Study Guide

Week Two: Argument - The Tools of the Trade

Materials Assigned for the Week
The Central Point of This Week's Material
Other Concepts and Points you are Expected To Master This Week
Miscellaneous Comments and Clarifications

I. Materials assigned for the week

Reading:

Lecture 2: Deductive Arguments
Lecture 3: Inductive and Abductive Arguments
(lightly, we return to them in Weeks 5 & 6)

Reading:

Review Questions: pp. 19, 34-5
Problems for Further Thought: pp. 19-20, 35-36

II. The central point of this week’s material

A philosopher’s main tool of investigation is not experimentation or simulation or field research, but argumentation. Just as there is a tight difference between good and bad experimental and field design, so too there is a tight difference between good and bad argumentation. This week introduces the method of using argumentation fruitfully, and some of the main tests for good versus bad arguing. Sober discusses three distinct forms of tried and true methods of argument: deduction, induction, abduction.

III. Other concepts and arguments you are expected to master this week

The difference between a list of examples (e.g. of morally good deeds and people), a general definition (e.g. of moral goodness) and an argument (e.g. that such and such law or act or person is or isn’t morally good)
The general form of an argument; and especially the difference between the premises of an argument and the conclusion of an argument
How to spell "premises" - this word can be spelled two ways: "premises" and "premisses" - it won’t be often that you will be allowed any margin of error for spelling in 134.101 (this is one of the exceptions which proves the rule)
The difference between the appraisal (of single sentences only) "true/false" and the appraisal (of whole arguments only) "valid / invalid"
The difference between validity and soundness (valid logical form plus premises which are true as well)
Conditionals and the difference between "if P then Q" and "if Q then P" - transposing ordinary English "if ... then..." sentences into their proper "if P then Q" logical form can sometimes be tricky; be patient and practice
The fallacy of begging the question - and why it is an error of argument rather than, say, morals
The difference between a particular observation and a universal law
The difference between an a priori concept or belief and an a posteriori one - more of this in Week Three, but best to have it under your belt sooner, see the Box on pg. 83 and Sober’s discussion on pp. 80-81 and 89-91
The difference between deductive, inductive and abductive arguments - see section IV.D below for more help)
The "Surprise Principle" versus the "Only Game in Town Fallacy" as methods for testing abduction

IV. Miscellaneous comments and clarifications

IV.A. A list of "argument words" for premises and conclusions

The arguments you meet with in Sober, and most philosophy textbooks, are usually set out quite carefully. The general skeleton of a deductive argument, for instance, is this:

Premise 1: blah blah blah

Premise 2: blah blah blah

therefore

Conclusion 3: blah blah blah

This argument starts off by listing the premises. Then follows a "logical" word such as "therefore". (Sober uses a long line to separate the premises from a conclusion - it’s much of a muchness.) At the end, the conclusion is set out. Real life is rarely so tidy. What is actually the conclusion of some piece of reasoning can occur practically anywhere in a piece of written prose: beginning, middle or end. Likewise what is actually a premise. And often there is no marker "therefore" or long line. To help you find your way, it might help to have a short list of "cue" words. These aren’t meant to exhaustive lists, only rough and ready guidelines.

Commonly one or more of the premises for something is preceded by words such as these:

"since"
"because" [though there are lots of exceptions here]
"firstly", "secondly"...
"for"
"as"
"assuming that"
"in view of the fact that"
"follows from"
"as shown by", "as indicated by"
"may be inferred from", "may be deduced from", "may be derived from"
"if" (as in "if X, then Y")
"only if" (as in "Y only if X").

A conclusion is commonly preceded by one of the following words:

"so"
"therefore"
"hence"
"consequently"
"suggests that", "proves that", "demonstrates that"
"entails"
"implies"
"it follows that"
"then" (in "if X, then Y").

