Given a value scale, an actor will choose his most highly preferred goal. How do we know this? It follows from the action axiom. Given a choice, a person will would rather choose the goal they prefer the most.
Some object to the idea that we always choose our highest preference. They say that that people choose less preferred over more highly preferred goals all the time. For example, a student who will be rewarded for getting an ‘A’ does not cheat if given the chance. This proves highly preferred goals are not necessarily chosen. In fact, however, this action actually shows that the student prefers not cheating more than getting an ‘A’.
Still others then criticize the above response. That “one’s highest preference is what one chooses” is tautological and therefore trivial. We learn nothing from this statement as the terms ‘choose’ and ‘preference’ are synonyms for one another.
In response Gordon clarifies the definition not as ‘one prefers what one has chosen’, but ‘one chooses what one most highly prefers’. He also notes that just because a statement is tautological does not make it trivial.
In fact, the notion of preference leads to the deduction of one the most important theories of economics, the theory of marginal utility.
Gordon illustrates the theory using an example. Imagine you have five preferences for using an orange. You happen to have one orange. Which preference will you use the orange to fulfill? Common sense dictates you will use the orange to fulfill your most highly valued preference. If you have two oranges, you will use them to fulfill your highest preference and next highest preference. An important implication is uncovered, however, if one starts with five oranges. Should you lose your third orange, will you forgo fulfilling your third highest preference? No, you will use your last orange to fulfill that preference. The implication arrives; one uses the last available unit (marginal unit) of a good to fulfill one’s least highly valued preference.
Some challenge the theory of marginal utility saying that it cannot help us in understanding cases of indifference. For example, what happens if I value the second and third preferences for orange use exactly the same. What will I do with the second orange? Burdian, a scholastic, famously illustrated the supposed implication of ranking preferences without considering indifference. He imagined a donkey that starves to death because it cannot decide which of two identical bales of hay to eat first. Rothbard, however, criticized this example. It implies that only two preferences exist (to eat the first bale of hay, to eat the second bale of hay) when actually there are three (eat the first, eat the second, starve to death). There is no indifference when it comes to eating a bale of hay in this case.
Indifference is not important in economics because it cannot be demonstrated in action. Economics is not concerned with how one might chooses between preferences one is indifferent about. Furthermore, the strength of one preference versus another is not important, only their ranking.
Gordon returns to Burdian’s Ass. He addresses the objection that it doesn’t matter whether the donkey wishes to avoid starving to death. The donkey must choose between two identical bales of hay and if a perfectly rational agent cannot do so. Gordon answers such a notion of perfect rationality is problematic. If perfectly rational, why should the donkey waste time reasoning as to how to choose a hay bale in order to avoid starvation?
Returning to the theory of marginal utility, Gordon seeks to address a frequent misconception. Restating the theory, as more units of good are acquired, an actor will apply each additional unit to the satisfaction of a subsequently less highly valued preference. Some economists (Gossen) seek to explain this process as the ‘satiation of wants.’ The ‘satiation of wants’ is a psychological theory may or may not be true, but it has no bearing on the science of economics. It is not deduced from action nor is it an axiomatic principle. Marginal utility says only that people apply units of a good to their most highly valued preference first, and so on down their preference scale. It is deduced solely form the action axiom and is not an attempt to explain why actors act in this way.
Gordon further claims that refuting the notion of choosing the most highly ranked preference based on psychological theory is unfounded. For example, an established psychological principle that a second bite of ice cream may be more pleasurable than the principle that an actor chooses their highest preference. Even if the psychological theory were true, this principle of action still stands. Preference scales need not consist of the single use of a good. Each preference could involve more than one good put to more than one use as well as different uses for different goods. Thus, two ice cream bites can be a single preference leaving the preference principle in tact.
The use actor’s see for goods, then, determines how goods are comprised in value scales. The uses actor’s see for goods is subjective. This does not mean the goods themselves are subjective as some ‘radical subjectivists’ claim. Goods have objective qualitative and quantitative attributes unlike the uses to which actors dedicate them.
In the real world an actor can satisfy their many different preferences with many different goods. Marginal utility recognizes this. Actors rank many different goods based on their assessment of how well these goods satisfy their many different preferences. As an actor acquires more goods, he will dedicate them to satisfy progressively less valued preferences.
