Appendix: Youtube transcripts

Chapter 1

Standard form

In this short video we’re going to take you through the basics of putting arguments into standard form. So here’s our argument: “It’s not the case that everything in the universe is physical unless consciousness is physical. Consciousness is not physical. Therefore not everything in the universe is physical.” Our first task is to identify the conclusion. In this argument this is very easy, because we have this indicator word “therefore” which shows us where the conclusion is. The conclusion is “not everything in the universe is physical”. So we can label that as our conclusion. Then we look for the premises. Again in this simple argument they are very easy to find. The first premise is “it is not the case that everything in the universe is physical unless consciousness is physical”. We can call that premise 1. And the second premise is “consciousness is not physical”. We’ll call that premise 2. Now when we put the argument into standard form it’s often easiest to write the conclusion down first: “Not everything in the universe is physical”. In standard form the conclusion is always separated from the premises which support it using an inference bar. You can just draw a line using a draw function. Or if you’re writing your answer in a Word document you can underline the final premise. Then we write in the premises: “It’s not the case that everything in the universe is physical unless consciousness is physical” and “consciousness is not physical”. We also, when we put arguments the standard form, always label the premises and the conclusion. This makes it easy to refer to them later. So we call the first premise P1, and the second premise P2, and the conclusion C. The argument is now in standard form. What it’s important to note about what we’ve done, is that these features – P1, P2, the inference bar, and the conclusion – are what we call the ‘frame’ of the standard form rendition.  Our standard form is now complete. In later videos we’ll look at some more complex arguments and put them into standard form also.

Chapter 2

Modus ponens

It’s often easier to identify an argument form if you take the argument and replace the particular statements that occur in the argument with letters. So this video is going to take you through an easy example of how to do this. It’s going to use the example of a Modus ponens argument. So here’s our basic argument: “If cucumbers are fruit then so are tomatoes. Cucumbers are fruit. Therefore tomatoes are fruit.” Now the first thing you might notice about this argument is that this phrase “so are tomatoes” in P1 actually means the same thing as “tomatoes are fruit”. So let’s replace that with “tomatoes are fruit”. This will make it easier to see how our form works in this argument. P1 is made up of this “if” claim, and then part of its statement is “cucumbers are fruit”. We then have a “then” phrase, and the consequent there is “tomatoes are fruit”. Now I’ve used green for “cucumbers are fruit” and red for “tomatoes are fruit” to help us see how those reoccur. So in P2 “cucumbers are fruit” is again in green to show that it’s the same statement as occurs in P1, and “tomatoes are fruit” in red: this is the consequent of P1. So our basic argument form goes P1, P2, we have an inference bar, and C for our conclusion. This word “if” signifies where the antecedent of P1 occurs, so let’s write that in: P1. Then we have the word “then”, we can put that in as well. This just shows that P1 is a conditional claim: the statement will have two parts. This “cucumbers are fruit” which I’ve underlined in green: we’re going to use a letter for that. It’s usual to start with P, so we’ll put P, and we’ll put it in green. Then we need to ask ourselves where else does that statement “cucumbers are fruit” occur in the argument, and it occurs in P2. And that is all of P2. So we just put the letter P next to P2 like that. Then we go looking for other propositions. “Tomatoes are fruit” is the consequent of P1, so we write Q to stand for that statement “tomatoes are fruit”. We notice that that recurs and the conclusion, so we write Q for our conclusion as well. Now you can see that the basic argument form here is “if P then Q, P, therefore Q” and that is our Modus ponens argument form. So because our original argument about cucumbers and fruit is of the Modus ponens form, we know that it must be valid.

Order of premises

You might wonder whether it matters what order the premises are in when you’re identifying an argument form. And the answer is it doesn’t matter at all. So let’s look at a quick example of this. Here’s our argument: “All events in the universe are causally determined. If all events in the universe are causally determined then free will is illusory. Therefore free will is illusory.” We’ve got two premises and a conclusion. Our first premise is “all events in the universe are causally determined”. Our second premise is the conditional one: “If all events in the universe are causally determined then freewill is illusory”. And the conclusion is “therefore free will is illusory”. So if we were to write down the form of that argument, the first premise is P on its own, the second premise is if P then Q, and the conclusion is going to be Q. So this is still Modus ponens, it’s just put the premises in a different order from usual. But we can definitely identify it as Modus ponens. And you can see that this is going to work because if we were to swap the order of P1 and P2 we would have the same argument, -the premises would just be in a different order. And then that would put P in the second premise position in a way that we identify as being Modus ponens. So it doesn’t make any difference what order the premises are in.