There is another set of words which you should become sensitive to as well, because they masquerade as premise-introducing or (more commonly) as conclusion-introducing words, but aren’t really either. Instead, their purpose is to stop further discussion cold. I call them "weasel words". Professor Schouls calls them "clobber words". Here are some:

"of course" [This is the worst offender; whenever you hear it be suspicious. Of course.]
"obviously"
"naturally enough"
"we are all agreed that"
"common-sense says", "reason says"
"it goes without saying that"
"it is obvious that", "it’s self-evident that"
"any fool can see that"
"it’s plain as a pikestaff that"
"science tells us that", "science has now proven that", "any scientist will tell you"
"it’s beyond argument".

A rewarding exercise would be to add as many similar items as you can to the three lists. Good hunting!

IV.B. The definition of "validity"

This is the absolutely crucial concept to master this week. If you do nothing else but that, you will be well ahead of the game.

Sober writes (pg. 11):

"An argument is valid or invalid solely by virtue of the logical form it has.... I will now define deductive validity:

A deductively valid argument is an argument that has the following property: IF its premises were true, its conclusion would have to be true.

I’ve capitalised the word IF. I’d print it in bright colours if I could, because it is important not to forget this two-letter word. A valid argument doesn’t have to have true premises. What is required is that the conclusion would have to be true, IF the premises were true."

Sober can print this in bright colours until the cows come home, but it will still be a Dark Saying. Take the following argument.

Premise 1: If the moon is made of green cheese, then I’m a typewriter

Premise 2: The moon is made of green cheese

therefore

Conclusion 3: I’m a typewriter

This is valid in logical form. (Compare Sober’s example about plants and ladders on pg. 11.) Caught in a panic, however, what are you going to do? Quick! Well, go through the mantra sotto voce: "If the premises were true - which wildly they aren’t - then the conclusion would have to be true". But how are you going to tell that? In a panic! Quick! That is, how are you going to tell whether some weird statement would have to be true in bizarre circumstances where the other statements it is supposed to depend on aren’t themselves true? Take a deep breath. Sober is asking you to consider a hypothetical situation, indeed what is sometimes called a counter-factual hypothetical situation. In that hypothetical situation, would so and so happen. If "yes", then the argument is valid. If "no", then the argument is invalid. Still, it’s a heck of a thing to ask a 101 student in only the second week of classes!

An equivalent definition of "validity" may help. It goes more directly to the "logical" words "would have to be true" in Sober’s definition, which is really where the action is.

An argument is deductively valid if it is logically impossible for the premises to be true and at the same time the conclusion be false.

This too asks about a hypothetical situation. So maybe it will help if I explain what thinking yourself into such little science fiction stories is supposed to reveal.

Take notes! Wherever you are going to do these things, write down the two definitions above. By the end of the following discussion, you should be able to see why they are two ways of expressing the very same concept. Validity should no longer be a Dark Saying to you.

Think of what the Building Inspector does when he gets out of the office and looks at a house going up. He is looking, really, at whether we’ve got a "well-formed" house here. For instance, a house will not be well-formed if the doors don’t have lintels, or if the roof doesn’t stand on walls, or if the wall above a window rests directly on that window. He has a list of all these structural requirements (suppose). They could be put in terms of hypothetical situations too: If the roof doesn’t rest on a wall, the house as a whole doesn’t pass the test of well-formedness. And the inspector uses a hypothetical situation to tell whether the roof is so resting: If the roof could fall down while the walls didn’t, then plainly the roof wasn’t really resting on those walls but on something else. After all, if the roof was - in our hypothetical situation - resting on a wall, then the roof couldn’t have fallen to the ground unless the wall did. We all know why these are proper tests for well-formedness in houses. If an actual house he is inspecting fails these hypothetical situations, then it may well fall down in a slight earthquake, it’s not trust-worthy to live in. So thinking in terms of hypothetical situations isn’t all that strange an idea for testing matters of actual structural integrity.