Marginal utility applies not only to single actors, but also to actors involved in exchange. Exchanges can be either voluntary or involuntary (involving force or fraud). Economics mainly concerns the former.
Actors voluntarily exchange goods because each expects to benefit. They value the goods they exchange in reverse order. This valuation is the basis for prices.
Sunday, March 22, 2009
Monday, March 16, 2009
Economic Reasoning - Chapter 2 - Action and Preference
Having covered deductive logic, Dr. Gordon turns to the foundation of economic science. The foundation, he argues, is the action axiom; man acts.
Action is conscious, purposeful behavior directed towards a goal. Action does not require physical movement. For example, one can remain seated to vote against a proposal. Still, most actions involve physical movement.
How does one know the axiom is true? According to Gordon we know it’s true because it is common sense.
That economics is based on an axiom understood to be common sense makes it different from the natural sciences. These sciences rely on controlled experimentation and observation because we do not know the underlying structure of natural phenomena; we must guess at it based on observation. On the other hand we, being acting humans, can understand what action is without having to experiment or observe.
Many economists reject the notion that one can develop economic science using deduction. Premises cannot be accepted because they are self-evident. One must work backwards starting with observable reality and formulating premises that explain it. If these premises predict an outcome that is eventually observed, then they are sound.
Having established the action axiom as true, Dr. Gordon next discusses what must follow from it. What first follows is that action is directed toward obtaining something. If we already possessed that which we wish to obtain, we would not act. The actions we employ to obtain something (our goal or purpose) involve means.
The structure of action involves the use of means to achieve a goal. From his one must acknowledge the goal will not come about without action. More precisely, one must not believe that one can obtain a desired goal no matter what action one takes. This must be distinguished from the idea that one cannot be certain of achieving a goal despite the action one takes. This is a much more powerful statement. It suggests a completely uncertain future. According to Gordon, it is also false. If you wish to reach a point across the room, and you know that if you walk there you will reach it, then the future is not uncertain. The forgoing distinction is subtle, but important. Some economists claim the future is “radically uncertain” and that actors can know very little about the outcome of their actions. If economics were the study of ignorant actors, it would not be of much use.
Dr. Gordon also states a corollary to action; one of ‘inaction’. One must not believe a goal will not be achieved no matter what one does. An actor will not act to achieve what they believe is impossible.
Next Gordon discusses the subjects of preference and utility. When one acts to fulfill a goal, one prefers this goal to some other goal. Some economists claim that one prefers one goal to another because it maximizes their utility, or increases there satisfaction. This notion adds nothing to the understanding of action; that is one acts to fulfill a goal one prefers versus another goal. In fact, acting to increase satisfaction suggests that actors are motivated to fulfill their goals based on the pleasure or pain they derive (or do not derive) from them. This is a psychological theory known as hedonism.
It is here that Dr. Gordon clarifies what economists mean by utility and welfare. These terms refer to the fact that an actor prefers one goal to another, not to any sensations these goals might elicit. The idea that people seek pleasure and avoid pain is known as hedonism. Reference to ‘hedonism’ is concerned with how or why people act. Whether it is true or not, hedonism has no place in economics. Economics is concerned only with the implication of actions.
Action not only involves choosing the best means to achieve a goal, but also choosing from various goals. Note that these facts do not follow from the action axiom. The axiom could apply to a single goal with a single means to achieve it. That economics is a science deduced from action, however, does not mean one cannot introduce other principles that are not derived from the axiom. Thus, Gordon argues the above principles can be introduced to derive a science of economics. Like the action axiom, they are common sense principles and require no explanation. (Dr. Gordon does note that there are economists who argue that these new axioms can be derived from the action axiom).
Gordon has now introduced 3 axiomatic principles as the basis of economic science (1) Man acts (2) Man has a variety of goals from which to choose (3) Man has variety of means from which to choose to achieve a goal.
Man has different goals; which does he choose? He chooses his most highly preferred goal. This goal is subjectively ranked against other goals, not measured. (Measurement implies an account of satisfaction and suggests hedonism). As the economist Lionel Robbins noted, utility, welfare, or satisfaction, in the sense Gordon specifies is like love. It is expressed as a comparison, not measured. In the next chapter Gordon addresses the status of preference; whether it is axiomatic or deduced from the principles noted above.
