as a structure for thinking (Explanation A) ‘If … then …’ thinking Introducing ‘If P, then Q’ as a structure for thinking Common uses: promising, predicting, and planning

B. ‘If he wins this race, (then) I’ll eat my hat.’ (Explanation A) ‘If … then …’ thinking In pairs, decide which of the following uses is a promise, which is a prediction and which is a plan. A. ‘If they’re going to give free drinks, (then) more people are going to visit their shop.’ B. ‘If he wins this race, (then) I’ll eat my hat.’ C. ‘If you can keep the door open, (then) I’ll be able to get away.’

(Explanation A) ‘If … then …’ thinking Then as a whole group discuss the similarities and differences between predictions, promises and plans.

(Exercise A) More ‘If … then…’ thinking In pairs and/or groups 1. Invent and write down a prediction of your own in the form ‘If …, then ...’ 2. Invent and write down a promise in the form ‘If …, then …’ 3. Invent and write down a simple plan, in the form ‘If …, then …’

(Exercise A) More ‘If … then…’ thinking Also in pairs and/or groups 4. Then try to come up with 3 other examples of ‘If … then ...’ thinking. That is, examples that are not predictions, nor promises, nor plans. (If you finish before others, then wait patiently until everyone is ready to share.)

(Exercise A) More ‘If … then…’ thinking 5. As a whole group, share the examples and see if any of them can be grouped and named in the same sort of way as predictions, promises or plans.

‘If P, then Q’ One of the most common and important uses of the form: (Explanation B) Causes and Effects One of the most common and important uses of the form: ‘If P, then Q’ is to suggest that event P is a cause of event Q

Event Q is then said to be an effect of event P. (Explanation B) Causes and Effects Consider the sentence, :‘If you have a cold, then you have a runny nose’, It suggests that having a cold (P) is a cause of having a runny nose (Q). Event Q is then said to be an effect of event P.

Notice that an effect can, in turn, be a cause of something else. (Explanation B) Causes and Effects Notice that an effect can, in turn, be a cause of something else. For example, if you have a runny nose (Q), (then) you want to sniff (R)

(Explanation B) Causes and Effects In pairs or as a whole group, discuss whether getting a cold might itself be an effect of a previous cause (as well as being a cause of a runny nose in the near future). Express any cause you can think of in the form: ‘If …, then you might get a cold’. You could also discuss whether having a runny nose might have other effects (apart from wanting to sniff).

(Exercise B, 1–4) Causal Chains See if you can make a chain of causes and effects, using the example of catching a cold: 1. ‘If …, then you might catch a cold, and if you catch a cold, then you might …, and if you …, then you might …, etc.’ 2. Discuss if there only one such chain possible, or whether there could there be many different ones. 3. Make up a different causal chain, using events that have actually happened, with perhaps 5 events in the chain.

(Exercise B, 1–4) Causal Chains 4. As a whole group, (prepare for some mind-boggling questions!) discuss: Could an actual causal chain have been different from how it was? (b) If so, would it have been by cause or by chance?

(Exercise B, 5 - 8) Immediate Causes/Effects In pairs or groups 5. Discuss how many causes might lead up to a particular event, such as your catching your last cold or (more challenging!) your discussing this question. 6. Discuss whether in some cases we can say that event P was the last event before event Q, and ‘triggered’ or caused Q to happen. If so, be ready to give an example to the whole group.

(Exercise B, 5 - 8) Immediate Causes/Effects 7. As a whole group, share your thoughts and examples, and discuss whether there is actually a ‘trigger’ or ‘immediate cause’ in every case. 8. If so, agree on one example where it is clear what the immediate cause is, along with its immediate effect, and then in pairs or groups again make up 2 more good examples.

can just as well be expressed using the word because: (Explanation C) If and Because A causal chain such as ‘If you have a cold (P), (then) you have a runny nose (Q),’ can just as well be expressed using the word because: ‘Because you have a cold (P), you have a runny nose (Q).’

But in our speech we sometimes mention the Q before the P, as in: (Explanation C) If and Because In reality, the cause (P – the cold) comes before the effect (Q – the runny nose). But in our speech we sometimes mention the Q before the P, as in: ‘You have a runny nose (Q) because you have a cold (P)’, or ‘You have a runny nose (Q) if you have a cold (P).’ This does not normally cause problems, because we know that the sentences still mean that P causes Q. They remain true, even though the two halves have been completely swapped round.

Unfortunately, people do sometimes make a mistake of thinking: (Explanation C) If and Because As a whole group, make up another causal chain of the form ‘If P, Q’, and check that it remains true whether you say ‘Because P, Q’ or ‘Q because P’ or ‘Q if P’ Unfortunately, people do sometimes make a mistake of thinking: (a) ‘If/because you have a cold (P), you have a runny nose (Q)’ remains true in this form: (b) ‘If/because you have a runny nose (Q), you have a cold (P)’. As a whole group, see if you can work out why this is not so, focussing on what causes what, and on whether the two halves have been completely swapped around.

(Explanation C) Rash Reversing Sentence (b) ‘If/because you have a runny nose (Q), you have a cold (P)’ does not remain true – we say, does not ‘follow’ from sentence (a) – for the simple reason that a runny nose (Q) could result from some other cause than having a cold (P). For example, you could have a runny nose if/because you have hay fever. As a whole group, can you think of any other things that could cause a runny nose?

(Explanation C) Rash Reversing We would not want a doctor to see a runny nose and jump rashly to the conclusion that her patient has a cold if he does, in fact, have hay fever or some other problem. And, in general, we would not want other people, or even ourselves, to make the mistake of ‘rash reversing’ – that is, reversing the events (P and Q), but leaving the ‘if’ or ‘because’ in place.