It’s much the same with trains of reasoning. There are lots of things to be tested in trains of reasoning. But one of those things, and usually the first of them, is their structural integrity. A Validity Inspector too is really just looking at whether we’ve got a "well-formed" argumentative structure. There is a list of such structural requirements for arguments just as much as there is for houses. In particular, if the conclusion (roof) doesn’t properly "rest" on its premises (walls), then it doesn’t pass the test of well-formedness for arguments (houses). Moreover, thinking in terms of hypothetical situations is not a bad way to tell whether the conclusion does so rest on the premises. If the conclusion could be false (fall to the ground) even were the premises true (standing), then it couldn’t have been that that roof (conclusion) rested on those walls (premises). If the conclusion (roof) really did rest on the premises (walls), then the roof couldn’t have fallen unless the walls had. So if, in a hypothetical situation, we find that when the conclusion (roof) has fallen, the walls (premises) must have fallen too, then the argument structure passes the test: it is a valid structure. Otherwise that conclusion wasn’t really resting on those premises after all, but on some others or on nothing at all: it is an invalid structure.

A Validity Inspector inspects for the structural relation between conclusion and premises exactly as a Building Inspector inspects for the structural relation between roof and walls. Both are testing for structural integrity.

Now apply these ideas to the following argument.

Premise 1: If I don’t pay my electricity bill, then Genesis Energy cuts off my power

Premise 2: I don’t pay my electricity bill

therefore

Conclusion 3: Genesis Energy cuts off my power

Let us test it for validity. What is such a test supposed to reveal? First of all, what it is not supposed to reveal? It is not supposed to reveal something about the truth or falsity of the individual premises used, or even the truth and falsity of the conclusion deduced. Instead, it is supposed to reveal that the set of premises are related to the conclusion in a certain way. That is, again, we are getting at a structural feature of the whole. This relation of premises to conclusion is tested easiest by forgetting entirely the actual world and stepping into a thought-experiment or hypothetical situation. Here are several equivalent thought-experiments.

First thought-experiment: Imagine the premises to be true; could the conclusion also be imagined to be false? Start off constructing a hypothetical situation in which the premises were true. Then ask yourself: could the conclusion - in that hypothetical situation - be false? If yes, the argument is invalid in its logical form. If no, it’s valid. Here the answer is plainly "No". I imagine a situation in which the first premise is true; it’s not a hard situation to imagine because it’s discouragingly close to real life in the Manawatu. Then I tinker with that hypothetical situation so that in it the second premise is also true; I imagine in that hypothetical situation that I clean forgot everything, like I did last February. Now I ask myself: in that hypothetical situation could the conclusion be false? No, in that hypothetical situation - where I imagine that Genesis Energy is God and where I imagine that I have forgotten - it couldn’t happen that the conclusion was still false: that my power hasn’t been turned off. My hypothetical world has no room for miracles; it’s a world in which Genesis Energy works like a machine and I don’t. If I don’t pay up, off it goes.
Second thought-experiment: Imagine the conclusion to be false; could the premises also be imagined to be true? Here I start off the opposite way . I imagine a hypothetical world in which my power hasn’t been turned off. I’m sitting nice and rosy. Could I - in that hypothetical situation - also imagine that both premises were true? Well, I could imagine being rosy and also being forgetful easily enough. That is, the hypothetical situation is easily tweaked so that Conclusion 3 is false in it and the Premise 2 is true. But would I be able to add into that hypothetical world the truth of Premise 1? No. If I’m to imagine myself sitting rosy and forgetful, then I must also imagine that something has broken down with Genesis Energy’s billing or supervisory system (i.e. that Premise 1 is false). Otherwise, how could I still be rosy?
Third thought-experiment: Can the conjunction of circumstances be imagined, the premises true plus the conclusion false? The Building Inspector is really checking whether two things can happen at the same time: the walls of my house standing and the roof falling down (let us suppose). Similarly, a Validity Inspector is really checking whether two things can happen at the same time: the premises being true and the conclusion being false. So let me try to imagine that. That is, I try to imagine two hypothetical situations coming together. First I construct a hypothetical situation in which the premise set is true. Easy enough, I imagine the situation to be much like last February. Next I construct another hypothetical situation, in which the power hasn’t been cut off and I am sitting rosy. Now I try to imagine both those hypothetical situations happening together at the same time. Nope, I can’t do it. If the first situation is in place, the power’s off. If the second situation is in place, something must have happened to change the first situation. I can’t imagine both together.
Fourth thought-experiment: Can you imagine a hypothetical situation in which the following assignments of truth-values are possible for your argument?
- Premise 1: true
- Premise 2: true
therefore
- Conclusion 3: false
This puts all of the previous tests into an explicit argument form with separate premises and conclusion. If you can imagine a hypothetical situation in which exactly this combination of truth-values are assignable to the various steps, then the argument is invalid. But remember, it has to be precisely the combination: {true, true, therefore false} and no other.

