PHILOSOPHER S TOOL KIT 1. ARGUMENTS PROFESSOR JULIE YOO 1.1 DEDUCTIVE VS INDUCTIVE ARGUMENTS

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1 PHILOSOPHER S TOOL KIT PROFESSOR JULIE YOO 1. Arguments 1.1 Deductive vs Induction Arguments 1.2 Common Deductive Argument Forms 1.3 Common Inductive Argument Forms 1.4 Deduction: Validity and Soundness 1.5 Induction: Strength and Cogency 1.6 Abductive Arguments 1. ARGUMENTS 1.1 DEDUCTIVE VS INDUCTIVE ARGUMENTS Philosophy aims to present what is true. To persuade someone of the truth of a claim, we need to give an argument. An argument is a reason for believing that a certain claim is true. There are two general classes of arguments, deductive (D) and inductive (I), and they form two different classes because they differ in the way the premises support the conclusion. More specifically: 2. Definitions and Philosophical Analyses 2.1 Lexical Definitions 2.2 Stipulative Definitions 2.3 Philosophical Analyses Conditional Statements Sufficient Conditions Necessary Conditions Conditions That Are Neither N or S Conditions That Are Both N and S 3. Thought Experiments 3.1 Testing the Adequacy of Analyses 3.2 Possible Worlds 3.3 Logical Possibility 3.4 Physical Possibility 4. Distinctions 4.1 Necessary vs Contingent Facts 4.2 Analytic vs Synthetic Statements 4.3 a priori vs a posteriori Knowledge DEDUCTIVE The information expressed by the conclusion is fully contained in the information expressed by the premises. The conclusion does not say anything more what the premises say. The conclusion of a deductive argument is not meant to generate new knowledge, relative to the premises. The conclusion is meant to follow from the premises with necessity. For example: 1. If it rains, then we stay home. 2. If we stay home, we play cards. 3. If it rains, we play cards. INDUCTIVE The information expressed by the conclusion goes beyond the information expressed by the premises. The conclusion does say something more than what the premises say. The conclusion of an inductive argument is meant to generate new knowledge, relative to the premises. The conclusion is meant to follows from the premises with probability. For example: 1. It rained last winter. 2. It rained the winter before. 3. It will rain next winter. 5. Applying the Tools 5.1 Analyzing Arguments 5.2 Diagram of the Method 5.3 Looking for Missing Premises 5.4 Analyzing Concepts Notice how the premises fully contain the conclusion. Notice how the premises support, but do not contain, the conclusion. Whether an argument deductive or inductive depends upon the type of inference the arguer intends to use. There are times when you want to argue for a point inductively and times when you want to argue for a point deductively. One type of argument is not better than the other. Philosopher s Toolkit Page 1 of 10

2 1.2 COMMON DEDUCTIVE ARGUMENT FORMS Modus Ponens (MP) If the car is scarlet, then it is red. P The car is scarlet. Q The car is red. Modus Tollens (MT) If the car is scarlet, then it is red. not-q The car isn t red. not-p The car isn t scarlet. Hypothetical Syllogism (HS) If the car is scarlet, then it is red. If Q, then R If the car is red, then it is colored. If P, then R If the car is scarlet, then it is colored. Disjunctive Syllogism (DS) Either P or Q Either Jane bought eggs or milk. not-p (or not-q) Jane didn t buy eggs. Q (or P) Jane bought milk. Categorical Syllogisms (There many more than the ones listed.) All A s are B s All men are mortal. x is an A Socrates is a man. x is a B Socrates is mortal. All A s are B s All apples are fruit. All B s are C s All fruit is healthy. All A s are C s All apples are healthy. All A s are B s All men are mortal. No B s are C No mortal things live forever. No A s are C. No men live forever. All A s are B s All men are mortal. Some A s are not C Some men are not omnivores. Some B s are not C Some mortals are not omnivores. 1.3 COMMON INDUCTIVE ARGUMENT FORMS Inductive Generalization (Let A and B be any feature.) a is A and is B Copper is a metal and is malleable. b is A and is B Aluminum is a metal and is malleable. c is A and is B Iron is a metal and is malleable. All A s are B s All metals are malleable. Enumerative Induction a is A and is B b is A and is B c is A and is B The x that is A is a B. Copper is a metal and is malleable. Aluminum is a metal and is malleable. Iron is a metal and is malleable. Gold is a metal and is malleable. Prediction (Let C mean the cause and E mean the effect.) C causes E Drinking a lot of beer causes getting drunk. C occurred Mo is drinking a lot of beer. E will occur Mo is getting drunk. Identifying the Cause (Let C mean the cause and E mean the effect.) a, b, c, d got E. Alf, Bob, Cam, and Dan got sick. a, b, c, d, all share C. They all had mayo on their sandwiches. C caused E The mayo caused the sickness. a has E but