4.1 Meaning
Critical Thinking Lecture 4: Definitions and Philosophical Analysis
We have been exploring conditionals and deductive arguments. As we have seen, conditional statements consist of a sufficient condition and a necessary condition. In this lecture we will shift our focus to the importance of definition in understanding claims and arguments. As we shall see, necessary and sufficient conditions play an important role in the project of constructing definitions.
Arguments are constructed with language, and language consists of words that have meanings. In order to understand and assess an argument or a dispute, we often have to ask prior questions about the meaning of terms being used in the argument.
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What is the meaning of a word? How can we get at such a meaning? Philosophers have argued about this issue in detail, especially since the late 19th century. As with most difficult and interesting philosophical issues, there is no agreement amongst philosophers on the correct theory of meaning. However, some of the theories and concepts that have been developed in this dispute are very useful in our assessment of everyday questions concerning the meaning of terms.
The Reference Theory of Meaning: It seems plausible that words stand for things or classes of things. e.g. The word “Sydney” stands for the particular city we are in right now, the word “peanuts” stands for all of those particular nuts, the word “red” stands for the property that is possessed by all red things, etc. We could say that each of these words points to or refers to these things. According to the reference theory of meaning, the meaning of a word is the object, property, event or state of affairs to which it refers.
There are some powerful objections to the reference theory of meaning:
Firstly, there seem to be many words and phrases that have meaning, but do
not refer to anything. e.g. “unicorn”, “ether”. We might be tempted in these cases to say that these words refer to non-existent objects, although that is a strange claim. In any case, it is not clear what would have to exist for them to refer to actual objects.
Secondly, there are other words that have meaning but do not refer to anything. e.g. “and”, “not”, “maybe”, “how”, “if”. These words are essential for everyday life (unlike “unicorn”), but they do not stand for anything. We might be tempted to say that they refer to concepts, but this is not very helpful because those concepts also have meaning. What is the meaning of the concept “or”? It is hard to see how we could account for this with a reference theory of meaning.
Thirdly, there are phrases whose meanings are very clearly known to us even though we do not know what they actually refer to. e.g. The biggest star in the universe, the loudest whale song ever, etc. If the reference theory of meaning were true, then we should not know what these phrases mean, since we do not know what they point to or refer to.
Fourthly, there are some interesting features of language use that suggest that the meaning of a word is not simply what that word refers to.
e.g. Suppose someone tells “Superman will save the day”. She understands the meaning of this claim, and believes it is true. Then someone else tells Lois ” will save the day”. Lois understands this claim, too, and believes it is false. After all, she does not know that is Superman, and she thinks of Clark only as the annoying and bookish reporter from the Daily Planet, whom she believes has no super powers. But if the reference theory of meaning is correct, then “Superman will save the day” means exactly the same thing as ” will save the day”. How could Lois understand two sentences with identical meanings yet believe one and not the other?
e.g. “The number of planets in our solar system” refers to the number 8. “5 + 3” also refers to the number 8. According to the reference theory of meaning, “The number of planets in our solar system” and “5 + 3” have exactly the same meaning.
But the sentence “5 + 3 could not possibly have been greater than 10″ is true, and the sentence ” The number of planets in our solar system could not possibly have been greater than 10″ is false. How could these phrases mean the same thing?
Descriptive theory of meaning: Words and phrases refer to things by containing implicit or explicit descriptions of those things. e.g. “Superman” means something like “Man of steel who can leap tall buildings in a single bound and wears underpants outside of his tights, etc.” whereas ” ” means “mild-mannered reporter from the Daily Planet who wears glasses, etc.” “Unicorn” means “horse-like animal with a horn growing out of its forehead, etc.”. Philosophers call this the sense of a term, as opposed to the reference of a term. (This is equivalent to the distinction between the intension of a concept and the extension of a concept. The extension is the thing or things the concept points to, and the intension is the implicit description by which it points to its extension.) According to the descriptive theory of meaning, words refer to objects via their senses, and the meaning of a word is the sense of the word.
The descriptive theory of meaning avoids many of the problems faced by the reference theory of meaning. But it has problems of its own. Descriptions themselves consist of words, and the meaning of those words has to be explained in some way. It seems we will get an endless regress of descriptions with this theory, which would not explain anything. Rather, it seems that some terms are basic in their meaning, e.g. red. A residual problem is that terms like “maybe” and “not” do not seem to have a sense by which they refer to things.
Use theory of meaning: Words and phrases have meanings in sentences, and their meanings are determined by the proper use of those sentences. Since the use of terms in sentences is highly context-specific, so too are meanings of terms. e.g. “Take my wife, please!” is a joke that depends on the fact that we use the word “take” in different ways. According to the use theory of meaning, we can always get at the meaning of a term by seeing how it is used. e.g. You understand the meaning of “or” when you understand how someone properly uses the sentence “Dave should go or Trev should go”.
The use theory of meaning seems plausible for some words. The problem with the use theory, though, is that many words do seem to stand for things, and have standard meanings that do not vary from context to context. For these words, especially names, it seems plausible that you understand the proper use of the word by grasping either what it refers to or its sense. According to some critics of the use theory, meaning determines proper use, and not vice versa.