Action is conscious, purposeful behavior directed towards a goal. Action does not require physical movement. For example, one can remain seated to vote against a proposal. Still, most actions involve physical movement.
How does one know the axiom is true? According to Gordon we know it’s true because it is common sense.
That economics is based on an axiom understood to be common sense makes it different from the natural sciences. These sciences rely on controlled experimentation and observation because we do not know the underlying structure of natural phenomena; we must guess at it based on observation. On the other hand we, being acting humans, can understand what action is without having to experiment or observe.
Many economists reject the notion that one can develop economic science using deduction. Premises cannot be accepted because they are self-evident. One must work backwards starting with observable reality and formulating premises that explain it. If these premises predict an outcome that is eventually observed, then they are sound.
Having established the action axiom as true, Dr. Gordon next discusses what must follow from it. What first follows is that action is directed toward obtaining something. If we already possessed that which we wish to obtain, we would not act. The actions we employ to obtain something (our goal or purpose) involve means.
The structure of action involves the use of means to achieve a goal. From his one must acknowledge the goal will not come about without action. More precisely, one must not believe that one can obtain a desired goal no matter what action one takes. This must be distinguished from the idea that one cannot be certain of achieving a goal despite the action one takes. This is a much more powerful statement. It suggests a completely uncertain future. According to Gordon, it is also false. If you wish to reach a point across the room, and you know that if you walk there you will reach it, then the future is not uncertain. The forgoing distinction is subtle, but important. Some economists claim the future is “radically uncertain” and that actors can know very little about the outcome of their actions. If economics were the study of ignorant actors, it would not be of much use.
Dr. Gordon also states a corollary to action; one of ‘inaction’. One must not believe a goal will not be achieved no matter what one does. An actor will not act to achieve what they believe is impossible.
Next Gordon discusses the subjects of preference and utility. When one acts to fulfill a goal, one prefers this goal to some other goal. Some economists claim that one prefers one goal to another because it maximizes their utility, or increases there satisfaction. This notion adds nothing to the understanding of action; that is one acts to fulfill a goal one prefers versus another goal. In fact, acting to increase satisfaction suggests that actors are motivated to fulfill their goals based on the pleasure or pain they derive (or do not derive) from them. This is a psychological theory known as hedonism.
It is here that Dr. Gordon clarifies what economists mean by utility and welfare. These terms refer to the fact that an actor prefers one goal to another, not to any sensations these goals might elicit. The idea that people seek pleasure and avoid pain is known as hedonism. Reference to ‘hedonism’ is concerned with how or why people act. Whether it is true or not, hedonism has no place in economics. Economics is concerned only with the implication of actions.
Action not only involves choosing the best means to achieve a goal, but also choosing from various goals. Note that these facts do not follow from the action axiom. The axiom could apply to a single goal with a single means to achieve it. That economics is a science deduced from action, however, does not mean one cannot introduce other principles that are not derived from the axiom. Thus, Gordon argues the above principles can be introduced to derive a science of economics. Like the action axiom, they are common sense principles and require no explanation. (Dr. Gordon does note that there are economists who argue that these new axioms can be derived from the action axiom).
Gordon has now introduced 3 axiomatic principles as the basis of economic science (1) Man acts (2) Man has a variety of goals from which to choose (3) Man has variety of means from which to choose to achieve a goal.
Man has different goals; which does he choose? He chooses his most highly preferred goal. This goal is subjectively ranked against other goals, not measured. (Measurement implies an account of satisfaction and suggests hedonism). As the economist Lionel Robbins noted, utility, welfare, or satisfaction, in the sense Gordon specifies is like love. It is expressed as a comparison, not measured. In the next chapter Gordon addresses the status of preference; whether it is axiomatic or deduced from the principles noted above.
Tuesday, February 10, 2009
David Gordon - Economic Reasoning Chapter 1 - The Method of Economics
Dr. David Gordon begins his book with the following statement;
"In economics, we operate with deductive logic."
In this first chapter of his book Dr. Gordon explains why deductive logic is a powerful tool, and some of its basic rules.