(Exercise C, 1) Reasonable Reversing In pairs or groups 1. Reverse the following sentences in the right way – swapping the two halves completely, including the ‘if’ or ‘because’ – and check that they remain true. A. If you boil water, it starts to evaporate. B. Because the road was slippery, the driver lost control of the car. C. You will be shown mercy if you will apologise for your mistake. D. I went to the police station because someone stole my bike.

(Exercise C, 2) Rash Reversing 2. Now reverse the same sentences ‘rashly’ - swapping the events, but leaving the ‘if’ or ‘because’ in place – and give simple reasons why the ‘rash’ reversals would not be true. A. If you boil water, it starts to evaporate. B. Because the road was slippery, the driver lost control of the car. C. You will be shown mercy if you will apologise for your mistake. D. I went to the police station because someone stole my bike.

(Explanation C) Reasonable Reversing ‘If P, Q’ sentences remain true if you take the ‘If’ with the P when you reverse them.

(Explanation C) Reasonable reversing [2] There is one special sort of ‘If P, Q’ sentence, however, that remains true even if you reverse only the P and Q. Here is an example: ‘If she is a pacifist (P), she is opposed to wars (Q)’ Reversing the P and Q, but leaving the ‘if’ in place, we get ‘If she is opposed to wars (Q), she is a pacifist (P)’. But this sentence is just as true as the original. The reason is that Q (being opposed to wars) gives the meaning of P (being a pacifist), not the cause. Put another way, the link between them is verbal (ie, to do with words) not causal.

(Exercise C, 3 - 4): Reasonable Reversing 3. In pairs and/or groups: Discuss which of the following sentences can reasonably be reversed – that is, remain true – even if you just reverse the P and Q, leaving the ‘If’ in place: A. If it’s got eight legs, (then) it is an arachnid. B. If it gets much colder, (then) I’ll decide to stay indoors. C. You get a shock if you touch that wire. D. Of course she’s a film star if she is famous for acting in films. E. If he’s an addict, (then) he’s going to find it very hard to break the habit.

(Exercise C, 3 - 4): Reasonable Reversing A. If it’s got eight legs, (then) it is an arachnid. B. If it gets much colder, (then) I’ll decide to stay indoors. C. You get a shock if you touch that wire. D. Of course she’s a film star if she is famous for acting in films. E. If he’s an addict, (then) he’s going to find it very hard to break the habit. 4. For each causal link above, be ready to say exactly what is the cause and what is the effect. For each verbal link, be ready to say which words are giving the meaning of which.

(Explanation C.1): Verbal not Causal Did you think that the sentence: ‘If he’s an addict, (then) he’s going to find it very hard to break the habit’, expressed a causal link? Perhaps you even reasoned that the person was going to find it very hard to break his habit because he was an addict – which certainly looks like a causal explanation. But causal explanations, strictly, have to say how things come to be – in this case, how the person might end up finding it very hard to break his habit. Fearing pain might lead him into that state, or perhaps even just liking a taste.

(Explanation C.1): Verbal not Causal As a whole group, discuss what other things might cause or lead someone to find it very hard to break a habit. Now notice that saying that someone ‘is an addict’ is not to say what might lead him into finding it very hard to break a habit. It is simply to say in other words that he finds it very hard to break the habit. So the sentence expresses a verbal link (giving a meaning) NOT a causal one (giving a cause).

(Explanation D): ‘If’ for Definitions Sentences in the ‘If P, Q’ form that are reasonably reversible, that is, remain true if you just reverse the P and Q, can be thought of as definitions: sentences which give the meaning of words in other words. ‘If he’s an addict, (then) he’s going to find it very hard to break the habit’, gives the meaning or definition of ‘addict’.

(b) ‘All pacifists are people who are opposed to wars’, or (Explanation D): ‘If’ for Definitions Definitions often come in a more general form than ‘If P, Q’, for example ‘All Ps are Qs’, or even, leaving out the ‘All’, as ‘Ps are Qs’. Or sometimes a definition is expressed in ‘singular’ form, namely, ‘A P is a Q’. So, (a) ‘If she is a pacifist (P), she is opposed to wars (Q)’ can be translated into: (b) ‘All pacifists are people who are opposed to wars’, or (c) ‘Pacifists are people who are opposed to wars’, or (d) ‘A pacifist is a person who is opposed to wars’.

(b) ‘All pacifists are people who are opposed to wars’, or (Explanation D): ‘If’ for Definitions So, (a) ‘If she is a pacifist (P), she is opposed to wars (Q)’ can be translated into: (b) ‘All pacifists are people who are opposed to wars’, or (c) ‘Pacifists are people who are opposed to wars’, or (d) ‘A pacifist is a person who is opposed to wars’. As a whole group, discuss which of the forms you like best – or even, whether you would use each form for a slightly different reason.

(Exercise D): ‘If’, ‘All’ and ‘A’ In pairs or groups: 1. Translate the following sentences so that you have each of them in all 4 forms: (‘If P, Q’, and ‘All Ps are Qs’, and ‘Ps are Qs’, and ‘A P is a Q’): An apprentice is a person learning a trade. All pirates are people who attack ships to rob from them. If you are a telepathist, you could read my mind. 2. Check that each of (a), (b) and (c) is ‘reasonably reversible’; in other words, it remains true when you simply swap the P and Q round.

(Exercise D, 2) Rash Reversing In pairs or groups: 3. The following appear to be definitions, but cannot be counted as such because they are not exact enough. Firstly, check that they cannot be ‘reasonably reversed’, and then discuss how they could be made more exact so as to be ‘reversible’. All picnics are meals eaten out of doors. If it is a meteorite, it has come from outer space.