b does not. a and b differ by C. C caused E Alf sick but Bob did not. Alf ate mayo but Bob did not. The mayo caused the sickness. C is increased/decreased Mo is exercising more. E is increased/decreased Mo is getting stronger. C causes E Exercises causes strength. Analogical Induction (Let A and B be any feature.) x and y are A 1 A 2 A n Mo and Jo are smart, eager, and diligent. x is also B Jo is a good student. y is also B Mo is a good student. No A s are B s x is an A x is not B No dolphins are fish. Flipper is a dolphin. Flipper is not a fish. Inference to the Best Explanation Facts F 1, F 2,, F n call out for explanation. E is the best explanation of F 1, F 2,, F n. E is probably true. Philosopher s Toolkit Page 2 of 10

3 1.4 DEDUCTION: VALIDITY AND SOUNDNESS Not all deductive arguments are good or successful. The ones that are good are sound, which means that it lives up to two virtues: 1) valid argument structure and 2) true premises. The issue of whether the premises are true is a matter of checking the facts. It is the concept of validity that needs explanation. This concept is defined in the following way: Soundness: An argument is sound = dfn The argument is valid AND all of its premises are true. Validity: An argument is valid = dfn It is impossible for all the premises to be true and the conclusion false. Explanation: The definition validity can be hard to grasp, but if you remember to separate the issue of an argument s validity from the truth or falsity of the premises, then you will understand the concept of validity more easily. To say that an argument is valid is to say that the premises fully contain the conclusion, and it does this is by following a correct form of reasoning. An argument that is not valid does not fully contain the premises in the conclusion. Now, suppose we have a valid argument and the premises happen to be true. Then this would guarantee a true conclusion, since the premises of a valid argument fully contain the conclusion. If we are dealing with an invalid argument, on the other hand, then all bets are off; we cannot be guaranteed that the conclusion is true, nor can we be guaranteed that the conclusion is false. Whereas a valid argument has the power to preserve the truth of the premises, an invalid argument lacks this power. This diagram makes the point visually: Consider these two common invalid argument forms. The first is known as the fallacy of affirming the consequent: Q P If the car is scarlet, then it is red. The car is red. The car is scarlet. The other is known as the fallacy of denying the antecedent: not-p not-q If the car is scarlet, then it is red. The car isn t scarlet. The car isn t red. Notice how the premises don t lead to the conclusion. Because the reasoning is incorrect, the conclusion does not have the power to preserve the truth of the premises, should the premises actually turn out to be true. That doesn t mean that the conclusion will be false with true premises; it just means that the argument s conclusion won t preserve the truth of the true premises. Deductive Arguments: This chart displays all the possible ways we can separate and combine validity and invalidity with true and false premises: True Ps True C True Ps False C Valid If Einstein did physics, then he was a scientist. Einstein did physics. Einstein was a scientist. (sound modus ponens) Invalid If Einstein did physics, then he was a scientist. Einstein was a scientist. (TRUE) Einstein did physics. (TRUE) (unsound affirming the consequent) If Einstein was a dancer, then he was human. Einstein wasn t a dancer. (TRUE) Einstein wasn t human. (FALSE) (unsound denying the antecedent) False P(s) True C False P(s) False C If you live in LA, then you live in Mexico. If you live in Mexico, then you live in CA. IF you live in LA, then you live in CA. (unsound) All mammals can fly. All fish are mammals. All fish can fly. (unsound) If Einstein was smart, then he was a scientist. Einstein was a scientist. (FALSE) Einstein was smart. (TRUE) (unsound affirming the consequent) If Einstein was smart, then he was a scientist. Einstein wasn t smart. (FALSE) Einstein wasn t a scientist. (FALSE) (unsound denying the antecedent) Note On Usage of Terms: It s important to understand that statements are not the kinds of things that are valid or invalid. Validity is a feature of arguments, not premises. And arguments are not the kinds of things that are true or false. Truth is a feature of statements, not arguments. Therefore, it is inappropriate to say things like. This premise is valid. That argument is true. Philosopher s Toolkit Page 3 of 10

