Chapter II
Analysis of Sense, Analysis of Structure
Propositions and Arguments
Claudio Gutierrez
Translated from Spanish by Inés Gutiérrez
Claudio Gutierrez
There are three different functions of language: the expressive function, which reveals the mood of the speaker or writer; the directive function, which shows the will or desire of the person speaking; and the informative function, which affirms or denies that something is happening and, by so doing, depicts the world in one aspect or another. This latter is also called a descriptive or categorical function. Let us look at some examples: “What a beautiful afternoon!” is a statement that fulfils an expressive function, revealing the speaker’s mood. The statement also complies –indirectly– with a descriptive function, since it gives certain information about the outside universe (we normally associate the absence of rain and a 20º temperature with beauty). Even more indirectly, it also fulfills a directive function, since it can be an invitation to interrupt our work and go for a stroll in the park. “Close the door”, or “Please follow me”, or “I would like a glass of water”, all fulfill a directive function, their intention being to make someone else do something. Nevertheless, the last sentence is also descriptive, because it affirms the existence of a desire in me, and my desires are mental states which are, of course, part of the universe. “I’m thirsty!” is an expressive statement; however, it can act as an insinuation to the owner of the house to offer me a drink.
Other statements are clearly informative, such as those we find in a newspaper article or in the pages of a textbook. For example: “Many effects of heat on matter are used as operative principles for the construction of heat detectors or thermometers.” This is a clearly informative statement which, furthermore, has no apparent expressive or directive connotations. Statements such as this, completely informative, are the most interesting to logic. But outside of textbooks, we will seldom find them in such a pure form; they will normally appear in ordinary language mixed with directive or expressive statements, or with statements that perform various functions at the same time. Hence the importance of sense analysis, which allows us to decipher exactly what functions are accomplished by the different statements present in a text.
Once we have uncovered the informative statements in a fragment of text, it is necessary to pay attention to their structure. The structure of a statement differs from its content, which we could also call subject matter. There are statements, such as the one about heat detectors quoted above, the content of which belongs in the physical sciences. If we examine the statement, we find that almost all the words refer to physical properties or material things. Other statements, like “insect eggs are fertilized internally and are usually laid in large numbers,” deal with a different subject matter, since its content belongs in the biological sciences. Apart from words about physical properties or material things, such a statement contains words representing living beings or their parts or organs, and their characteristic operations. Yet another statement: “In a system of perfect competence, the supply and demand of particular goods determine their price.” The content of this statement is economics, and as such it belongs in the social sciences. The specific words “price”, “supply”, “demand”, “competence” refer to things that are neither material nor biological, but strictly cultural.
We have to be cautious about important ambiguities which can arise in connection with this subject. The word “thermometer” of our example describes not a straightforward physical object but rather a cultural creation. It represents an object created by human technique and hence it is a cultural term.
If we examine the previous statements again, we will see that, aside from the words that express content –physical, biological, or cultural– there are others pertaining to neither an object nor an event in the external world. For example: “many”, “from”, “are”, “generally”, “and”, “determine”. These terms are structural words, not content words, and if we ask ourselves which science they belong in –as “egg” belongs in biology or “heat” to physics– we have to answer that they belong in logic, they are logical terms. In an extensive text of an informative nature, it can be of the utmost importance to establish the structure of the fragment, by appropriately identifying the logical terms it contains. Structural issues can be something like these: how many propositions are there in the text? Where does each one begin and end? Are they indivisible propositions, or rather propositions composed by other propositions? How do they relate to one another? Are all of them asserted independently, or can it be said that if we assert one, we have to assert some other? Does the writer or speaker believe that such or such proposition is true or is he simply quoting it? Is he trying to prove or refute it? How does he do this? By what method or strategy?
The analysis of structure assumes that we have a clear understanding of some concepts or technical terms. It is time to propose them to our readers. First of all, the concept of "proposition". This could be defined as a thought which is complete and descriptive, understanding "thought" not in a psychological sense but rather in the logical sense explained above. A proposition is the affirmation or negation of an event. “It is raining” is a proposition. “Today is not Monday” is also a proposition. Any of the three scientific statements in sections 5 and 6 is also a proposition. Some parts of these are also propositions by themselves , such as “insect eggs are fertilized internally” or "[eggs] are usually laid in large numbers”.