Contrast! As you read the following non-examples, keep flicking up to the shaded assignment of truth-values and comparing. Tick off which step is different; Work out why the difference makes a difference.

Non-example:

Premise 1: true
Premise 2: false

therefore

Conclusion 3: false

Non-example:

Premise 1: true
Premise 2: false

therefore

Conclusion 3: true

Why aren’t these examples? The reason is this. The validity/invalidity test requires the conclusion to be able to be false while the premises are able to be true. It says nothing about the very different hypothetical situation in which you can imagine the conclusion to be true, say, or in which you can imagine one of the premises to be false. I know it’s confusing. However, validity is the single most important tool in the philosophical toolkit. You must become comfortable using it. The shaded assignment of truth-values will invariably test for validity of logical form. If those truth-values are a logical possibility, then you have an invalid argument on your hands. If they are logically impossible, your argument is valid.

IV.C. Deduction, induction and abduction

Each of the three different types of arguments Sober sets out has a characteristic form. The deductive forms are plainly set out in Lecture 2, the others less so in Lecture 3.

The format of deductive arguments

These are mostly the types of examples we have met already:

Premise 1: if Q then R

Premise 2: if P then Q

therefore it follows that

Conclusion 3: if P then R

and the like. [The example is actually a "stretched" modus ponens called "hypothetical syllogism" - see the next section IV.D for some of these labels.]

Here we take a whole sentence, any sentence will do, and substitute it for the letter "P" in the shaded argument form. (The letter "P" is just a place-holder for a sentence; it doesn’t mean anything itself.) Then we take another sentence, any other sentence, and substitute it for the letter "Q". We work down the rest of the structure making the same substitutions. (Sober’s own substitutions are about where Sally lives, pg. 13.) Bertrand Russell is responsible for making this argument form the first choice for more philosophers.

But there is another format for deductive arguments which is almost as common:

Premise 1: all Bs are Cs

Premise 2: all As are Bs

therefore

Conclusion 3: all As are Cs

Here we substitute not whole sentences but kinds of things or kinds of properties for the placeholders "A" and "B". We owe this account of the logical form of deduction to Aristotle.

The first is often called propositional logic and the second syllogistic logic. This is not a difference which makes a difference in 101, because almost any argument which can be written the first way can also be written the second way, and vice versa. Take Sober’s "all fish swim" example from pg. 10. His perfectly ordinary English argument can be written either way:

Premise 1: all fish things (Bs) are swimming things (Cs)

Premise 2: all shark things (As) are fish things (Bs)

therefore

Conclusion 3: all shark things (As) are swimming things (Cs)

Equivalently:

Premise 1: if this thing is a fish (Q) then this thing swims (R)

Premise 2: if this thing is a shark (P) then this thing is a fish (Q)

therefore

Conclusion 3: if this thing is a shark (P) then this thing swims (R)

Kinds in the first. Whole sentences in the second. The thrust of the reasoning is the same.

The format of inductive arguments

Induction is a different kettle of fish(!) Inductive arguments are neither deductively valid nor deductively invalid, for they are not deductive at all. One way to emphasise this is to qualify the word "therefore". It does not carry the force of "guarantees" in the sense of "it is logically impossible for the premises to be true and the conclusion false".

