(A) What logic is about.
In short, logic is the theory and practice of correct reasoning. It is about the processes of reasoning used to arrive at truth and avoid falsehood; about the rules for reasoning that we should follow to get at the truth.
Logic is actually a whole lot simpler than most people think. It has for a number of reasons developed a kind of aura around it as being strangely formidable and intellectually intimidating. This may be due to the "Mr. Spock" image of logic as being something accessible only to highly and rigidly intelligent people, or as being something which tells what we must do, and if we do not follow its dictates we are somehow sub-rational. Logic is simply about the rules of reasoning, rules which we should follow (even if we don't) in order to make good judgments. We have these rules for the purpose of avoiding mistakes, to keep us from jumping to conclusions on the basis of too little evidence, or the wrong kind of evidence. Rules of reasoning say: To avoid making a mistake of reasoning, you should do so-and-so; or in order to minimize the chance of making a mistake of reasoning, you should do so-and-so.
Now of people who are naturally inclined to disdain rules of any kind or who find it hard to do anything without breaking rules, this statement about rules of reasoning does not scare them at all. They can ask: “Why should we follow rules of reasoning? Who cares what these rules say when I'm just going to go ahead and make whatever statements that I want to anyway?” In response we can say: “Well that's fine, you can make whatever statements you want, but that’s not really the issue here. The real issue here is what we are justified in stating based on something else.” The statements we make just by themselves aren’t what are logical or illogical. The concern of logic is the statements we can make based on others as givens. The rules of logic, of correct reasoning, don't tell us anything just by themselves, but tell us what we are justified in saying based on what we have before us, whether that is known or even just assumed. So, technically, logic doesn’t say anything in and of itself, but only when it is coupled with information from outside of itself. It is a matter of process, not content.
As an example of a rule of logic there is a very basic one that goes like this:
Given you know that if A then B, and also that A, you are justified in saying that B.
Note that this example rule illustrates the above points in the following ways: First, it tells you what you can say given what you have to start with, that if you have two pieces of information (if A then B, and A), you are allowed to arrive at another piece (B). Second, it shows that this rule applies to any subject matter of whatever content; A and B can have to do with any subject out there, and the rules of and processes of logic apply no matter what subject they are about.
(B) How the subject of logic is different from some other subjects.
Now this notion of having rules for reasoning from one thing to another thing is very different from a number of other concepts that look and sound like they are similar, but that are completely different. Contrast the nature of logic from other similar things such as these:
Thinking
There is the notion of thinking as a physiological process involving brain activities. This is just descriptive of the processes involving (maybe) chemical and electrical events (as far as we can tell). This is different because it just describes what goes on as far as the physical processes of thinking go, and does not tell us anything about rules that we should follow.
Chain of reasoning/train of thought
There is also the idea of reasoning just by itself without any rules being applied to it, where people just describe the thoughts they have and then what thoughts come after those thoughts. This is different because it is a process that just describes a chain of thoughts and does not concern itself with how those thoughts are related to each other, or whether they are related at all.
Reasons
Then there is the idea of reasons in the sense of motives, rather than as elements of a reasoning process. Sometimes we act the way that we do because of ideas that we have and point to those ideas as what drove us to act. This is different because having reasons as driving motives doesn’t mean that you are reasoning from one thing to another, according to rules or not.
Reasonable belief
Then there is the idea of some statement being reasonable to believe, that it is reasonable to believe that it is true. This, by the way, is what is meant by the common mis-statement that some view or belief is logical. This idea is relatively close to what logic is about but its only one part, namely, the result of a logical process. A reasonable statement would be a conclusion that results from a logical process, where there are actually good grounds for believing in it, but where the grounds are not specified.
Rationality
Then also there is the idea of being rational in the context of decision-making. In rational decision-making we are to compare alternatives of action with regard to how likely they are to happen and how good or bad it would be if they were to happen, and choose the one that has the best combination of likelihood and consequence. This is the subject of a whole other, different science.
Rational persons/rational beings
Then there is the idea of some entity being a rational being, a highly complex living thing that has the capability to weigh alternatives and make decisions on its own. A rational being is certainly capable of following the rules of logic, but is also just as capable of breaking them, so being a rational person does not make one logical, someone who follows rules.
(C) How logic works at its elemental level.
The fundamental building blocks of music are tones, the basic parts of the chemical elements are atoms, and the assembly components of most houses are pieces of lumber. In the same vein, the building blocks of logic are arguments.
In logic an argument is best defined as: A claim with evidence that is intended to back it up. Another way of stating that is: A reasoned conclusion. Or another way: A set of evidence used to support a stated conclusion.
Note that this is entirely different from the popular sense of an argument, where an argument is an emotionally charged disagreement. There’s not supposed to be any emotional content in a logical argument; there’s just the idea that a claim is being made and some statements are being made to back up that claim. It is certainly true that people get excited sometimes over claims and evidence for them, but that does not get factored into the processes of logic.