Our job in this lecture is not to assess these three theories of meaning, but to understand the role of meaning and definition in argument. Each of these three theories suggests ways in which we can try to clarify the meaning of words, and ways in which we can solve disagreements over meaning.
4.2 Why Define?
The meaning of sentences usually, perhaps always, is determined by the meaning of the words from which they are built. Sometimes we cannot assess a claim or an argument until we have thought carefully about the meaning of one or more terms used to state it. e.g.
If you are designing an engine without fuel injection, you had better include
a carburettor.
What is a carburettor?
Communism sounds fair in theory, but in practice ordinary people who live under a communist regime have no political representation. For all of its flaws, democracy gives ordinary people political representation, so it is preferable to communism.
In the above argument, what is meant by “political representation”? Is the term too vague to be useful? Or is it being used in a specific way here?
Scientist: Darwinism is the theory that gives the correct explanation for the existence of the various species of plant and animal.
Creationist: The scientist and I agree that Darwinism is a theory, and so is Creationism. In this respect are equal, so no one can claim to know that either is true. The choice between them is a matter of faith.
The above argument contains the ordinary words “theory” and “know”. In many contexts, the meaning of these terms is clear, e.g. Do you know where the keys are? But in this argument, these ordinary words are being put to a special use. What is meant by “theory”? Do both disputants mean the same thing? Is the Creationist right to suggest that something which is a theory cannot be known? What is knowledge? And what does it mean to say that a choice is a matter of faith?
Dave: What you see on Big Brother is not real.
Trev: Yes it is. Everything that they show on screen really happens. None of it is faked.
Dave: Of course it is faked. As soon as someone points a camera in your face, what happens is fake.
In the above disagreement, both Trev and Dave are using the concepts of “real” and “fake”. Are they really disagreeing about the facts concerning reality TV, or is their disagreement due to a difference in what they mean by the terms “real” and “fake”?
In each of these cases we need to define these key terms before we can understand and evaluate the claims. Which kinds of definition might we offer?
4.3 Kinds of Definition
Some kinds of definition rely on a pretty clear prior understanding of the concept in question.
e.g. Sometimes we define a term by giving a synonym, i.e. a word or term that has the same meaning as the initial term. e.g.
A bogan is a Westie.
A Tory is a conservative.
“Getting leathered” means getting drunk.
Sometimes definition by synonym is not helpful because the person who lacks understanding of the term in question also fails to understand the synonym. It is completely hopeless when the person is trying to acquire a concept.
Another kind of definition that relies heavily on prior understanding is genus- species definition, which defines something by describing it as a subclass of a broader class. e.g. a Philips-head screw is a screw with a cross-shaped indent on the head. A ruby is a sapphire with red colouring. A father is a male parent. Again, such definitions are useful only to those who have a clear understanding of the genus, and are no use to people trying to acquire both the concept of the genus and the species.
Thankfully, there are other kinds of definition available.
Ostensive definition consists of pointing out the thing referred to by the term that requires definition. In some cases, ostensive definition is the most useful form available. e.g. What is the Charleston? Describing it is pretty tricky, and it might not really get the idea across.
Wikipedia describes the Charleston as follows: “the basic step resembles the natural movement of walking, though it is usually performed in place. The arms swing forward and backwards, with the right arm coming forward as the left leg ‘steps’ forward, and then moving back as the opposite arm/leg begin their forwards movement. Toes are not pointed, but feet usually form a right angle with the leg at the ankle. Arms are usually extended from the shoulder, either with straight lines, or more frequently with bent elbows and hands at right angles from the wrist
(characteristics of many African dances). Styling varies with each Charleston type from this point, though all utilise a ‘bounce’.”
The Jitterbug, as described by dancer Al Minns: “The jitterbug… We called people who would just jump on the floor, without any knowledge of what they were doing, and go mad with the drumming what not and just go boodedoo boodedoo doo and shakin’ their head and just jump up and down without any control … that’s what we called the jitterbug.”
It is much better if you can show the person by pointing to an example of the Charleston, and contrasting it with examples of the Jitterbug, the Shing-a-Ling and the Funky Broadway.
Ostensive definition is not always appropriate. Sometimes the examples to which the definer points are not easily recognised by the person who lacks understanding of the term because they cannot be seen. e.g. Could we define “justice” or “gene” or “average” by ostension?
Use in context can also help to clarify the meaning of terms. This is often combined with ostensive definition. We train kids to speak by a combination of ostensive definition and rewards for correct use in context.
Ostensive definition and use in context can be very informative, but in many cases they are not the best means of definition. Sometimes this is because the concept is complex or abstract, and examples stand out much more clearly when the content of the concept has been described to us. e.g. Carburettor, gene. In other cases, there is significant disagreement in everyday use of the term, and over which things count as examples. e.g. Political representation, “human being” in the context of abortion debates. In cases such as these, the meaning of terms is often unclear to the audience not simply because the audience is unaware of some widely-known facts, but because the meaning of the term itself is unclear.