Premise 1: In observed case n, an example of A is an example of B

Premise 2: In observed case n+1, an example of A is an example of B

Premise 3: In observed case n+2, an example of A is an example of B

Premise...
therefore probably

Conclusion: In the as yet unobserved case n+x, an example of A will be determined to be a case of B as well

The conclusion here is not a deductive "must" but an inductive "probably".

More usually, induction is used to generalise not to predictions such as "The next A will be a B" but to generalise to universal conclusions such as "all As are Bs":

Premise 1: In observed case n, an example of A is an example of B

Premise 2: In observed case n+1, an example of A is an example of B

Premise 3: In observed case n+2, an example of A is an example of B

Premise...
therefore probably

Conclusion: In all cases (observed and unobserved, past and present), examples of As are examples of Bs

Induction also delivers "probabilistic" conclusions another way, by dealing openly with fractions and percentages and statistics (which is just a measure of the number of cases observed in which A is B after all). Thus Sober’s example on pg. 21.

Premise 1: In 60% of the cases called, the phone respondents (As) said they were Democrats (Bs)

therefore probably

Conclusion 2:In 60% of the cases in the whole country, the phone respondents (As) are Democrats (Bs)

This is a just terrible deductive argument. Because it is quite easy to imagine a hypothetical situation where the premise was true and the conclusion false: the phone respondents are fed up with surveys and lied. But it’s not quite so awful an inductive argument: voter polls are some guide to voter allegiances.

Note there is something very differently wrong with Sober’s second example on pg. 21. It is neither a good deductive nor a good inductive argument.

Premise 1: In 60% of the cases called, the phone respondents (As) said they were Democrats (Bs)

therefore probably

Conclusion 2:In 60% of the cases in the whole country, voters (As) are Democrats (Bs)

Notice that the substitution for the placeholder "A" has changed going from the premise to the conclusion. In the premise As were phone respondents; in the conclusion they have become not people who answer their phones but people who actually go out and cast votes on voting day. So we really have three placeholders working here: phone respondents (As), Democrats (Bs), and voters (Cs). Or maybe it is really four: phone respondents (As), people who belong to the Democratic party (Bs), voters (Cs), people who will vote for a Democratic candidate (Ds). Arguing carefully is never a piece of cake!

The format of abductive arguments

Abduction is sometimes confused with induction, because it is usually one half of how scientists actually work and it is often confusedly thought that scientists work by induction. It is better to think of induction as "straight generalisation". Think of abduction as "inference to the best explanation". They will be less easy to confuse then. Mark, again, the difference from the deductive "therefore". Here is the typical inference form:

Premise 1: It is a surprising fact that A is B

Premise 2: If theory T were true, then it would follow as a matter of course that A is B (and it would continue to be a surprising fact that A is B were theory T not true)

therefore the best explanation we have got so far is

Conclusion 3: Theory T is true

This way of putting it was first articulated by the twentieth-century American philosopher Charles Sanders Peirce; it is what Sober puts in his "Surprise/No Surprise" box, pg. 31. Such a form of argument does not deductively prove that theory T is true, of course. It is not meant to. Abduction is not deduction and doesn’t pretend to be. All the argument does is move theory T to the top of the heap of explanations currently being worked on. The second part of the scientific method uses good old-fashioned deduction (modus tollens in fact), to try to prove the theory false:

Premise 1: if theory T is true then consequence Y should happen

Premise 2: Y did not happen after all

therefore

Conclusion 3: theory T can not be true

That is why scientists are always on the lookout for disconfirmations of theories. A counter-example deductively proves a theory is false. By contrast, a mere example helps establish that some experiment was well-designed (it is "replicable" by other experimenters). Rarely, however, are inductive confirmations, no matter how plentiful, taken to show that some theory has been proven to be true, only that it may be interesting. Indeed, scientists are so embraced of disconfirmability that a theory which is designed not to be disconfirmable even in principle is thereby a Bad Theory. A Good Theory is one which has survived many attempts to disconfirm it, the more the merrier. (Compare Sober’s treatment of Mendel, pp. 25-28.)