What makes deductive logic so powerful? Starting from premises one knows to be true, the rules of deductive logic deliver conclusions that must be true.
Dr. Gordon begins with a simple example to illustrate; if all of a class A are part of a class B, and all of a class B are part of a class C, then all of A are part of C.
(It is after this example the reader comes upon the first of Dr. Gordon's 'thought starter's -I'll call them- that are found throughout his book. I appreciate his adding of these questions. They forced me to think more about what I had read. I list these questions at the end of each Chapter and attempt to answer them if Dr. Gordon has not answered them already.)
In the next section he continues the discussion with Aristotle' Laws of Reality (sometimes misnamed the 'Laws of Thought);
Aristotle's Laws of Reality:
1) A=A: The Law of Identity
2) Not (A and not A): The Law of Non-Contradiction
3) A or not A: The Law of Excluded Middle
The first rule, restated, says a thing is what it is. For example; a ball is ball, not something else.
The second rule, restated, says that a thing cannot be a thing and not a thing at the same time. For example, a thing cannot be a ball and not a ball.
The third rule, a bit trickier, says that a thing is either something or not something. For example, a thing is either red or non-red. It cannot be neither, or both.
The next section is on validity. Dr. Gordon now reviews the implications of an argument based on false premises. An argument based on true premises that follows the rules of logic yields a true conclusion every time. What about an argument beginning with false premises? Does it yield a false conclusion if it too, follows the rules? No. It may, but it also may not. Examples are given showing this to be the case.
An argument yields a true conclusion only if its premises are true and it is valid. It is valid if it follows the rules of logic. An argument resting on true premises that does not follow the rules of logic may also yield a false conclusion.
The next section, Deduction Extended, adds the hypothetical syllogism as another argument type. Up to this point Gordon discusses arguments of the type known as the categorical syllogism which has two factual premises and a conclusion. A hypothetical syllogism consists of premises that are not factual and yield non factual conclusions. An argument if X then Y does not say X or Y is a fact, only that if X is a fact then Y is a fact. Hypothetical syllogisms can have one or two premises that yield a conclusion.
Deduction Further Extended discusses the nature of certain premises. All premises are meant as facts, but their factual ‘nature’ fall under two different categories. In the first category, a premise is a fact, but does not necessarily have to be a fact. The statement ‘A communist is a two-headed monster’ does not say a communist must be a two headed monster; a communist could be something else.
Under the other category, a premise is necessarily a fact. That is, it cannot be anything else but what it is. The statement ‘No one can be their own father’ is a necessarily true statement. It must be the fact that no one can be their own father. Propositions of this nature are very important in economics.
Furthermore a categorical syllogism containing premises that are not necessarily true can yield a conclusion that it also not necessarily true even though the conclusion must necessarily follow from the premises. (If the premises are true, then the conclusion is true. This is not the same as saying that the conclusion must be true).
On the other hand, it is possible for premises that are not necessarily true to yield conclusions that are necessarily true. For example, some fathers are football players, all football players are males, from which it follows some fathers are males; the conclusion is necessarily true, though the premises are not.
(Note that some logicians argue the following; all X are Y means if X, then Y, which does not mean X exists. At the same time, they maintain that some X is Y means that there is at least one X that is Y, which implies the existence of X. This was discussed in Logic and Scientific Method by Cohen).
A final extension of deduction is that not all deductive arguments are syllogistic. For example, one can deduce all fathead socialists are fatheaded subversives from all socialists are fatheads alone. This inference is especially important in Austrian Economic Theory as several non syllogistic inferences are drawn from the concept of action, which is central to Austrian Theory.
In the final section of economics vs. mathematics, Dr Gordon explains economics, like math, is a deductive science. Yet, he continues, it is unlike math in that one cannot just ‘fill in the blanks’ and operate mechanically. For example, the immediate inference all Russian socialists are Russian subversives does not necessarily follow from all socialists are subversives. The Russian socialists could be Bulgarian subversives; wanting to overthrow the Bulgarian government, but not their own. Immediate inference, then, requires judgment as opposed to simple mechanical operations like 2x=10, x=? in mathematics.