4 1.5 INDUCTION: STRENGTH AND COGENCY Just as with the case of deductive arguments, not all inductive arguments are good or successful. The ones that are good are cogent, which means that it lives up to two virtues: 1) strong argument structure and 2) true premises. As with deductive arguments, the issue of whether the premises are true is a matter of checking the facts. The new concept that needs explanation is inductive strongth. This concept is defined in the following way: Cogency: An argument is cogent = dfn The argument is strong and all of its premises are true. Strength: An inductive argument is strong = dfn It is improbable for all the premises to be true and the conclusion false. Explanation: Unlike valid arguments, inductively strong arguments do not have conclusions that follow necessarily from the premises. They follow only with a degree of probability. Both deductive and inductive arguments need to be evaluated according to two separate criteria: 1) the structure of the argument and 2) the truth of the premises. In the case of deductive arguments, structure is a matter of validity or invalidity. In the case of inductive arguments, structure is a matter of degrees of strength. Inductive Arguments: This chart displays all the possible ways we can separate and combine strength and weakness with true and false premises: True Ps True C True Ps False C False P(s) True C False P(s) False C Strong 96% of US presidents are college graduates. The current president is a college graduate. The next president will be a college graduate. (cogent) 95% US presidents are over 60 years old. The current president is over 60 years old. The next pres will be over 60 years old. 95% US presidents were born in CA. The current president was born in CA. The next pres will be from CA. Weak 15% politicians are male. The current VP is male. The next VP will be male. 15% presidents are bald. The current pres is bald. The next pres will be bald. 15% presidents lived in CA. 15% of CA residents are US citizens. The next presidents will be a US citizens. 15% presidents lived in CA. 15% of CA residents are females. All presidents are females. Note On Usage of Terms: As a technical matter of fact, all inductive arguments are invalid. But this does not make all invalid argument inductive. Whether an argument is deductive or inductive is a function of what the argument-giver intends to demonstrate. If she wants to show that the conclusion can give us further knowledge on the basis of the premises, then she intends to give an inductive argument. On the other hand, if her intention is to show that the conclusion is contained in the premises, then she intends to give a deductive argument. 1.6 INFERENCE TO THE BEST EXPLANATION (IBE) Depending on how much data you have in your premises, the premises can support a conclusion with a high degree of probability or a low degree of probability. Strength comes in degrees, unlike validity, which is a binary (yes/no) affair. We can think of an argument s strength as a function of its sample size: when it comes to concluding that it will rain next winter, a data set of only two rainy winters is not as strong as a data set of 5, 15, or 50 rainy winters. Also known as an abductive argument, an argument of this sort is often classified as a form of inductive argument. But its credibility is not a function of sample size. Its credibility is a function of explanatory plausibility. AN IBE argument proceeds by noting some facts that call out for explanation, then postulating some explanation that explains them. If the explanation is the best among competing explanations, then there is a good reason for thinking that it is true. Form of IBE Facts F 1, F 2,, F n call out for explanation. E is the best explanation of F 1, F 2,, F n. E is probably true. Philosopher s Toolkit Page 4 of 10

5 Example: Comets travel in an elliptical orbit around the sun. Newton s laws of motion explain why comets travel elliptically. Newton s laws of motion best explain of why comets travel in an elliptical orbit around the sun. Newton s laws of motion are probably true. Explanation: An inference to the best explanation is probably the most frequently used among all types of arguments. It is crucial to both scientific as well as philosophical inquiry. IBE is a type of inductive argument since arguments of this type expand our knowledge. But there is a difference between IBE and the other forms of inductive argument, such as inductive generalization, enumerative induction, prediction, and causal arguments, as listed in 1.3 To illustrate the difference between IBE and Inductive Generalization, for example, suppose that you went camping in the mountains and boiled some water. You observe that the water boils more quickly high up in the mountains that in the valley. Here s how an inductive generalization (IG) and an inference to the best explanation differ in the kind of information given in the conclusion. IG: This body of water boiled quickly at this altitude. Other bodies of water boiled quickly at this altitude. All water boils