Sober’s introductory discrimination of abduction from induction gives an equivalent logical form for abduction, without all the qualifications above on "therefore":

Premise 1: Facts X Y Z need explaining

Premise 2: Theory T explains facts X Y Z

Premise 3: Although there may be other theories which will also explain facts X Y Z, none of those theories explains those facts so simply or so economically or so elegantly or so systematically or so fruitfully or so parsimoniously … as theory T

therefore

Conclusion 4: Theory T is the best explanation available to us right now of facts X Y Z

therefore

Conclusion 5: Theory T is probably true. (Or at least is more probably true than any of its present competitors.)

Again, this doesn’t prove once and for all that theory T is true. But such an abductive justification of theory T can be well-done - and badly done too of course. Sober nicely discusses how to do it well (pp. 29-34).

IV.D. A checklist of valid versus invalid deductive arguments - for reference purposes

Sober pg. 19 sets out four similar looking logical forms. Very similar looking. They each have special names. (a) is called "modus ponens"; (b) is called "affirming the consequent"; (c) is called "denying the antecedent"; (d) is called "modus tollens". Do not memorise these names. But do memorise - there is no simpler way - that (a) and (d) are valid, while (b) and (c) are invalid!

Advice! Best, of course, not to simply memorise, but to prove this to yourself.

Sober makes the excellent point that holding up a confusing real-life example against the list of argument forms is a good - sometime the best - way to proceed. Here is a bit more on why each of the basic forms is what it is (valid or invalid).

Valid Argument: "Modus Ponens"

Premise 1:if P, then Q

Premise 2: P

therefore

Conclusion 3: Q

Example (note the true premises):

Premise 1:If I drop this piece of toast, then the toast will fall jam side down

Premise 2:I drop this piece of toast

therefore

Conclusion 3:The toast will fall jam side down

The hypothetical situation we need to construct to test validity is easy here: is it possible for the premises to be true and the conclusion false? Plainly "no". Imagine a hypothetical world in which nature works according to the law "Dropped toast falls jam-side down" (i.e. imagine a hypothetical world in which Premise 1 is true). Inject yourself into that hypothetical world and drop some toast (i.e. imagine that Premise 2 is also true). Can you imagine that law being obeyed and yet the toast flying upwards (i.e. the Conclusion being false)? Or the toast landing jam-side up? Nope.

What’s nice about having the structure in the shaded box available is this. If your powers of constructing hypothetical worlds are shaky (or get shaky under the pressure of exams and caffeine), all you need is to double-check that you have sentences which are substitutions for the "if P then Q, P, therefore Q" structure, and you’re home free. You need to understand the idea of constructing hypothetical situations in order to understand the idea of validity. But when you come actually to test some argument for validity, you are actually forced to go through the rigmarole of constructing one. All you really need is a list of valid forms, and to be able to check the argument against them.

Example (note the false premise this time):

Premise 1:If I drop this piece of toast, then the piece of toast will soar off to the moon

Premise 2:I drop this piece of toast

therefore

Conclusion 3:The piece of toast will soar off to the moon

This argument is exactly as valid as the previous one. It passes exactly the same tests for validity. (What gives it its whiffy smell is not that it is invalid in its logical form, but that one of the premises is so ridiculously false.)

Valid Argument: "Modus Tollens"

Premise 1:if P, then Q

Premise 2:not Q

therefore

Conclusion 3:not P

Example (true premises):

Premise 1:If the IRA offensive succeeds, then there will be more bomb attacks in Manchester

Premise 2:There are no more bomb attacks in Manchester

therefore

Conclusion 3:The IRA offensive has failed

Example (false premises):

Premise 1:If two plus two make eleven, then civilization as we know it is at an end

Premise 2:Civilization as we know it is not at an end

therefore

Conclusion 3:Two plus two do not make eleven

Cockeyed as the first premise is, this argument is exactly as valid as the one before it. It substitutes sentences for letters in exactly the same formula. And if you constructed a hypothetical situation in which the premises were true (a pretty strange world that), in that hypothetical situation it would be impossible for the conclusion to be false.