Chapter 3

Connecting premises

The purpose of this video is to give you some help on how to find the right sort of connecting premise to make an argument valid. Here are some general hints. An implicit premise or a connecting premise doesn’t add any new reasons to the argument: it’s just providing a connection between what’s already there. If you find yourself adding new information to the argument in your connecting premise, then you’re doing too much. Anything which is in the conclusion must be in the premises somewhere. So if something’s mentioned in the conclusion, and it doesn’t occur in the premises which are already present, then it needs to go in your connecting premise. Check that each thing in the premises connects to something else: you shouldn’t have anything that’s mentioned only once, because that means it doesn’t connect to anything, and the idea is to connect together the parts of the argument. Okay, let’s look at how some of these hints work in practice. So whatever is in the conclusion must be in the premises somewhere. Let’s take this argument: “All politicians earn high salaries. Winston earns a high salary”. So, we know that we have to get from premise one to the conclusion, and we’re looking for what’s going to need to go in P2 as the connecting premise. So we notice that “earns a high salary” is in the conclusion, but “earning a high salary” is also in premise one, so that doesn’t help us at this point. However, “Winston” is in the conclusion and “Winston” doesn’t occur in premise one. So that tells us that we’re going to need a premise that talks about Winston. Premise two is going to be about Winston. Then we look for what else has not yet been mentioned. “Politicians” is in premise one, but at the moment it doesn’t occur anywhere else in the argument. That means that premise two is going to have to be about politicians so that politicians is connected in to the rest of what’s said. Once we realize that we can see that the connecting premise needs to say “Winston is a politician”. This argument is now valid: “All politicians earn high salaries. Winston is a politician. Therefore Winston earns a high salary”. Let’s look at another simple example. We need to make sure all of the parts of an argument connect. So consider this argument: “Daisy is a cow. Therefore Daisy is a mammal”. Let’s start by looking at the conclusion. We notice that the conclusion is about Daisy. “Daisy” is also in premise one: premise one is about Daisy. So probably the connecting premise doesn’t need to be about Daisy. The conclusion says that Daisy is a mammal and the first premise says that Daisy is a cow, so we know that the connecting premise, premise two, needs to connect being a cow to being a mammal. Well it’s clearly not going to say “all mammals are cows” because that would be false, and it wouldn’t be useful – what the connecting premise needs to say is “all cows are mammals”. So this argument is now valid: “Daisy is a cow. All cows are mammals. Therefore Daisy is a mammal”. These examples are both very simple: they’re just to get you started. Let’s look at a more difficult example. So here’s our argument: “Premise 1: Making University education free will encourage lazy people to attend university. Premise 2: Lazy people will get no benefit from attending university. Conclusion: The government should not make university education free”. So once again let’s start with what the conclusion says. The conclusion is about making university education free, and making university education free also occurs in premise 1. So a connecting premise is probably not going to need to mention that. The conclusion is also about what the government should not do. Now neither the government, nor what should or should not happen, occur anywhere else in the argument. So the connecting premise is going to have to talk about what the government should not do. So let’s write this in: “The government should not …” Premise three is going to be about that. All right, and then we look at what else needs to be connected into this argument. So in premise one we talk about lazy people attending university, and premise two also talks about lazy people and their attending University. So those concepts are already connected together in the argument. Premise two also talks about getting no benefit from something, and that hasn’t occurred anywhere else yet. So premise three is going to have to say something about not getting benefit. And in premise one what’s still hanging out there, not circled, is this encouragement. So we have to connect what the government should not do to getting no benefits and encouragement, and we might have to think quite carefully about how we’re going to do that. But I know I’m going to want to say “the government should not encourage …” And then I have to think quite hard about how to get the rest of the premise to say what I want it to say in order to make the argument valid. I want to say “the government should not encourage…” and then I have to think a bit about how to get the benefit in. It turns out I do end up repeating some phrases, because to make this argument valid I’m going to say “the government should not encourage people to attend university if they will not benefit from it”. Now my argument is valid. Premise one says “making university education free will encourage lazy people to attend university”. Premise two says “lazy people will get no benefit from attending university”. And Premise three says “the government should not encourage people to attend university if they will not benefit from it”. Then the conclusion follows “the government should not make university education free”. This was a more complicated example, and sometimes you have to think quite hard about what that connecting premise needs to say. But with practice you’ll get better at it.

