. ◦ Explanans: what does the explaining. Ex. Navel oranges are called by that name because they have a growth that resembles a human navel on the end opposite the stem. �The thing that distinguishes an explanation from an argument is its intent: an explanation is aimed at telling us why something is the case; an argument at proving to us that something is the case.
A Comparison �Compare ◦ Because you started lifting weights without first getting a physical checkup, you will probably injure your back. ◦ Your back injury occurred because you lifted weights without first getting a physical checkup. � The first passage is an argument, the second is an explanation. ◦ Argument: (premise) Because you started lifting weights without first getting a physical checkup, (conclusion) you will probably injure your back. ◦ Explanation: Your back injury occurred because you lifted weights without first getting a physical checkup (an already accepted fact).
Exercise 1 C Example I couldn’t do my homework because I had to work a double shift yesterday. Answer Explanation. It is already a fact that the homework was not done, so an explanation is being offered.
Truth and Logic � As I’ve already suggested, logic is about truth, but it’s not about truth in the way that the special sciences are. ◦ Those disciplines are concerned to identify truth, and systematically organize and express it. � Logic doesn’t do that. ◦ As a formal discipline, logic can’t tell us whether a particular statement is true or not. We need to look to the world, or to those special sciences, to determine the truth value of a particular statement. � What logic does do is help us understand whether or not premises articulated in support of a conclusion do in fact offer such support. ◦ The inferential claim of every argument is that the truth of the premises establishes (to one degree or another) the truth of the conclusion. ◦ When we evaluate an argument, what we’re doing is evaluating it’s inferential claim: is the claim correct (is the claimed support actually provided)?
Types of Inferential Claims �Not all inferential claims are equal. There are two classes of such claims. If the conclusion is claimed to follow with strict certainty or necessity, the argument is said to be deductive; but if it is claimed to follow only probably, the argument is inductive. ◦ A Deductive Argument is one in which the truth of the premises guarantees the truth of the conclusion (it is impossible for the conclusion to be false if the premises are true). ◦ An Inductive Argument is one in which the truth of the premises establishes some likelihood that the conclusion is true (it is improbable that the conclusion is false if the premises are true).
Making the Distinction � From a logical standpoint, the difference between the two lies in the relative strengths of their inferential claims. Unfortunately, it is sometimes difficult to assess whether a particular inferential claim is deductive or inductive in nature. � There are three factors that can help determine whether an argument is inductive or deductive. 1. Character of inferential link. 2. Occurrence of indicator words (probably, necessarily). 3. Argument form (certain forms of arguments are typically deductive or inductive)
Common Deductive and Inductive Argument Forms Deductive Arguments � Arguments based on mathematics � Arguments from definition � Categorical syllogisms � Hypothetical syllogisms � Disjunctive syllogisms Inductive Arguments � Inductive generalizations � Arguments from authority � Arguments based on signs � Predictions � Arguments from analogy � Causal inferences
Exercises 1 E In this exercise, you are asked to determine if arguments are deductive or inductive. Example Most college freshmen have part-time jobs. Sue is a college freshman. Thus, Sue has a part-time job. Answer Inductive. If the premises are true, then it is probably true that Sue has a part-time job. However, the conclusion can be false, since we are told only that "most" college freshmen have part-time jobs. Compare the first argument to this related deductive argument. All college freshmen have part-time jobs. Sue is a college freshman. Thus, Sue has a part-time job. If the premises are true, then it follows necessarily that Sue has a part-time job.
Principles of Argument Evaluation � Now that we have a handle on what an argument is, we have to develop the machinery to evaluate them. � As we have noted, all arguments (deductive and inductive) must contain both factual claim(s) and an inferential claim(s). � Because the inferential claim is the heart of the argument, our evaluation machinery will test those first. � If an argument turns out to make a legitimate inferential claim, then we can use our knowledge and experience of the world (as well as that of relevant experts) to consider the status of the factual claims.
Deductive Arguments �A deductive argument is one where the conclusion is claimed to follow necessarily from the premises. ◦ If the inferential claim has this necessary character, then the argument is a Valid Deductive Argument (it is impossible for all of the premises to be true and the conclusion false). ◦ If the inferential claim does not hold up with strict necessity then the argument is an Invalid Deductive Argument (it is possible for all of the premises to be true and the conclusion false). �Some important implications of these definitions: 1. All deductive arguments are either valid or invalid—there is no middle ground. 2. Validity is a matter of the form, not the content, of an argument. That is, it is a matter of the relationship between the premises and the conclusion, not their truth or falsity. 3. There are no valid sentences or claims, only arguments can be valid. 4. There is an informal test of validity. Assume that the premises are true and see if the conclusion follows necessarily. This is not a perfect test, because we could be wrong about the conclusion, but it gets us started.
What about the Factual Claims? �Once we’ve determined that a particular deductive argument is valid, we are in a position to evaluate the truth of the factual claims asserted in support of the conclusion. �A Sound deductive argument is a deductively valid argument with true premises (and thus a necessarily true conclusion). �All other deductive arguments (valid and invalid) are Unsound.