We should make a distinction between “statement” and “proposition”. A statement, a series of letters and sounds, is not a proposition. A statement is the linguistic form in a specific language that may or may not express a proposition. The proposition is the complete thought that describes an event or world feature. For example, the statement from the biological sciences used in section 6 is in English, but it has the following Spanish counterpart: "los huevos de los insectos son fertilizados internamente y por lo general puestos en cantidades muy abundantes". On the other hand, the proposition expressed by these so different statements is exactly the same, namely the idea conveyed by any of them.
A good definition of proposition would be that it is the semantic unit of which we can say it is true or false. In deed, expressive statements can be sincere or unauthentic, but not true or false. Neither commands nor recommendations can be true or false: we call them only wise or foolish. “Falsehood” or “truth” are other logical terms of technical character. Their meaning is close to the ordinary one, although more precise. Truth is the quality of a proposition insofar as accepted by whomsoever states or accepts it. Or, even more exactly, the quality of a semantic unit that adequately describes the world for the user. Truth and falsehood can also be considered to be simply the possible logical values of a fully meaningful descriptive semantic unit. That value is what most interests the logician in the proposition. The three scientific propositions quoted in sections 5 and 6, for example, can be considered by the logician to have identical value, since all are equally true, apart from the fact that one refers to heat, another to insects, and the last to supply and demand, which –remember– are neither part nor parcel of the subject matter of logic.
Language analysis prepares the way for the second great mission of logic: the explication of the methods of
thought. Let us here also introduce some technical terms. First of all, “argument”. An argument is a special set of
propositions. When we speak, we almost always use several propositions, one after the other. In writing, each proposition is
separated from the others by a comma, a period, or any other punctuation mark. Now, it is possible to assert these propositions
separately and independently. For example, in a story: “I went to the market, I saw John, I gave him your message.” This is
a set of propositions independent from one another, except inasmuch as their order of enunciation gives a direct view of the
seriality of the events in question. Any of them can turn out to be false, without making the others false. But on other
occasions the propositions have a very specific logical relation between them. For example: “If John goes to the market, I
will see him; John goes to the market; I will see John.” In this case, it is not possible for the first two propositions to be
true and the third one false. Thus, we say that the first two implies the third, or that the third can be inferred from the first two, or that the three
propositions together form an argument (in the sense of a reasoning, not of a quarrel). In cases such as these, we call the propositions that imply the last one, premises, and the implied proposition, conclusion. The proposition we call conclusion cannot be false if all the propositions we call premises are true. This is the special logical relationship existing between propositions that form an argument.
“Conclusion” and “premises” are relative terms. The same proposition can be premise in one argument and conclusion in another.
This circumstance creates chains of arguments, such as: “If John goes to the market, I will see him. John goes to the market.
I will see John. If I see John, I will give him the message. I will give the message to John.” The third proposition is the
conclusion of an argument –the one formed by the first three propositions– and likewise a premise of another argument –the one formed by the last three.
There are groups of propositions that are not really an argument, although they seem to be one. They are independent propositions connected by inference relations only in appearance. An example: “If John goes to the market, I will see him. I see John. John goes to the market.” The last proposition seems to be the conclusion of the other two; however, it is not dependent on them. The first two can be perfectly true, while the third is false. It can be true that if John goes to the market I will have to see him, and it can also be true that I see John, maybe when we both walk across the park. In fact, it can well be the case that John took a vow never to return to the market the day his wallet was stolen. The argument in section 8, with which this set of propositions has a family resemblance, is an authentic argument; this new one, on the contrary, is totally spurious. In the former, the premises cannot be true and the conclusion false. Thus, we rightly call it valid argument. In the latter, the alleged conclusion may be false while the alleged premises true; thus, we rather call it invalid argument.
The validity or invalidity of an argument is different from the truth or falsehood of the propositions involved. There can be a valid argument (set of related propositions), which is a sterling reasoning, even if their premises are not all true; or an invalid argument whose premises, and even the conclusion, are true –although in this case we would have to justify the truth of the conclusion independently from the truth of the premises. What definitely cannot exist is a real argument which has true premises and false conclusion, because that would go against the very definition of what we understand as “valid argument”.