And also, it is very important to note that there is nothing about the definition of an argument that presumes that evidence being presented actually does back up the claim being made, that it does support the conclusion. So there are good arguments, where evidence does back up a claim, and bad arguments, where it does not. The key to making good arguments versus bad arguments lies in the rules that are being followed (or being broken), rules that tell us what we should say in order to make an argument a good one. A good argument follows reliable rules, and a bad argument occurs when rules are broken.
(D) Summarizing and formatting arguments
There are some technical terms used in the making of arguments. The claim that is being made in an argument is called the conclusion, while the evidence being presented that is supposed to back it up is called the premise or premises. Every argument has one and only one conclusion and at least one premise, many times more than one. The normal, summary way that arguments are laid out is in what is called standard form; this is where premises are listed on separate lines, where there is a line drawn under them, and then the conclusion is listed. So an example of an argument in standard form is:
All whales are mammals
All mammals are our friends
All whales are our friends
Of course, we do not ordinarily speak in a way that puts arguments in standard form, but we do use a lot of terms in our everyday language that show that we are in fact using premises and conclusions, these terms being called indicator words. Indicator words tell us that premises and conclusions are on the way. Indicators for conclusions include (and there are many others):
Thus
Therefore
And so
Hence
We can conclude that
Indicators for premises include (and there are many others):
Since
As
For
For the reason that
Because (But watch out here: We have to be really careful about this one, as it sometimes indicates an explanation rather than a premise.)
There is a big caution flag to wave when it comes to some words that look like they are indicating something when they are not. The prime example of that kind of case is with the words: “If . . . then . . .” It sure looks like if would indicate a premise and then a conclusion, but this is not so. If-then statements are completely different kinds of things, and this will be covered later in detail.
Using this terminology, we can deal with an argument being made by taking it out of ordinary language, where premises and conclusions can be all mixed up, and then putting it in standard form, as in this example:
Since we know that grass is green, and as flowers are red, therefore, the sky is blue, since the dirt is brown.
When this argument is put into standard form, the premises and conclusion are put into order, and the indicator words drop out, as they will have served their purposes. And so the argument would be displayed like this:
Grass is green
Flowers are red
Dirt is brown
The sky is blue
(E) Finding arguments in the midst of all our communication.
There’s a whole lot of different things going on when we say stuff. Within the language of our everyday communication is found all kinds of different sounds that do all kinds of different things. And this is because our language has many different functions. Here is a list of a number of those functions and how they work:
Informative: Language has an informative function when we say something about the world around us, and us in it. This is most common kind of speech, where it is about something. Because this is the only kind of language in which claims are made and evidence is presented, this is the only place where arguments can be found. An example of this kind would be: “The grass is green.”
Interrogative: Our language is serving an interrogative function when we use it to request information or responses from others. This means when we ask questions. Questions don’t actually refer to the things around us but serve to elicit informative responses. So an example would be: “What color is the grass?”
Directive: Commands come in the form of directive language. So an example would be: “Make the grass green now!” Note that we have to be careful with directive language because it can be motivated by mental and emotional states that can also generate informative statements. Supposing that someone wanted the grass to be green, they could make the command for it to be green but also at the same time could make the statement: “I prefer green grass to brown grass.” This last statement is actually in informative language, as its about something, namely preferences.
Expressive: Expressive language is when “the saying is feeling”. The best example of expressive language is poetry, which also includes, much more commonly, musical lyrics. It also includes sayings like “Ouch!” Again, as in the case of commands, it is possible for our internal mental states to motivate expressive language but also informative statements, such as: “That really hurts bad.”
Performative: Performative language is when “the saying is doing”. As an example: “I promise to make the grass green.” By saying that you promise, you do.
The reason why it is so important to be able to identify the different functions in our language is that it is necessary to filter out all other speech from what people say except the informative parts in order to get at arguments, and thus in order for logical rules to apply. It’s not that all these other functions are unimportant, its just that we can’t use logical rules until we have only informative language in front of us.
(G) Sample problems and answers.
With these examples, the goal is to determine whether there are any arguments being made and, if so, put them into standard form.
(1) The end is near.
There is no argument here: There certainly is a claim being made, but there is no evidence presented to back it up.
(2) Jack and Jill went up the hill to fetch a pail of water. All the King’s horses and all the King’s men needed water. But Jack and Jill ended up tripping in a rabbit’s hole and spilling the water.
There is no argument here: There is a string of claims made, more so just statements of fact, but none have any evidence to back them up. Note that statements of fact are not in and of themselves arguments.
(3) Sing, O Goddess, the anger of Achilles, son of Peleus, that brought countless ills upon the Achaeans. Many a brave soul did it send hurrying down to Hades, and many a hero did it yield a prey to dogs and vultures, for so were the counsels of Zeus fulfilled from the day on which the son of Atreus, king of men, and great Achilles first fell out with one another.
(The Iliad, trans. Samuel Butler)
There is no argument here: This is a prime example of poetic language, and no claims are made in such language.
(4) The hip bone is connected to the shin bone. And thus, all people everywhere should be happy.
