The Difference Between Content and Form

“Linguistic forms are not merely instrumental, but fundamental—not only to persuasion, but to thought itself.”

(Gideon O Burton)

To recap, when analyzing an argument, it is best to first rearrange the data so that the relationship between premises and conclusion can be seen clearly. We need to focus on the structure; the form.

In analyzing the structure or ‘form’ of an argument, its content is irrelevant. It will be easier to understand the difference between the content and form of arguments if you consider another example with the same underlying form as the one above:

Assertion: “A spaceship landed near my farm”.

Argument: “I know it did because there’s a crop circle in my corn field.”

Analysis (the speaker is assuming the premises (1) and (2) below to be true, and drawing the conclusion (3)):

(Unspoken premise) Crop circles are made by spaceships landing.

(Spoken premise) There’s a crop circle in my corn field.

(Spoken conclusion) So a spaceship landed near my farm.

Like the previous argument, IF the premises are true, THEN the conclusion must be true. You can question whether or not the premises are true (for instance, you might think that a spaceship landing is not the only reason for a crop circle). But IF the premises are true, THEN the FORM of the argument is such that it follows that it’s true that a spaceship landed near the farm.

Conclusions are often stated in ordinary conversations as though they were facts, thus contributing to general confusion between those who do not share the same unspoken premises, especially when this disparity of underlying assumptions is not known.

In most conversational contexts one or all of the underlying premises remains unspoken. For instance, if I said:

“Androids are humanoid”

“So they have four limbs”

it is fairly obvious that I assumed you would realize I believe the unstated premise:

“All humanoids have four limbs”

even though I hadn’t spelt that out for you. With scientific arguments, it is usual to try to make explicit any such unstated premises so that the underlying structure of the argument becomes clear as an hypothesis. Unstated premises are called ‘implicit’ premises.

To make sure you’ve grasped the idea of implicit premises, do the following exercise:

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Implicit premises

What is the unstated premise in each of 1-5 below? For each one, write down your answers in the following ways:

1. unstated premise
2. stated premise
3. conclusion

1. Alice is creative, so of course she likes problems to solve.

2. Your landing gear is damaged, so your craft will never get off the ground.

3. Bob is a man, so he is mortal.

4. Laughing helps to improve your thinking skills, so you should laugh frequently.

5. I am the Internet. I think, therefore I exist.

Now check your answers against those shown at the end

The Difference Between Truth & Validity

"Evil does seek to maintain power by suppressing the truth."

"Or by misleading the innocent."

(Spock and McCoy, "And The Children Shall Lead")

We looked earlier at the following argument:

• “If free will did exist, nobody would ever have to do anything they didn’t want to do.”
• “Some people do have to do things they don’t want to do”
• “So free will doesn’t exist.”

This is a VALID argument. IF the premises are true, THEN the conclusion must be true. We use the words ‘valid’ and ‘invalid’ only to refer to the structure of arguments. AN ARGUMENT CAN NEVER BE TRUE OR FALSE; IT CAN ONLY BE VALID OR INVALID.

Things that can be true or false are things like statements, conclusions, assertions, assumptions, hypotheses, beliefs or premises. But NOT arguments. You may have to work at remembering this.

You will understand that the way we use language to describe reality in rational analysis is not the same as it is commonly used in colloquial or everyday ways –we are using specific words here to define specific ideas, and these ideas are what it is intended you should grasp. In ordinary conversation the terms ‘true’ and ‘valid’ are interchanged largely through ignorance of their meaning, so do not let this confuse you. People often say “That’s a valid point” when in reality they mean “I think what you said is true”.

There is a great deal of difference between validity and truth.

A valid argument has a structure that works like a calculator program: it guarantees a true conclusion provided you feed in true data. It is ‘truth-preserving’. However, if you feed in false premises, you may or may not get a true conclusion, and you certainly couldn’t be sure of getting one.