quickly at this altitude. Scope: This notion is understood best when we compare competing theories. The scope of an explanatory domain has to do with how much phenomena can be covered or explained by a certain theory. The better theory typically has greater explanatory scope. Simplicity: This is also known as Occam s Razor. The idea is that among competing theories, the simpler theory is the better theory. By simpler, philosophers don t mean easier to understand. It means postulating fewer entities of fewer hypotheses. The application of this principle is much more difficult than it appears. When comparing competing theories, the competitors rarely have equal explanatory value. Thus, many factors have to be weighed in at the same time, Occam s Razor being one of them. Conservatism: This final constraint is the most difficult to apply. The idea is that among competing theories, the one that least challenges our accepted beliefs is the one that is preferable. The principle of conservatism, however, is the most subtle because we often have a number of very different constraints that we have to weigh at the same tie. IBE: This body of water boiled quickly at this altitude. Being well above sea level explains why this happened. We must be well above sea level. Whereas these inductive argument forms draw their strength from sample size, IBE draws its strength from other criteria. These are testability, fruitfulness, scope, simplicity, and conservatism: Testability: An untestable theory is one where there is not possible procedure for checking its truth. If the theory does not have a stable way for one to assess its proclamations, then the theory is worthless. One good sign of a testable theory is that it makes a novel prediction, novel in that the theory had no idea such a prediction could have been made. Fruitfulness: A good empirical theory opens up areas of research that were unforeseen. An example of this is the germ theory of disease. Before this theory, people had no idea how illnesses were transmitted. But after the theory was proposed, scientists were able to track down specific germs that caused specific illnesses, opening up many new fields of research in bacteriology, pathology, and epidemiology. Philosopher s Toolkit Page 5 of 10

6 2. PHILOSOPHICAL ANALYSES 2.1 LEXICAL DEFINITIONS Lexical definitions give you information about the meaning of a word. These are found in the dictionary. sufficient conditions are very useful for expressing an important set of logical relationships between concepts, properties, and situations. To understand necessary and sufficient conditions, it would help to have a grasp of what is known as the conditional. A conditional is any statement of the form: consequent: Q is a necessary condition for P 2.2 STIPULATIVE DEFINITIONS These are made-up or stipulted meanings that you assign to terms. For example, when you say, By blip I mean brown cow, you are stipulating the meaning of blip in your definition. 2.3 PHILOSOPHICAL ANALYSES These are our main concern. Philosophical analyses (also called conceptual analyses ) go beyond mere lexical definitions; instead of merely giving information about the meaning of a term, philosophical analyses attempt to determine the conditions under which the term applies. Consider this philosophical analysis of being a bachelor. analysandum / definiendum analysans / definiens X is a bachelor if and only if (i) X is a male (ii) X is unmarried (iii) X is an adult Conditions (i) (iii) are individually necessary for being a bachelor, which means that each of them is a necessary condition for being a bachelor, and they are jointly sufficient, which means that, considered as a collection, they are sufficient for being a bachelor. Bachelor is the analysandum or definiendum; it is the term that needs to be analyzed or defined. Conditions (i), (ii), and (iii) are the analysans or definiens, which are the things that do the analyzing or defining. Notice that the analysis is formulated in terms of something s being the case if and only if something else is the clase. The if and only if expresses a biconditional (often abbreviated as IFF ) CONDITIONAL STATEMENTS Since a firm grasp of the concepts of necessary and sufficient conditions is crucial to doing philosophy, we should examine carefully examine them. Necessary and antecedent: P is a sufficient condition for Q If you are a sister, then you are a female. You are a sister only if you are a female. You are a female if you are a sister. You can t be a sister unless you are a female. The Antecedent: P is the antecedent. The antecedent (underlined statement) expresses the sufficient condition for the consequent. The Consequent: Q is the consequent. The consequent (italicized statement) expresses the necessary condition for the antecedent. A conditional statement expresses both the