Logical forms II

3 Outubro 2025, 11:00 • David Yates

In the lecture we covered the four arguments that can be based on the logical form of the closure argument for scepticism. One important thing to bear in mind is the following question, which may have occurred to you:

• How can we say that an argument is logically equivalent to an inconsistent set of propositions, but then say that an inconsistent set of propositions can be used to generate more than one argument?
• The answer is that the logical form of an argument is not all that it has! All four arguments that can be constructed using the logical form of the causal argument for physicalism have exactly the same logical form. However, each one involves defending a different set of 3 propositions in order to reject the 4th. 
• It is when you decide which set of 3 propositions to defend, and hence what your conclusion will be, that you turn an inconsistent set of propositions into an argument.

In the slides you will find colour-coded versions of the 4 arguments that can be constructed using the Cartesian sceptical argument. Previously we had seen 2 of these: the original sceptical argument and Moore's repsonse. Now you will see that there are two more: an argument against epistemic closure, and an argument against the apparently obvious truth that if I am a brain-in-a-vat, then I do not have two hands.

For more on the possibility that we still have hands, cars, homes, children, partners, food, etc. even if we are brains-in-a-vat, see David Chalmers The Matrix as Metaphysics. In Chalmers' view, sceptical scenarios (at least, most of them) are really just alternative hypotheses about the fundamental metaphysical nature of our world. In these scenarios, he claims, almost all of our ordinary beliefs about the world are still true - but they are made true by a different kind of fundamental reality.

Here is another example:

Example 3 - The Causal Argument for Physicalism

This argument is more complex and has three premises rather than two. It is not entirely clear that the argument is deductively valid, but we will assume for the purposes of this class that it is valid. If you want to challenge its validity, tell me about that in Friday's class!

P1 Mental events cause physical effects ("efficacy of the mental")
P2 All physical effects have sufficient physical causes ("causal closure of the physical")
P3 In general, effects do not have more than one sufficient cause ("no-overdetermination rule)"
C Therefore, mental events are identical with physical events

Pick a mental event such as a conscious pain, and suppose that this events causes you to say "ouch", which is a physical event. This is an instance of P1. By P2, yousaying "ouch" had a sufficient physical cause - it was caused by some complex brain event B. But by P3, you saying "ouch" did not have more than one sufficient cause. It follows (or at least it seems to follow) that your conscious pain must be identical with the brain event that caused you to say "ouch". If the pain is not identical to B, then you saying "ouch" had two sufficient causes, but that is ruled out by P3. 

Try to apply the recipe above to generate the alternative arguments! It works in exactly the same way, but here the alternatives are far more interesting, and every one has a conclusion that has at some point been defended by some philosopher. It is therefore not obvious at all which of the resulting arguments (how many are there?) is the one that is sound.

Logical forms

30 Setembro 2025, 11:00 • David Yates

The Logical Form of a Valid Argument

We concluded last week with some material that can be a little bit confusing. But don't worry, we will clarify everything this week with some further examples. Here are the central points, please read this carefully (several times, if necessary):

Now we will give several worked examples of this logical form so that students will at the very least learn a recipe for constructing the alternative possible arguments from any particular case, and hopefully also why this recipe works!

Example 1 - Aristotelian Syllogisms

P1 David is a man
P2 All men are mortal
C David is mortal

In this example argument, we have divided the three propositions into two premises (P1 and P2) and a conclusion (C). The argument is clearly valid. Now, for any valid argument with N premises and a conclusion, we can construct N+1 valid arguments, each with a different conclusion. Recall the definition of logical validity:

• An argument A is valid if, and only if, it is not possible for A's premises to be true and A's conclusion false. 

That is, validity is necessary truth preservation: necessarily, if the premises of a valid argument are true, then the conclusion is also true. That is what it means for an argument to be valid! Why is validity important? The main reason is that if you use a valid argument form, then if you also start with true premises, you are guaranteed to reach a true conclusion. In other words, if you reason logically from true premises, you will end up with a true conclusion. That is why e.g. deductive mathematical proofs are important - if we have a proof of some theorem in maths, and we know that its premises are true, then we can know the theorem is true as well.