Finding a more general connecting premise

When you’re not sure how to add a connecting premise to make an argument valid, using a corresponding conditional is a guaranteed way to succeed. But it’s often unsatisfying, and corresponding conditionals can be difficult to assess. In this example we’re going to take you through how to use the technique of starting with a corresponding conditional in order to find other, more meaningful premises to use as the connecting premise. So here’s our argument. “Rents are rising to unaffordable levels. Housing is a basic need. The government should intervene.” The first question to ask ourselves is ‘what is the conclusion?’. Here there is no conclusion indicator, but as is quite common, the conclusion is the prescriptive claim: it tells us what should happen. So this is the conclusion. We add it at the bottom of the page: “the government should intervene”. And we can see immediately that it’s incomplete: the government should intervene in what? It’s clear from the context, but when we put the argument into standard form we need to make it explicit: the way in which the government should intervene. So here we need something like “the government should intervene to stabilize rents at affordable levels”. Then because we have our conclusion, we put in our inference bar, and then we look for our premises. The premises here are quite straight forward. “Rents are rising to unaffordable levels” is the first premise. And the second premise is “housing as a basic need”. Now if we were going to use a corresponding conditional here, because we have two premises and then a conclusion, our corresponding conditional will just join both premises together with an “and”, and there’ll be an “if” before the premises, and the conclusion will go after the “then”. So the corresponding conditional for this argument is “If rents are rising to unaffordable levels and housing as a basic need then the government should intervene to stabilize rents at affordable levels”. As I said corresponding conditionals are sometimes a bit satisfying. But we can use it. We know that this argument must be valid – it must be valid because it uses a corresponding conditional, and corresponding conditionals make any argument valid. So we can use this as a base to work out how else we might express the same points, and then we’ll know that the resulting argument is valid. Okay, so we have this claim that says if rents are rising to unaffordable levels and housing is a basic need. So what’s really important here is that there’s a basic need and that basic need is becoming unaffordable. So the first part of the connecting premise just needs to say, “when a basic need becomes unaffordable…” Our consequent here says “then the government should intervene to stabilize rents at affordable levels”. One of the things to ask yourself is, “is this specific to this government, or does it mean any government?” And I suspect that the person who asserts this premise means it not to be specific to our government but to apply to any government. So we just change “the government” to “a government”. So “a government should intervene to stabilize rents at affordable levels”, but we don’t want to make this specific to rents anymore, this is the basic need that’s become affordable. So, “when the basic need becomes affordable a government should intervene to stabilize that thing at affordable levels”. So we know that this connecting premise must make the argument valid because it has just formed straight from the corresponding conditional. But it gives us a more general premise that somebody is more likely to be happy to accept. So our connecting premise to make this argument valid is now “when a basic need becomes unaffordable a government should intervene to stabilize it at affordable levels”. And this argument is valid.