Chapter 1 Questions;
p.4
1. Can something be both red and not red?
No. A thing is either red or it is not. It cannot be both at the same time. If a thing is red, then it is not not-red. If a thing is not-red, then it cannot be red.
2. Some philosophers have denied that these laws are always true. Marxists say, e.g., that everything is constantly changing; therefore, the Law of Identity isn’t true. Why is this objection based on a misunderstanding of the Law of Identity?
Saying that everything is constantly changing and that therefore the Law of Identity (a thing is what it is) is not true is a misunderstanding because the Law does not say anything about change. The Law says a thing is what is, not that a thing cannot be something else at some future point in time. For example, a caterpillar is a caterpillar, and not something else, until it becomes a chrysalis.
Also, what about the Law of Identity as it applies to the word ‘change?’ Change is what it is, it cannot be something else.
Questions p. 8
1. Diagram the argument just given. Show why the conclusion does not follow.
2. Give examples of (a) valid arguments w/ true premises (b) valid arguments w/ at least one false premise (c) invalid arguments with at least one false premise (d) invalid arguments with true premises. Must any of these types always lead to a false conclusion?
a. All dogs are mammals
All mammals are warm-blooded
All dogs are warm blooded
b. All dogs are domesticated mammals
All domesticated mammals are warm-blooded
All dogs are warm blooded
c. Some dogs are trained reptiles
Some trained reptiles are 4-legged
Some dogs are 4-legged
d. Some dogs are trained mammals
Some trained mammals are large
Some dogs are large
As one can see, none of the above arguments leads to a false conclusion, so none of the argument types need lead to a false conclusion. (Valid arguments with true premises always yield a true conclusion. False conclusions derived from valid arguments must have at least one false premise).
Pg 9.
1. Show, using diagrams, that the argument about Mises is valid.
2. Give examples of a valid argument with a false conclusion that has (a) one false premise and one true premise; (b) two false premises
a. All dogs are mammals.
All mammals are cats.
All dogs are cats.
b. All dogs are cats
All cats are fish
All dogs are fish
3. Suppose you have an invalid argument with a false conclusion. What can you tell about the premises?
You cannot tell anything from an invalid argument. The premises may be true or false. A false conclusion implies a false premise only if the argument is valid.
p. 10
1. Give examples of syllogisms with (a) one and (b) two hypothetical syllogisms
a. If money grew on trees then we would encourage CO2 emissions
b. If money grew on trees then we would encourage CO2 emissions
If we would encourage CO2 emissions then Al Gore would have to find a new job
2. Can you convert a hypothetical premise into a categorical one?
(With help from Cohen)
Hypothetical: If A then B
Categorical version of Hypothetical: All A that exist are B
p. 13
1. How can you find out if a statement is necessarily true?
A statement is necessarily true if by denying it you contradict the nature of the meaning of the subject.
2. If a statement is necessarily true, do you need to test it to find out whether it is true?
You do not need to test a necessarily true statement to determine its truth. You can tell if it’s true by deduction.
p. 14
1. How do we know the rules of mathematics are correct?
I answer first by noting that we cannot expect the rules of mathematics to be correct based on experimentation. We expect 2+2=4 all the time, not only under certain conditions, or until some experiment, test or observation proves that 2+2 could equal 5. The rules of mathematics are logically deduced based on propositions that we understand to be self evident.
2. Would it be a good idea to use symbolic logic in economics, if economics relies on immediate inferences?
It is not a good idea to use symbolic logic in economics because of its reliance on immediate inferences. Immediate inference requires evaluating the terms involved in order to determine if the inference is valid.
3. Is it always best to begin by “defining your terms”? Why or why not?
I argue it is always best to begin by defining your terms. The terms you use must be understood clearly in order to ensure your premises, conclusions and arguments are sound.
Note that certain terms must be assumed to be commonly understood; otherwise one would have to define the terms used to define your terms, and so on, ad infinitum.
4. Deduction only tells us what we already “know.” How might a supporter of the deductive approach reply?
Deduction does not tell us what we already know. The application of deduction uncovers the implication and relationship between certain propositions and conclusions. It tells us what must follow if we assume certain things to be true, or false. Though these relationships have always existed, we only come to know them through the application of deductive logic.
"In economics, we operate with deductive logic."