4.4 Descriptive Definition
Descriptive definition consists of offering a description which captures the meaning of the term. This can either be a description of the things referred to by the term, or a description which captures the sense of the term. (Usually these will be equivalent, but in some cases the sense of a term fails to get at the essential properties of the class of things referred to by the term. More on this later.) A descriptive definition often is a form of genus-species definition.
Since the description in a descriptive definition is supposed to be a definition, it is not enough for it correctly to apply to the things to which the term refers. In addition, the descriptive definition should distinguish the things to which the term applies from those to which it does not apply. A definition of F should sort the Fs from the non-Fs. Thus, a good descriptive definition will apply to ONLY the things to which the defined term refers. i.e. The description will be true of only the things to which the defined term refers.
e.g. What does the word “car” mean? We might offer a descriptive definition in response to this question: a car is a machine on wheels whose function is to transport people. This description is true of cars, but it is not a good descriptive definition of “car”. The problem is that the description is also true of lots of things that are NOT cars, e.g. bikes, buses, passenger trains, skateboards.
Since the description is supposed to be a definition, it is also not enough for it to apply to only some of the things to which the defined term refers. A good descriptive definition will apply to ALL of the things to which the defined term refers.
e.g. A car is a machine on at least three wheels, that is run by a petrol engine, that does not run on tracks, whose function is to transport up to roughly 8 (?) people.
The only things this description applies to are cars, but it is not a good descriptive definition because it does not apply to ALL cars. e.g. To cars with electric motors and not petrol motors.
So, a good descriptive definition of a term will apply to all and only the things referred to by that term. It tells us what is necessary and what is sufficient in order for something to be the kind of thing to which the term refers. This should sound familiar from our earlier work on conditionals.
Let us suppose that F is the term we want to define and G is the descriptive definition. If the definition is a good one, then all F’s are G’s and only F’s are G’s. This is equivalent to “If a is F then a if G and if a is G then a is F”. Such a claim is called a biconditional and is expressed as “If p then q and if q then p”, or “p if and only if q”, or “p iff q” (the “iff” is read as “if and only if”).
What is a plumber? A person whose job directly involves installing or repairing piping, fixtures, and appliances in connection with the water supply, drainage systems, etc., both in and out of buildings.
One conditional: If you are a plumber then you are a person whose job directly involves installing or repairing piping, fixtures, and appliances in connection with the water supply, drainage systems, etc., both in and out of buildings.
The other conditional: If you are a a person whose job directly involves installing or repairing piping, fixtures, and appliances in connection with the water supply, drainage systems, etc., both in and out of buildings, then you are a plumber.
The biconditional definition: You are a plumber iff you are a person whose job involves installing or repairing piping, fixtures, and appliances in connection with the water supply, drainage systems, etc., both in and out of buildings.
Constructing a good descriptive definition of F requires finding the necessary and sufficient conditions for something counting as F. Often philosophers who want to understand a concept try to give an informative descriptive definition of that concept. In much 20th-21st century philosophy, this practice is known as “philosophical analysis”, and the informative definition of the concept is called the “analysis” of that concept. This same practice goes back as far as Socrates. Classic examples of philosophical analyses include:
Knowledge = justified true belief. Justice = the will of the stronger. Causation = constant conjunction.
These analyses are equivalent to:
a is knowledge if and only if a is a justified true belief.
a is just if and only if a is in accordance with the will of the stronger. a causes b if and only if a is constantly conjoined with b.
4.5 Testing Definitions with Counterexamples
Once we see that descriptive definitions are biconditionals, it should be clear that we can test the truth of definitions in the same way that we can test the truth of conditionals, i.e. by seeking counterexamples. Remember, a counterexample to a conditional claim is a thing or state of affairs that meets the sufficient condition but not the necessary condition.
e.g. If you are Russian then you live in Russia.
A counterexample to this claim is someone one who meets the sufficient condition but not the necessary condition, i.e. a Russian who does not live in Russia.
Since descriptive definitions are supposed to be biconditionals, there are two kinds of counterexample which would undermine such a definition. “p iff q” will be false if there could be a case in which p is true but q false, OR if there could be a case in which q is true but p is false. If “p iff q” is true, then the truth of p must always go with the truth of q, and the truth of q must always go with the truth of p. Thus, one kind of counterexample to the biconditional “p iff q” would be a possible case in which p was true but q false, and another would be a possible case in which q was true but p false.
Trev: How would you define a fire engine?
Dave: A fire engine is a red vehicle that is housed in the fire station.
Has Dave offered a correct definition? In order to figure this out, we can phrase the definition as a biconditional and look for both kinds of counterexample.
X is a fire engine iff X is a red vehicle that is housed in the fire station.
One kind of counterexample would be something that is a fire engine but is not a red vehicle that is parked in the fire station. e.g. A blue fire engine, or a red fire engine that is kept outside rather than in the fire station.
The other kind of counterexample would be something that is a red vehicle that is housed in the fire station but is not a fire engine. e.g. A red car that is housed in the fire station.
The two kinds of counterexample reflect two kinds of error in a descriptive definition of a term.
If the term applies to things to which the description does not apply, then the definition is too narrow.
If the description applies to things to which the term
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