sufficient condition and the necessary condition; in fact, if you re determined one, you ve also determined the other SUFFICIENT CONDITIONS The sufficient condition (antecent) is the condition that guarantees. Saying, P is sufficient for Q just means that once you have P, you are guaranteed to have Q. To determine whether P is a sufficient condition, ask yourself: Does P guarantee Q? If the answer is Yes, then P is a sufficient condition for Q. If the answer is No, then all you know is that P is not a sufficient condition for Q. If P is not a sufficient condition, then there may be some condition other than P that guarantees Q. Examples: eating a carrot is sufficient for eating a vegetable owning a car is sufficient for owning a vehicle being a sister is sufficient for being a sibling being a senior is sufficient for having been a freshman Philosopher s Toolkit Page 6 of 10

7 2.3.3 NECESSARY CONDITIONS The necessary condition (consequent) is the condition you can t do without. Saying Q is a necessary condition for P just means that you can t have P without having Q. To determine whether P is a necessary condition, ask yourself: Is Q possible without P? If the answer is No, then P is a necessary condition for Q. If the answer is Yes, then all you know is that P is not a necessary condition for Q and nothing more. If P is not a necessary condition, then there may be some condition other than P required for Q. Examples: eating a vegetable is necessary for eating a carrot being a female is necessary for being a sister being an animal is necessary for being a cat owning clothes is necessary for owning a shirt CONDITIONS THAT ARE NEITHER N NOR S This is true of most pairs of things and coming up with examples is easy. Being beautiful is neither necessary nor sufficient for being a work of art. Being beautiful is not necessary for being a work of art because there are works of art that are rather ugly, and being beautiful is not sufficient for being a work of art because there are beautiful things, such as sunsets and landscapes, that aren t works of art. Having printed words is neither necessary nor sufficient for being a book. Having printed words is not necessary for being a book because some children s books contain only pictures. And having printed words is not sufficient for being a book because newspapers and bubblegum wrappers contain printed words but are not books. Having a sister is both necessary and sufficient for having a female sibling. Having a sister is necessary for having a female sibling because having a sister simply is having a female sibling, so surely you can t have a female sibling without having a sister. And having a sister is sufficient for having a female sibling for the same reason it s because having a sister simply is having a female sibling, so having a sister guarantees having a female sibling. 3. THOUGHT EXPERIMENTS 3.1 TESTING THE ADEQUACY OF ANALYSES Surely, not all philosophical analyses are acceptable. Good analyses must hold under all circumstances, even ones that are quite outlandish. To make sure that they cover these circumstances as well, we conduct thought experiments. Consider this analysis of thinking: X can think IFF X has a normal human brain While having a normal human brain may be a sufficient condition for being able to think, it s is arguably not necessary, and we can show this through a thought experiment. Conceive of a creature that lacks a normal human brain but is capable of thinking as well as an ordinary person. For all we know, this hypothetical creature may never exist in our world. But because an adequate philosophical analysis must hold in all circumstances, and not just in those that happen to obtain in our world, we need to rely upon such thought experiments CONDITIONS THAT ARE BOTH N AND S Some conditions are both necessary and sufficient. In other words, the implication runs in both directions. This typically occurs in definitions. And as we will see, the search for conditions that are both necessary and sufficient are crucial to philosophical analyses of important concepts, such as the concept of a person, the concept of truth, the concept of moral goodness, and so on. P is necessary and sufficient for Q = P IFF Q P guarantees Q and can t obtain without Q (and vice versa) 3.2 POSSIBLE WORLDS Thought experiments are attempts to describe hypothetical or possible situations, or simply, whatever is possible. These are what philosophers call possible worlds. And because possible worlds often differ dramatically from the world as we know it (the actual world) we need to rely upon our imagination and creativity when considering the worlds that are possible. But not just any world is possible. There can be no worlds that violate: a) the principles of logic, b) the principles of mathematic, or c) the meanings of terms So there is no possible world in which it is raining and not raining in the same place at the same time (according to the first rule), there is no possible world with a four-sided triangle or where 1+ 1 = 3 (according to the second rule), and there is no Philosopher s Toolkit Page 7 of 10