In this first chapter of his book Dr. Gordon explains why deductive logic is a powerful tool, and some of its basic rules.
What makes deductive logic so powerful? Starting from premises one knows to be true, the rules of deductive logic deliver conclusions that must be true.
Dr. Gordon begins with a simple example to illustrate; if all of a class A are part of a class B, and all of a class B are part of a class C, then all of A are part of C.
(It is after this example the reader comes upon the first of Dr. Gordon's 'thought starter's -I'll call them- that are found throughout his book. I appreciate his adding of these questions. They forced me to think more about what I had read. I list these questions at the end of each Chapter and attempt to answer them if Dr. Gordon has not answered them already.)
In the next section he continues the discussion with Aristotle' Laws of Reality (sometimes misnamed the 'Laws of Thought);
Aristotle's Laws of Reality:
1) A=A: The Law of Identity
2) Not (A and not A): The Law of Non-Contradiction
3) A or not A: The Law of Excluded Middle
The first rule, restated, says a thing is what it is. For example; a ball is ball, not something else.
The second rule, restated, says that a thing cannot be a thing and not a thing at the same time. For example, a thing cannot be a ball and not a ball.
The third rule, a bit trickier, says that a thing is either something or not something. For example, a thing is either red or non-red. It cannot be neither, or both.
The next section is on validity. Dr. Gordon now reviews the implications of an argument based on false premises. An argument based on true premises that follows the rules of logic yields a true conclusion every time. What about an argument beginning with false premises? Does it yield a false conclusion if it too, follows the rules? No. It may, but it also may not. Examples are given showing this to be the case.
An argument yields a true conclusion only if its premises are true and it is valid. It is valid if it follows the rules of logic. An argument resting on true premises that does not follow the rules of logic may also yield a false conclusion.
The next section, Deduction Extended, adds the hypothetical syllogism as another argument type. Up to this point Gordon discusses arguments of the type known as the categorical syllogism which has two factual premises and a conclusion. A hypothetical syllogism consists of premises that are not factual and yield non factual conclusions. An argument if X then Y does not say X or Y is a fact, only that if X is a fact then Y is a fact. Hypothetical syllogisms can have one or two premises that yield a conclusion.
Deduction Further Extended discusses the nature of certain premises. All premises are meant as facts, but their factual ‘nature’ fall under two different categories. In the first category, a premise is a fact, but does not necessarily have to be a fact. The statement ‘A communist is a two-headed monster’ does not say a communist must be a two headed monster; a communist could be something else.
Under the other category, a premise is necessarily a fact. That is, it cannot be anything else but what it is. The statement ‘No one can be their own father’ is a necessarily true statement. It must be the fact that no one can be their own father. Propositions of this nature are very important in economics.
Furthermore a categorical syllogism containing premises that are not necessarily true can yield a conclusion that it also not necessarily true even though the conclusion must necessarily follow from the premises. (If the premises are true, then the conclusion is true. This is not the same as saying that the conclusion must be true).
On the other hand, it is possible for premises that are not necessarily true to yield conclusions that are necessarily true. For example, some fathers are football players, all football players are males, from which it follows some fathers are males; the conclusion is necessarily true, though the premises are not.
(Note that some logicians argue the following; all X are Y means if X, then Y, which does not mean X exists. At the same time, they maintain that some X is Y means that there is at least one X that is Y, which implies the existence of X. This was discussed in Logic and Scientific Method by Cohen).
A final extension of deduction is that not all deductive arguments are syllogistic. For example, one can deduce all fathead socialists are fatheaded subversives from all socialists are fatheads alone. This inference is especially important in Austrian Economic Theory as several non syllogistic inferences are drawn from the concept of action, which is central to Austrian Theory.
In the final section of economics vs. mathematics, Dr Gordon explains economics, like math, is a deductive science. Yet, he continues, it is unlike math in that one cannot just ‘fill in the blanks’ and operate mechanically. For example, the immediate inference all Russian socialists are Russian subversives does not necessarily follow from all socialists are subversives. The Russian socialists could be Bulgarian subversives; wanting to overthrow the Bulgarian government, but not their own. Immediate inference, then, requires judgment as opposed to simple mechanical operations like 2x=10, x=? in mathematics.