Summing it up
Logical Form �As we’ve already noted, our ordinary language(s) include many elements that are of no significance for a logical analysis of arguments. ◦ Many of the things that we want or need to do with language are not reducible to arguments and thus are not addressed by such analysis. �In some cases at least, this ’excess’ can impede our understanding of the arguments we are presented with and thus limit our ability to evaluate them. �For this reason, logicians typically isolate the form or structure of an argument, removing the linguistic content so that they can analyze the structural relationship between the premises and conclusion. ◦ This is what we are analyzing when we are determining validity.
An Example All beagles are dogs All B are D. All dogs are mammals. All D are M. All beagles are mammals. All B are M. � This is a valid argument, not because the premises are true, but because of the form of the argument. � Any substitution instance of this form is also a valid argument. All berries are delicate. All delicate things are easily ruined. All berries are easily ruined.
Counterexample Method �We can use this notion of logical form to develop a test of the validity of simple arguments. It’s known as the counterexample method. �The method works by identifying substitution instances of argument forms that have true premises and false conclusions. ◦ If an argument form is valid, such instances cannot be produced. ◦ If you can produce one, you’ve proven that the argument is invalid. All B are S. All G are S. (T) All B are G. Substitution: All men are human beings. (T) All women are human beings. All men are women. (F)
Exercise 1 F Example No C are B. No C are S. No B are S. Answer Invalid. Counterexample (it’s possible to find true premises together with a false conclusion using this logical form): No crocodiles are boas. (T) No crocodiles are snakes. (T) No boas are snakes. (F)
Inductive Arguments �An inductive argument is one where the conclusion is claimed to follow from the premises with some degree of probabilistic likelihood. ◦ If the inferential claim does in fact indicate this probability, the argument is a Strong inductive argument (it is improbable that the premises are true and conclusion false). ◦ If the inferential claim doesn’t suggest this probability, the argument is a Weak inductive argument (there is a reasonable probability that the premises can be true and the conclusion false). �Some implications of these definitions. 1. All inductive arguments are either strong or weak—there is no middle ground. 2. Strength is a matter of the form, not the content, of an argument. That is, it is a matter of the relationship between the premises and the conclusion, not their truth or falsity. 3. There is an informal test of strength. Assume that the premises are true and see if the conclusion probably follows. This is not a perfect test, because we could be wrong about the conclusion, but it gets us started.
Some Examples �An opaque jar contains exactly 100 marbles. There are 99 blue marbles in the jar. There is 1 red marble in the jar. The next marble picked is blue. ◦ This is a strong inductive argument. If the premises are true, it is probable that the conclusion is true. �An opaque jar contains exactly 100 marbles. There are 99 blue marbles in the jar. There is 1 red marble in the jar. The next marble picked is red. ◦ This is a weak inductive argument. If the premises are true, it is improbable that the conclusion is true.
The Factual Claims? �After we analyze the inferential claim of an inductive argument, we can go on to say something about the truth of the premises. �A Cogent Inductive Argument is a strong inductive argument with true premises. �All other inductive arguments are Uncogent.
Role of New Information � Though any particular inductive argument is either strong or weak, adding new information to an inductive argument (essentially creating a new inductive argument) can often produce a different verdict. � The new information can either produce a stronger argument than was originally offered or a weaker one. � Consider these examples: ◦ Some philosophers are crazy. Max is a philosopher. Therefore, Max is crazy. �What happens if I add the information: All crazy philosophers live in Memphis. ? ◦ Many logic students struggle to distinguish arguments from explanations. Alphonse is a logic student. Therefore, Alphonse struggles to distinguish arguments from explanations. �What happens if I add the information: Those students who struggle don’t study, but Alphonse studies. ?
Exercise 1 G Example Most politicians are liars. Madison is a liar. Thus, she is a politician. Answer Weak. Even if both premises are true, they do not support the probable truth of the conclusion. Compare “Most politicians are liars. Madison is a politician. Thus, she is (probably) a liar. ” This is a strong inductive argument. Example My computer won’t turn on. My computer is broken. Add the information: My computer is unplugged. Answer This weakens the argument.
One last note � As we’ve already observed, it is not uncommon for both deductive and inductive arguments to be advanced that lack information. ◦ This is different than adding new information to an inductive argument. �Arguments that lack information have premises or conclusions that are implied, rather than stated. �This is often the case because people assume that we will interpret their utterances in a ‘natural’ or ’obvious’ way. �On occasion, however, people will deliberately leave out information because it is controversial or because they are trying to mislead others. � Arguments with missing premises or conclusions are called Enthymemes. � An enthymematic argument must be reconstructed before it can be analyzed. We do this by supplying the missing information, making it explicit. � There is a interpretive principle that should guide such reconstructions. It’s called the Principle of Charity: We should choose the reconstructed argument that gives the benefit of the doubt to the person presenting the argument.