For instance, in the argument we’ve been examining, if the premises are true, then the conclusion that free will doesn’t exist must be true. This is a valid argument. However, IF one or both of the premises are false, THEN there is no guarantee that the conclusion is true, despite the argument’s validity. The question of validity or invalidity must be addressed separately from the question of truth or falsehood. Validity is about the form of the argument; truth of premises & conclusion is about its content.

A valid argument presented with true premises is the best way of guaranteeing true conclusions. Such an argument is called “sound”.

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At this point it is worth practicing some of the key ideas introduced so far. Use the answers at the end of the tutorial to help consolidate your understanding.

Key ideas

 Underline or highlight the conclusion in each of the following arguments:

• Robots don’t eat animals. Chickens are animals. I eat chickens. So I’m not a robot.
• You can’t have any pudding. The only way to get any pudding is to eat your meat. You won’t eat your meat.

 Underline or highlight those of the following that are valid arguments:

• Robots don’t contain animals. Nuts and bolts are animals. So robots don’t contain nuts and bolts.
• All humans are mortal. Robots are machines. So robots are mortal.
• Anyone who walks on a cliff has a small chance of falling off. Alice walks on cliffs. So she has a small chance of falling off.
• All forms of killing are morally wrong. Criminal execution and war are forms of killing. Therefore war and execution are morally wrong.

Match the following terms with the appropriate definitions, (a)-(h):

• Argument
• Assertion
• Prejudice
• Conclusion
• Implicit assumption
• Sound argument
• Premise
• Valid argument

• (a) an unstated premise
• (b) a structure that guarantees a true conclusion if the premises are true
• (c) a statement from which an argument’s conclusion is derived
• (d) a statement given without providing any reasons or supporting evidence
• (e) a belief that is formed without considering evidence for or against it
• (f) a statement derived from premises, from which it follows
• (g) reasons leading to a conclusion
• (h) a valid argument with true premises

Fake Argument Formulas that Can Con or Coerce: Fallacies

“There is some fiction in your truth, and some truth in your fiction. To know the truth, you must risk everything”.

(Animatrix)

Logic also reveals incorrect ways of reasoning. A set of statements that appears to be an argument but is not is called a fallacy. Consider the following statements:

• All starfleet officers wear uniforms
• My granny wears uniforms
• So my granny must be a starfleet officer

Is this a valid argument? NO. At first glance you might take it to be so. The structure seems similar to examples we’ve seen. However, if it had the exact same form, it would read:

• All starfleet officers wear uniforms
• My granny is a starfleet officer
• So my granny wears uniforms

THIS is a valid argument. IF the premises were true, THEN the conclusion would be true. 

The first example is known as a ‘fallacy’, because the conclusion doesn’t necessarily follow from the premises (regardless of whether or not the conclusion happens to be true.) The way the supposed argument is structured allows for the fact that someone could wear uniforms and yet not be a starfleet officer. As an argument, it is invalid; it does not fit the correct formula to produce a valid conclusion from premises.

Here’s another example of a fallacy:

• All wizards wear pointy hats
• My neighbor wears a pointy hat
• So my neighbor must be a wizard

Again you can see that the conclusion would only follow if the first premise read:

ONLY wizards wear pointy hats

So regardless of whether or not it is true that my neighbor is a wizard, the argument is fallacious: it is an invalid structure; one which is not truth-preserving. Even if the two premises were true, there is still the possibility of other people besides wizards wearing pointy hats.

Fallacies are exactly the sort of reasoning that advertising executives, religious leaders and politicians love, because less experienced thinkers can fall for and be conned or coerced by them (as the Monty Python team so aptly lampoons in the witch-trial scene of “Monty Python & the Holy Grail”). In addition to faulty reasoning, such fallacies are often based on possibly false premises such as ‘wizards actually exist’. This can lead to certain characteristics (such as wearing pointy hats) being used as conclusive evidence that this or that person is a wizard.

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Fallacies

Which of the following are fallacies, and which are valid arguments?