The hip bone is connected to the shin bone
All people everywhere should be happy
The reason why this is an argument is that it fits the definition exactly: A claim is being made and there is evidence presented that is intended to back it up. It is also a prime example of an argument where there is no connection in fact between the premise and the conclusion; there does not have to be any such connection in order for there to be an argument. Also note that any indicator words drop out, as they have done their part, and that all premises and conclusions are full and complete sentences and can stand on their own as complete pieces of information.
(5) If you are happy, then you are lucky. Oh, let’s cheer for luck! If you are lucky, you should try gambling. Consequently, happiness should make you rich.
If you are happy, then you are lucky
If you are lucky, you should try gambling
Happiness should make you rich
This is case where someone says something that is partly informative and partly expressive; but clearly the expressive part has to drop out, as it is not part of any argument. And also, the if-then statements are just standard premises just like any other statements can be.
(6) Since roses are red and violets are blue, hence, grass is green. But for the reason that grass is green, thus, flowers are yellow.
Roses are red and violets are blue
Grass is green
Grass is green
Flowers are yellow
There are two arguments here; note by the definition of an argument, every argument has one and only one conclusion. There are two indicators for conclusions, so there must be two conclusions, which means two arguments. It just happens that the conclusion of one argument is the premise of another.
(H) Quiz questions for next time.
In the following passages, determine whether there are any arguments being made and, if so, put them into standard form.
(1) Put your money where your mouth is! No one wants to hear mere words. Do you think I’m interested in your opinions?
(2) The roof is supported by the walls, and which also are supported by the foundation, and which also sits on the ground. Therefore, the roof is supported by the ground.
(3) The ocean tides are caused by effects of the Sun and Moon; they happen because of the gravitational effects of these bodies, even though they are far away.
(4) We can claim that many people are just not happy, since happiness is hard to find. Therefore, since money can’t buy happiness, people who have money will be sad.
(5) We should declare war on drug dealers; and this is so for the reasons that they bring about poisonings, they corrupt our children, and they bring blight to neighborhoods.
Suggestions for further reading:
The classic textbook on the subject of basic logical rules and procedures is Introduction to Logic by Irving Copi; any edition is a good one.
Also there is Introduction to Logic and Critical Thinking, Merrilee H. Salmon; this is strong on certain types of arguments where probabilities are at issue.
published 3/16/20
(1) Put your money where your mouth is! No one wants to hear mere words. Do you think I’m interested in your opinions?
No argument here. There is only one claim being made here: No one wants to hear mere words. The other sentences are not in informative language and so cannot be part of any argument.
(2) The roof is supported by the walls, and which also are supported by the foundation, and which also sits on the ground. Therefore, the roof is supported by the ground.
The roof is supported by the walls, and which also are supported by the
foundation, and which also sits on the ground
The roof is supported by the ground
It is tempting to think that there are three premises here, and so that the argument would be laid out in the following way:
The roof is supported by the walls
The walls are supported by the foundation
The foundation sits on the ground
The roof is supported by the ground
But this is not the correct way to diagram this argument. The temptation to interpret this as having three premises comes from thinking that the words “and which also” are indicators of premises, but they are not. Words like “and,” “or,” and so on are connectors of information, not indicators. We will use these and other connectors in the future.
(3) The ocean tides are caused by effects of the Sun and Moon; they happen because of the gravity of these bodies, even though they are far away.
No argument here. This was a trick question that makes use of the term “because,” making you think that this indicates a premise. Sometimes it does and sometimes it does not; in this case it does not indicate a premise but an explanation. The key as to why this is an explanation is that it says: “A happens because of B.”
(4) We can claim that many people are just not happy, since happiness is hard to find. Therefore, since money can’t buy happiness, people who have money will be sad.
There are two arguments here; there has to be because there are two conclusions.
Happiness is hard to find
Many people are just not happy
Money can’t buy happiness
People who have money will be sad
Note that “we can claim that” is serving to indicate a conclusion for the first argument, and the second conclusion is indicated by “therefore,” even though that indicator is separated from that conclusion.
Now it’s possible also to diagram these arguments in the following way; in other words, treating the first conclusion as a premise for the second conclusion:
Happiness is hard to find
Many people are just not happy
Many people are just not happy
Money can’t buy happiness
People who have money will be sad
In many cases it is not obvious whether we should treat the conclusion of one argument as a premise for another in the same passage; that will all depend on the intentions of the person making the argument, and this is something that we have to guess from the connection between that statement and the end conclusion. In this case there is no clear connection between many people not being happy and people having money being sad; there needs to be a relevance between them for there to be a reason to think that the person making the argument intends this as evidence, at least without further information. So we can’t be sure of this diagramming until we know more about the intentions involved.
(5) We should declare war on drug dealers; and this is so for the reasons that they bring about poisonings, they corrupt our children, and they bring blight to neighborhoods.
Drug dealers bring about poisonings
Drug dealers corrupt our children
Drug dealers bring blight to neighborhoods
We should declare war on drug dealers
Notice here that the premises have to be complete sentences, so the “they” in each case has to be removed and replaced with what it refers to. Also note that there are three premises intended here, as the indicator words for the premises says: “for the reasons that.” If the intention of the person making the argument was to produce one piece of evidence, they would have said: “for the reason that.”
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