Chapter 1 Questions;
p.4
1. Can something be both red and not red?
No. A thing is either red or it is not. It cannot be both at the same time. If a thing is red, then it is not not-red. If a thing is not-red, then it cannot be red.
2. Some philosophers have denied that these laws are always true. Marxists say, e.g., that everything is constantly changing; therefore, the Law of Identity isn’t true. Why is this objection based on a misunderstanding of the Law of Identity?
Saying that everything is constantly changing and that therefore the Law of Identity (a thing is what it is) is not true is a misunderstanding because the Law does not say anything about change. The Law says a thing is what is, not that a thing cannot be something else at some future point in time. For example, a caterpillar is a caterpillar, and not something else, until it becomes a chrysalis.
Also, what about the Law of Identity as it applies to the word ‘change?’ Change is what it is, it cannot be something else.
Questions p. 8
1. Diagram the argument just given. Show why the conclusion does not follow.
2. Give examples of (a) valid arguments w/ true premises (b) valid arguments w/ at least one false premise (c) invalid arguments with at least one false premise (d) invalid arguments with true premises. Must any of these types always lead to a false conclusion?
a. All dogs are mammals
All mammals are warm-blooded
All dogs are warm blooded
b. All dogs are domesticated mammals
All domesticated mammals are warm-blooded
All dogs are warm blooded
c. Some dogs are trained reptiles
Some trained reptiles are 4-legged
Some dogs are 4-legged
d. Some dogs are trained mammals
Some trained mammals are large
Some dogs are large
As one can see, none of the above arguments leads to a false conclusion, so none of the argument types need lead to a false conclusion. (Valid arguments with true premises always yield a true conclusion. False conclusions derived from valid arguments must have at least one false premise).
Pg 9.
1. Show, using diagrams, that the argument about Mises is valid.
2. Give examples of a valid argument with a false conclusion that has (a) one false premise and one true premise; (b) two false premises
a. All dogs are mammals.
All mammals are cats.
All dogs are cats.
b. All dogs are cats
All cats are fish
All dogs are fish
3. Suppose you have an invalid argument with a false conclusion. What can you tell about the premises?
You cannot tell anything from an invalid argument. The premises may be true or false. A false conclusion implies a false premise only if the argument is valid.
p. 10
1. Give examples of syllogisms with (a) one and (b) two hypothetical syllogisms
a. If money grew on trees then we would encourage CO2 emissions
b. If money grew on trees then we would encourage CO2 emissions
If we would encourage CO2 emissions then Al Gore would have to find a new job
2. Can you convert a hypothetical premise into a categorical one?
(With help from Cohen)
Hypothetical: If A then B
Categorical version of Hypothetical: All A that exist are B
p. 13
1. How can you find out if a statement is necessarily true?
A statement is necessarily true if by denying it you contradict the nature of the meaning of the subject.
2. If a statement is necessarily true, do you need to test it to find out whether it is true?
You do not need to test a necessarily true statement to determine its truth. You can tell if it’s true by deduction.
p. 14
1. How do we know the rules of mathematics are correct?
I answer first by noting that we cannot expect the rules of mathematics to be correct based on experimentation. We expect 2+2=4 all the time, not only under certain conditions, or until some experiment, test or observation proves that 2+2 could equal 5. The rules of mathematics are logically deduced based on propositions that we understand to be self evident.
2. Would it be a good idea to use symbolic logic in economics, if economics relies on immediate inferences?
It is not a good idea to use symbolic logic in economics because of its reliance on immediate inferences. Immediate inference requires evaluating the terms involved in order to determine if the inference is valid.
3. Is it always best to begin by “defining your terms”? Why or why not?
I argue it is always best to begin by defining your terms. The terms you use must be understood clearly in order to ensure your premises, conclusions and arguments are sound.
Note that certain terms must be assumed to be commonly understood; otherwise one would have to define the terms used to define your terms, and so on, ad infinitum.
4. Deduction only tells us what we already “know.” How might a supporter of the deductive approach reply?
Deduction does not tell us what we already know. The application of deduction uncovers the implication and relationship between certain propositions and conclusions. It tells us what must follow if we assume certain things to be true, or false. Though these relationships have always existed, we only come to know them through the application of deductive logic.
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