Invalid Argument: ("Fallacy of Denying the Antecedent")

Premise 1:if P, then Q

Premise 2:not P

therefore

Conclusion 3:not Q

Example (true premises):

Premise 1:If the marker has given you an A, then you are a happy chappy

Premise 2:The marker has not given you an A

therefore

Conclusion 3:You are not a happy chappy

I expect that this argument looks perfectly valid to you (first glance anyway). But it isn’t. It is quite invalid! It appears valid - and this appearance is very beguiling - particularly because it is a sort of cross between the two main valid forms. In Premise 2: "not P", it is really taking the "not" from Modus Tollens and combining it with the "P" from Modus Ponens. This encourages us to run quickly, too quickly, from Premise 2 to Conclusion 3: not getting a mark of A would be upsetting, so of course there must be a valid connection here.

How can one tell that this combination makes things invalid? For a start, you can tell by rote memory. The crossed-out argument form is an invalid one - I’ve just told you - and the sample argument was constructed simply by filling in the letters with sentences. That’s not an adequate answer of course. Philosophers don’t accept anything on authority alone, and that goes for anything I say too. Better back to basics. Always better back to basics. Ask yourself: is it possible for the premises to be true and the conclusion false? It is not hard to construct a hypothetical situation in which the first two premises are true. The first is human nature. And by the rules of the university the second has to be true for at least 85% of you. Now inject yourself into that hypothetical situation; imagine being one of those 85%. Is it possible to be one of them and for the conclusion to be false? Certainly. The conclusion will be false if - in that hypothetical situation - you still manage, somehow, to be a happy chappy. Well, that’s certainly possible: you might have won Lotto, you might be delirious with just a B, you might have got promoted, or married, or have a new baby … or a zillion other things.

The key is that the first premise really just sets out one of the things that can make you a happy chappy. As long as there are other things that will make you happy, then the absence of that specific happiness-maker doesn’t put a lid on it. More abstractly: The first premise "if P then Q" says that P is one way to effect Q. The second premise "not P" merely says that that particular antecedent didn’t happen. But as long as it is logically possible that other things can bring about Q, there is no reason to think that if P doesn’t happen it is impossible for Q to happen. It can be easy to confuse this with the Modus Tollens form: "if P then Q", "not Q" , therefore "not P"; there the non-happening of Q does indeed guarantee the non-happening of P. In the invalid form, however, we are trying to argue the other way around: that the non-happening of P guarantees the non-happening of Q. It doesn’t do any such thing.

Example (false premises):

Premise 1:If this is a weekday, then this is a day I have no teaching

Premise 2:This is not a weekday

therefore

Conclusion 3:This is a day I have teaching

Premise 1 happens to be false. But that is not why the argument is invalid. (That is never why an invalid argument is invalid.) It is invalid because it is logically possible for both premises to be true and the conclusion still be false. Here is such a hypothetical situation: I have retired from Massey - so Premise 1 is true, because I no longer have any teaching duties during the normal teaching week. Today is Saturday - so Premise 2 is also true. Lo and behold, there I am sitting in front of the tele all day - Conclusion 3 is false.

I’ve given you two of the simplest valid forms and one corresponding invalid form. Actually there are two corresponding invalid forms. The second is this:

Invalid Argument: ("Fallacy of Affirming the Consequent")

Premise 1: If P then Q

Premise 2: Q

therefore

Conclusion 3: P

Exercise! Do for this new invalid form what I did for the previous one.

That is:

Determine that it is indeed invalid. Apply the test: is it logically possible for the premises to be true and at the same time for the conclusion to be false?
Find some examples of invalid arguments of this form. Substitute some whole sentences for the placeholder letters.
Become comfortable with the argument form and why it is different from the others. Make its invalidity leap off the page for you.

Contents
Previous Week: Philosophy and the Craft of Giving Reasons
Next Week: What is Knowledge?