Argument diagrams 1

This video introduces you to the basics of argument diagrams. It’s often useful to diagram the structure of an argument, especially a complex argument. These are called ‘argument diagrams’ or ‘argument trees’ or ‘tree diagrams’. I will take you through the basics of how this works. So when you want to show the structure of an argument, conclusions are always represented below the premises which support them, with a downwards arrow representing the inference: like this. Where the premises work together to support the conclusion they’re braced together before the arrow points down: so you have premise one and premise two and you want to get to the conclusion which has always put below them. As premise one and premise two are working together, then we indicate that by joining them together before we have the arrow. Where premises or arguments threads support the conclusion independently, that’s indicated by each having their own arrow to the conclusion. So suppose once again we have two premises and a conclusion, but in this argument premise one supports the conclusion on its own, and premise two supports the conclusion on its own. So our argument diagram looks slightly different. Let’s look at some examples of how this works, and practice. Consider this simple argument: premise 1 Daisy is a cow, premise 2 all cows are mammals, conclusion Daisy is a mammal. In this argument premise one and premise 2 are working together to yield the conclusion. Now when you have an argument that is this simple it’s about hard to see why anybody would want to bother to diagram arguments. But as we look at a couple of more complicated examples, you’ll be able to see why it’s useful. So here’s a longer argument. Every action I perform is either caused or uncaused. If my action is caused then it does not come about through an exercise of my free will. If my action is uncaused then it does not come about through an exercise of my free will. Therefore none of my actions come about through an exercise of my free will. If my actions don’t come about through an exercise of my free will then I’m not responsible for them. Therefore I’m not responsible for my actions. So this is an extended argument, and we’ll be able to map how the parts of the argument are related by putting it into a diagram. We can start off by noting that premises 1, 2, & 3 are all working together to get us to the first conclusion. So, we show that they’re all working together – none of them are supporting that conclusion independently – by bracing them together with an arrow to get to C1. We can then see that C1 is operating also as a premise, and the premise that it’s working with is P4. So C1 and P4 are working together to get to C2. So this is the argument diagram for this argument. The first three premises work together to support C1, and C1 works with P4 to support C2. It’s a very common kind of diagram. Let’s look at another example. If the reason eating meat is wrong is because it curtails the life of a sentient being, then eating meat is not wrong so long as it doesn’t curtail the life of the sentient being. Eating roadkill does not curtail the life of a sentient being. Therefore eating roadkill is not wrong. Eating animals which have died of natural causes does not curtail the life of the sentient being. Therefore eating animals which have died of natural causes is not wrong. Therefore not all eating of meat is wrong. Now the reason that argument diagram is going to help with this argument is that we really only have one way in standard form of dealing with complex arguments, and that’s to stack all the premises one after another. But when we do a diagram we’re able to show what the structure of this argument is. So P1 and P2 are working together to give us C1 in this argument. So that part of the argument structure is unsurprising. But C1 says eating roadkill is not wrong. We can see that the final conclusion, C3, not all eating of meat is wrong, follows from C1 alone. So C1 supports C3 on its own. So what’s happening with the rest of the argument? P3 says eating animals which have died of natural causes does not curtail the life of a sentient being. This is not connected to P1 and P2 and C1. It is independent from that thread of the argument. So P3 does give a reason for us to accept C2. But P3 is not enough on its own for us to accept C2, so we know that P3 must be working with something else. So what goes over here? What is P3 working with? It’s actually working with P1. If the reason eating meat is wrong is because it curtails the life of a sentient being, then eating meat is not wrong so long as it doesn’t curtail the life of the sentient being. And then P3 says eating animals which have died of natural causes does not curtail the life of a sentient being. Those two premises together support C2, eating animals which have died of natural causes is not wrong. I could have tried to diagram this differently so that P1 was attached by lines in two places, but in this particular diagram is just going to be cleaner if I write P1 down twice. And it is being used twice: It’s being used in two different arguments threads. The final part of diagramming this argument is just to make C2 connect to C3, and once again C2 is a reason to accept C3 on its own. So now that we have this diagram completely mapped out, we can see something very interesting about the way that it works. Although both argument threads use P1, these are two separate arguments for C3: we have two independent reasons for why it’s the case that not all eating of meat is wrong. This isn’t really brought out by the standard form, and so sometimes an argument diagram is a very useful way of seeing what the structure of an argument is.