1. All geniuses have been slightly crazy. I’m slightly crazy, so I’m a genius.
2. All children feel insecure. You’re a former child, so you must have felt insecure.
3. If you do something wrong, you get questioned by the police. You’ve been questioned by the police, so you must have done something wrong.
4. Some creative people have bipolar disorder. You’re not very creative, so you can’t have bipolar disorder.
5. All religions get donations. Sex in spaghetti is a religion. So spaghetti-sex worshippers should get donations.

The answers are at the end of the tutorial.

All the examples here of fallacies are of ‘formal fallacies’, which break specific rules of logic, but there are also ‘informal fallacies’ which usually are phrased to appear as an argument but the statements purporting to be premises to do not support the conclusion. One example of this is called a "circular argument", in which the conclusion is used as the premise; for example: “Why is taking drugs illegal? I’ll tell you why. It’s because it’s against the law!”

Since "illegal" and "against the law" are the same concept, the speaker in the above informal fallacy is using the fact that taking drugs is against the law to prove that it is illegal. In effect the speaker is just repeating the same statement two times. Nothing has been proven.

Deduction and Induction

“I fail to comprehend your indignation, sir. I have simply made the logical deduction that you are a liar.”

(Spock, ‘The Alternative Factor’)

The examples of arguments we have considered so far have all been ‘deductive’ arguments; that is to say that they have all been constructed in a form such that if the premises are true then the conclusion must be true. However, there is another type of valid argument, and this second type DOESN’T guarantee the truth of the conclusion even if the premises are true.

A deductive argument is one in which the conclusion is certain based on the premises. In a deductive argument the conclusion is contained in the premises, much as in classical physics conclusive results are based on physical mechanics.

An inductive argument is one in which the conclusion is a probability based on the premises. In an inductive argument the conclusion goes beyond the premises, much as in quantum physics probabilistic results are based on quantum mechanics.

Inductive arguments are usually based on evidence which by its nature is not easily conclusive: conclusions can only be probabilities; never certainties. For instance, the following is an inductive argument:

All the scientists Bob has ever met had brown hair.

Therefore all scientists have brown hair.

The fact that Bob has met quite a few scientists, and that they all had brown hair, seems to support the conclusion that all scientists have brown hair. However, it only takes one non-brunette scientist to undermine this generalization. Bob cannot be absolutely sure that there is not a blonde or redhead scientist on the planet somewhere. For all he knows, brown-haired scientists worldwide may even be in a minority.

If other people from other places also report in that they have never met a scientist whose hair wasn’t brown, this lends further support to Bob’s conclusion. Yet even then the possibility would remain that a non-brunette scientist would show up.

This inductive argument is very different from a deductive one because even if the premises are true, you cannot be certain that the conclusion is true. It just gives us a probability; a likelihood, of truth. The more information we have, the higher our probability of truth, but we can never say with 100% certainty that we are correct.

Inductive reasoning draws general conclusions from specific examples, deductive reasoning draws logical conclusions from definitions and axioms. A similar pair of complementary processes are analysis and synthesis (Analysis takes an object of study and examines its component parts, and mainly uses the processes of network 5 of your brain; and synthesis considers how parts can be combined to form a whole, and mainly uses network 4.)

A common form of inductive argument is argument by analogy. This is an argument in which a conclusion is drawn about a situation based on analogies (similarities of this situation to previous, other or imaginary situations). For example, if we predict that since we have some heavy lifting to do in the cargo bay today a certain colleague will be suddenly absent, because in the past when there was similar hard work to do this person was always suddenly absent, we are making a probabilistic inductive argument based on an analogy with the past similar occurrences.

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Deduction & Induction

Which of the following use deductive reasoning and which use inductive? 

1. All mythical supreme beings are immortal. Zeus is a mythical supreme being. Therefore Zeus is immortal.
2. The sun has always risen in the past, so it will rise tomorrow.
3. All the people I have ever met enjoyed drinking beer. So all people must enjoy drinking beer.
4. If you make porridge on a full moon, it will always go lumpy. You made the porridge on a full moon, so it went lumpy.
5. All animals have a sense of smell. Humans are animals. Therefore humans have a sense of smell.

Answers are at end of tutorial