Recipe for Constructing Alternative Arguments - Example 1

Step 1 Write down the two premises and the negation of the conclusion as three propositions, i.e. not separated into premises and conclusion. The negation of the conclusion is its opposite: take whatever the conclusion says, deny it, and you get another proposition. In Example 1, the negation of "David is mortal" is obviously "David is not mortal". Following step 1, here are the three propositions we get:

P1 David is a man
P2 All men are mortal
P3 David is not mortal

Step 2 Write down the argument as an inconsistent set of propositions. Now, we know that the original argument was valid, which means that P1 and P2, if they are true, guarantee the truth of "David is mortal". But what that means is that it is not possible for the above three propositions to be true. This is pretty simple when you think about it: there is no way it can be true, all at the same time, that I am a man, that all men are mortal, and that I am not mortal. Thus we can rewrite the original argument form, assuming it is valid, as follows:

Not possibly (P1 & P2 & P3)

This just says that it is not possible for all three propositions P1, P2 and p3 to be simultaneously true. But now we can see that there are three possible arguments here, all with the same logical form, and all valid. If we know that it is not possible for all three of P1, P2 and P3 to be true, then we know that at least one of them must be false. But that means that if you defend any two of them, you must reject the other one!

Step 3 Write down the logical forms of the possible arguments. The original argument went like this:

P1 is true (David is a man)
P2 is true (all men are mortal)
Therefore, P3 must be false - it is not true that David is not mortal. In other words, I am mortal.

But we can also reason as follows:

P3 is true - David is not mortal
P1 is true - David is a man
Therefore, P2 must be false: it is not true that all men are mortal, i.e. at least one man is not mortal.

And finally:

P3 is true - David is not mortal
P2 is true - all men are mortal
Therefore, P1 must be false: David is not a man!

Thingts to note: (1) all three arguments presented here are valid, (2) only one of these arguments can possibly be sound, (3) in this case, it is very obvious which of the arguments is the sound one - it is the one whose premises are true (sadly, the original argument that concludes that I am mortal). 

In class, we will see an example of a real philosophical argument and apply the recipe to generate the alternatives. In this case, it is not at all obvious which of the arguments is the sound one!

Sceptisicm and Moore's refutation

26 Setembro 2025, 11:00 • David Yates

In this class we will consider two opposing and very well-known philosophical arguments:

• The "Brain-in-a-vat" argument for spepticism
• Moore's common-sense "refutation" of the sceptic

As we will see, both arguments involve the same set of inconsistent propositions, and both depend on what is known as the principle of closure of knowledge under known logical entailment (proposition (3) below is an instance of the closure principle). We will cover all this in class, but here are the inconsistent propositions:

1. I do not know that I am not a brain-in-a-vat
2. I do know that I have two hands
3. If I know that I have two hands, then I know that I am not a brain-in-a-vat
   
   

If these three propositions are inconsistent (i.e. you cannot endorse all three of them), then you must reject one. Which one, and why?

We will use this case to illustrate a very common saying that one hears in English language philosophy: "one man's modus ponens is another man's modus tollens". We will see in class what this saying means, and explain both "modus ponens" and "modus tollens" for those who do not know. It basically means this: just about any argument can be "turned on its head" so that it becomes an argument for the opposite conclusion to the one the author intended. We will see exactly how to do this and thereby understand why progress in philosophy is so veeeeeeeeeeeeeeeery slooooooooow.

Para quem quiser ler sobre o ceticismo (e o caso do "cérebro numa cuba") em português, recomendo o seguinte artigo no compêndio em linha de problemas de filosofia analítica, partes 1 e 5 (a segunda parte também é relevante) - mas atenção: os artigos do compêndio são artigos que apresentam o "estado da arte" de vários debates, e assim, as vezes são um bocado difíceis. https://compendioemlinha.letras.ulisboa.pt/wp-content/uploads/2014/06/ceticismo.pdf. A leitura inglesa recomendada abaixo será mais fácil e mais curta!