8 possible world where a bachelor happens to be married or a red car is colorless (according to the third rule). Not all possible worlds have to be so fanciful. In fact, the actual world is one among the many, many, possible worlds. But for any situation that did not actually obtain, but could have obtained, there is a possible world in which it did obtain. So there is a possible world in someone other than George Washington was the first US president. 3.3 LOGICAL POSSIBILITY The kind of possibility that is relevant to conducting thought experiments is logical possibility (also called metaphysical possibility). A world is logically possible = dfn It is consistent with a) the principles of logic, b) the principles of mathematics, and c) the meanings of terms 3.4 PHYSICAL (CAUSAL / NOMOLOGICAL) POSSIBILITY Some logically possible worlds violate the laws of nature, but some honor them. A world is physically possible = dfn It is consistent with the laws of nature (laws of physics, chemistry, bio, etc.) For example, there is a physically possible world where everyone rides a bicycle. In some physically impossible world a car can travel faster than the speed of light. As long as this world is consistent with the principles of logic, mathematics, and the meanings of our terms, this physically impossible world is still logically possible. Physical possibility as a proper subset of logical possibility. 3.5 DIAGRAM OF RELATIONS BETWEEN CONCEPTS not LP logical possibility (LP) physical possibility (PP) actually the case (@) PP but GW was the first US president. Some people ride bicycles. Every American speaks four languages. Everyone rides bicycles. LP but not PP: Water freezes at 50 degrees F. Everyone can fly by flapping their arms. Not LP: 2+ 2 = 3. Round square. Philosophical analyses are primarily concerned with what can happen within the largest circle (the blue region) because philosophy is about covering all coherently possible cases. Things that lie beyond it are things that are incoherent, like 2+ 2 = 3, round squares, married bachelors, and non-h 2 O water. When we explore things inside the largest circle, we often encounter scenarios or things that go against the laws of nature, like 1,000 year-old humans, cows that don t need food or oxygen to live, rocks that defy gravitiy, and other exotic things. 4. DISTINCTIONS 4.1 NECESSARY VS CONTINGENT FACTS A fact is logically necessary = dfn It obtains in every LP world. Examples: The fact that all doors are either open or not open, the fact that the number 2 is even, the fact the fact that bachelors are unmarried. A fact is logically contingent = dfn It does not obtain in some LP world. Examples: The fact some dog runs faster than the speed of light, the fact that there are nine planets on our solar system. A fact is physically necessary = dfn It obtains in every PP world. Examples: The fact that water freezes at 32 degrees F, the fact that animals require oxygen. A fact is physically contingent = dfn It does not obtain in some PP world. Examples: The fact that some triangles are red, the fact that there are nine planets in our system. Philosopher s Toolkit Page 8 of 10

9 4.2 ANALYTIC VS SYNTHETIC STATEMENTS A statement is analytically true Example: It is analytically true that a sister is a sibling. = dfn It is true because of the meaning of the words. A statement is synthetically true = dfn It is true because of the meanings of the words and the way the world is. Example: It is synthetically true that some sisters are attending college. 4.3 A PRIORI VS A POSTERIORI KNOWLEDGE Something can be known a priori = dfn It can be known independently of experience or observation. Example: That a red car has some color is can be known a priori. Something can be known a posteriori = dfn It can be known only on the basis of experience or observation. Example: That grass is green can be known only a posteriori. 4.4 RELATIONS BETWEEN THESE DISTINCTIONS It s tempting to think that these distinctions neatly line up in the following way: all the facts that are logically necessary are expressed by sentences that are analytically true (if true at all) and are knowable a priori; and all the facts that are logically contingent are expressed by sentences that are synthetically true (if true at all) and are knowable only a posteriori. This picture of the relations between these distinctions holds for the most part, but there are some instances of crossclassification: synthetic sentences that are knowable a priori logically necessary truths that are knowable only a posteriori logically contingent truths that are knowable a priori 5. APPLYING THE TOOLS 5.1 ANALYZING ARGUMENTS The purpose of an argument is to establish the truth of a claim (the conclusion) on the basis of rationally arranged true premises. There are three ways of doing this: deductively, inductively, and abductively (inference to the best explanation). We will look at each of these ways of reasoning as applied to arguing for God s existence, and then we will look at how to evaluate their acceptability. A deductive argument for God s existence: 1. If the universe exists, then God is what created the universe. 