Argument diagrams 2

This video takes you through the way that you can use diagrams in a two-step process to help you put together your argument reconstruction. With a complex argument it’s often useful to sketch out the structure of the argument before you begin your reconstruction. Then once you know the basic structure it’s easier to put the argument into standard form, and to add any implicit premises. When you finish your reconstruction you can do a final argument diagram which maps out the structure of the argument in a more complete way. Let’s look at an example of this. Here’s our argument: “Auckland will continue to have a housing shortage unless the construction industry can suddenly produce 20,000 houses. But that’s not going to happen. It’s too hard to get a building consent for starters, and they just don’t have the workers. So the housing shortage isn’t going anywhere.” To help us deal with this argument I’m going to label each of the statements that are made in the argument. So our first statement is “Auckland will continue to have a housing shortage unless the construction industry can suddenly produce 20,000 houses”. The next sentence is “but that’s not going to happen”. Then we have “it’s too hard to get a building consent”. And the next relevant sentence is “they just don’t have the workers”, so we’ll call that ‘4’. Then ‘5’ is “so the housing shortage isn’t going anywhere”. Once we’ve labeled all the parts of the argument we can look for the conclusion. The conclusion is very easy to find in this argument: it’s got a nice conclusion indicator, “so”, so we know that sentence five is going to be our conclusion. So that’s going to go at the bottom of the page. And because it’s a conclusion we know that it’s going to be supported by something, so we mark that with an arrow. Now we need to think about the structure of the argument. So what is it that supports 5? 5 says that the housing shortage isn’t going to stop. What is the main reasons that are given for why the housing shortage isn’t going to stop? Here we can see that 5 is supported by 1 and by 2. So 1 says “Auckland will continue to have a housing shortage unless the construction industry can suddenly produce 20,000 houses”, 2 says “that’s not going to happen”. So what 2 really says is “it’s not the case that the construction industry can suddenly produce 20,000 houses”. So 1 and 2 are working together to support 5. Right. Then we will need to know what to do with the rest of the argument. Well, the two claims here are to do with why it’s not going to happen, why the construction industry cannot suddenly produce 20,000 houses. So 3 “it’s too hard to get a building consent”, and 4 “the workers just aren’t available”, these are both reasons for why it’s not going to happen. These are reasons for 2, and at the moment they’re independent reasons: so there are two reasons why it’s not the case of the construction industry can suddenly produce 20,000 houses. The first reason is “it’s too hard to get a building consent” and the second reason is that “the workers just aren’t available”. So we’ve now mapped out the basic structure of the argument. This is going to help me a great deal when I put the argument into standard form, because I know that I’m going to want to start with sentences 3 and 4, and then I’m going to have sentence 2. Then I’m going to have 1 in order to get to 5. So I now know how to lay out my standard form: this has been made much easier because of my initial sketch. All right, so then we’re going to speed up the reconstruction process. Here’s what my standard form looks like. P1 It’s difficult to get building consents in Auckland. P2 If it’s difficult to get building consents in Auckland then the Auckland construction industry cannot quickly produce 20,000 houses. P3 There is a shortage of construction workers in Auckland. P4 If there’s a shortage of construction workers in Auckland then the Auckland construction industry cannot quickly produce 20,000 houses. Those reasons support C1 The construction industry in Auckland cannot quickly produce 20,000 houses. P5 Auckland will continue to have a shortage of houses unless the construction industry can quickly produce 20,000 houses. And then our final conclusion: Auckland will continue to have a shortage of houses. So now that we have the standard form laid out we can do a final argument diagram to show how the parts of the argument are structured. So we’ve got these four premises P1 – P4, but we can see quite clearly that P1 and P2 work together, and P3 and P4 work together. But these are separate argument threads. So P1 and P2 support C1 on their own, and P3 and P4 support C1 on their own: these are independent argument threads for the claim that the construction industry in Auckland cannot quickly produce 20,000 houses. Then C1 works with P5 to yield the final conclusion that Auckland will continue to have a shortage of houses. So here is our final standard form argument, and a final argument diagram. But the construction of the standard form that we have here was made much easier by the initial sketch that we did, which showed us which reasons we should put at the beginning of our standard form reconstruction. Here’s a couple of hints for when you go to do your own argument diagrams. When you do your own diagrams, if you have an arrow pointing anywhere but down, you’ve done something wrong. Arrows only point down because they always mark an inference to a conclusion. There’s no need to do fancy computer graphics when you do your own argument diagrams for an assignment. It’s often easiest just to draw the diagram quickly piece of paper, photograph it with your phone, and paste it into a document. When you do that your diagram will look something like this. It doesn’t have to be flashy, it just needs to be clear how the structure of the argument works.