Here is the very famous paper by G. E. Moore that I will refer to in this week's lecture. For Friday, please try to read Chapter 4 "Certainty" in advance, and see whether you think Moore's argument succeeds in refuting the sceptic.

Aula 3 - Mais sobre falácias (petição de princípio)

23 Setembro 2025, 11:00 • David Yates

Homework challenge / role of context in the fallacy of begging the question: the fallacy depends on whether we could come to know the premises independently of already knowing the conclusion. This means that our epistemic context - what we can and cannot come to know given our situation - is relevant to the fallacy of begging the question! We can know that all men are mortal without waiting to see if I die - this is an item of general scientific knowledge (inductive) about the world. But in the case of the homework argument, in order to know whether all students at FLUL really are less than 85 years old, I would need to check your age. Even if I have checked the ages of all but one of the students, that would not entail anything about the age of the final student, because there is no law of nature (or of FLUL) that says you cannot study here if you are over 85 years of age. I would still need to check the age of the final student to know whether any students at FLUL were over 85 years old.  But I do not need to check whether you are mortal to know that all human beings are mortal. That is something we can know without verifying it in each individual case. 

What this illustrates is that context matters. Now suppose that there were a law against students over a certain age being registered (there isn't, but suppose for the sake of argument that there is). In such a context, you would be able to know in advance that all the students a FLUL were younger than that age, and so you would be able to use argument (5) to persuade someone that a particular student was younger than that age. Whether or not an argument begs the question depends on the context of and on what can and cannot be known in that context.

Aula 2 - Argumentação

19 Setembro 2025, 11:00 • David Yates

This week we will first introduce the course and the topics to be covered, and make sure that all students understand the attendance requirements and assessment methods to be used. We will then introduce the concept of a philosophical argument and the related concepts of validity and soundness.

• What is an argument?
• What is an argument for?
• What are (i) soundness, (ii) validity? Why are they important?

Summary of class 1

Examples of valid, invalid, sound and unsound arguments

Argument 1—sound

David is a man

All men are mortal

Therefore, David is mortal

Argument 2—valid but unsound (all propositions false)

David is a reptile

All reptiles can fly

Therefore, David can fly

Argument 3—valid but unsound (1 false premise, true conclusion)

If David is an ostrich (avestruz), then David walks on two legs

David is an ostrich

Therefore, David walks on two legs

Argument 4—invalid and unsound (but has true conclusion and true premises)

David is bald

Baldness is hereditary

Therefore, David is a philosopher

Argument 5—???

Everyone studying at the faculty of letters is less than 85 years old

[your name here] is studying at the faculty of letters

Therefore, [your name here] is less than 85 years old

Homework challenge: what is the difference between arguments 1 and 5? Could you use both of them to convince someone of their conclusions?

On Friday we will continue to consider the differences between good and bad arguments, by considering what arguments are supposed to do and hence the various ways in which an argument can go wrong. Is soundness enough, or is there more to a good argument than that? Through our discussion of soudness, validity, and good argumentation, we will introduce a very important distinction that occurs a lot in contemporary philosophy: the distinction between necessary and sufficient conditions. As we will see, soundness is only a necessary condition - and is not a sufficient condition - for being a good argument.

We will introuce some of the main fallacies of argumentation, including:

• "ad hominem" arguments (ataque pessoal)
• Begging the question (petição de princípio)
• The fallacy of "post hoc, erco propter hoc" (depois disso, por causa disso)
• The "slippery slope" (derrapagem, ou "bola de neve")
• The "strawman" fallacy (falácia do espantalho)
• The fallacy of composition (falácia de composição - vê também divisão)
• The fallacy of equivocation (equívoco - uma falácia de ambiguidade)
• The faulty analogy (a falsa analogia)
• The false dilemma (o falso dilema)

Vejam aqui uma guia das falácias em português: https://criticanarede.com/falacias.html

Focusing on fallacies will help us tell the difference between good and bad argumentation. As we will see, almost all arguments in public discourse are fallacious in one or (typically) more ways!