2. If God is what created the universe, then God exists. 3. The universe exists. 4. God exists We want soundness in case of deductive arguments. The best way to do this is to first check to see whether the argument s structure is valid. If it isn t, then we don t even need to determine whether each premise is true, because we know that the argument is flawed. If the validity checks out, then we have to examine each premise to see if it is true. If a premise is false, then the argument can be rejected. If all the premises check out true, and the validity is already determined, then we have a sound argument, and a sound argument is an argument whose conclusion you must accept as a rational human being. An analogical inductive argument for God s existence: 1. The universe and machines have many similarities: they both have intricate design. 2. Machines have a designer. 3. The universe has a designer, namely, God, and therefore, God exists. We want cogency in the case of inductive arguments. As with the procedure we follow for evaluating deductive arguments, we first check to see if the inductive argument has a strong argument structure. If it does, then we proceed to examine whether each of the premises is true. These hybrid cases are fascinating, but the material that deals with them is difficult and somewhat advanced for an introductory philosophy course. This is only a warning against oversimplification. Philosopher s Toolkit Page 9 of 10

10 An IBE argument for God s existence: 1. Human beings have a sense of morality. 2. The best explanation for how human beings have a sense of morality is the existence of a God who created humans with a moral sense. 3. God exists. In the case of abductive arguments, we need to examine whether there are competing explanations that are capable of explaining the facts better. We always aim for the best explanation with abductive arguments. Abortion is wrong. This is because it is always immoral to kill an innocent person. In the process of abortion, the life of the fetus is terminated. That is why it is wrong to do abortions. Many arguments are presented as in this passage with a missing premise. What is the missing premise in this case? A fetus is a person. Filling in missing premises is hard because it is not always announced by the author whether the argument is intended to use deductive reasoning, inductive reasoning, or abductive reasoning. Sometimes, you have to try several reconstructions and see which type would fare the best. Then we examine the best of the reconstructions and proceed from there. 5.2 A DIAGRAM OF THE METHOD What kind of argument is it? Deductive Inductive Abductive 5.4 ANALYZING CONCEPTS When we do philosophy, we are often searching for a deep account of the thing we re curious about. Typically, in analytic philosophy, that amounts to gathering all the correct necessary and sufficient conditions for the thing we want to understanding: X romantically loves Y IFF Valid? N: reject Y: all true P? Strong? N: reject Y: all true P? Better Explanations? N: accept Y: reject i. X desires the company of Y ii. X makes sacrifices for Y iii. Even if Y gained weight, X s feelings for Y wouldn t change iv. Even if X and Y lived to 1000 years, X s feelings for Y wouldn t change v. N: reject Y: accept N: reject Y: accept 5.3 LOOKING FOR MISSING PREMISES Notice that with condition (iv), we have to imagine a scenario that is not physically possible. When we analyze concepts philosophically, we often need to go beyond the boundaries of what nature or the laws of physics allow. What we aim for is conceptual coherence instead. Things that are conceptually coherent, and yet not physically possible, are logically or metaphysically possible. Philosophical analysis is in the business of knowing the logical or metaphysical facts about things. Not all arguments are presented in numbered premise form. As a philosopher, often we read articles that contain arguments, but then need to be unpacked by the reader in numbered premise form. We apply the Principle of Charity when doing this, and make sure that the argument s structure is as good as it can be, depending on the kind of reasoning used. Suppose you come across this passage: Philosopher s Toolkit Page 10 of 10