Logical reasoning exercises

Do they contain arguments?

How do we identify arguments in real life? There are no easy mechanical rules, and we usually have to rely on the context in order to determine which are the premises and the conclusions. But sometimes the job can be made easier by the presence of certain premise or conclusion indicators.  Words that might be used to indicate the premises to follow include :

• this is because ...
• since
• firstly, secondly, ...
• for, as, after all,
• assuming that, in view of the fact that
• follows from, as shown / indicated by
• may be inferred / deduced / derived from

Of course whether such words are used to indicate premises or not depends on the context.   Conclusions, on the other hand, are often preceded by words like:

• therefore, so, it follows that
• hence, consequently
• suggests / proves / demonstrates that
• entails, implies

Here are some examples of passages that do not contain arguments.

• When people sweat a lot they tend to drink more water. [Just a single statement, not enough to make an argument.]
• Once upon a time there was a prince and a princess. They lived happily together and one day they decided to have a baby. But the baby grew up to be a nasty and cruel person and they regret it very much. [A chronological description of facts composed of statements but no premise or conclusion.]
• Can you come to the meeting tomorrow? [A question that does not contain an argument.]

Exercise

Please see exercise#2 here: https://philosophy.hku.hk/think/arg/arg.php

Validity

An argument is valid if and only if there is no logically possible situation where all the premises are true and the conclusion is false at the same time.

Exercise

Some exercises on Validity (we can consider the Soundness of the arguments as well):  
https://philosophy.hku.hk/think/arg/valid1.php

Hidden assumptions

In everyday life, the arguments we normally encounter are often arguments where important assumptions are not made explicit. It is an important part of critical thinking that we should be able to identify such hidden assumptions or implicit assumptions.

So how should we go about identifying hidden assumptions? There are two main steps involved. First, determine whether the argument is valid or not. If the argument is valid, the conclusion does indeed follow from the premises, and so the premises have shown explicitly the assumptions needed to derive the conclusion. There are then no hidden assumptions involved. 

But if the argument is not valid, you should check carefully what additional premises should be added to the argument that would make it valid. Those would be the hidden assumptions. You can then ask questions such as : (a) what do these assumptions mean? (b) Why would the proponent of the argument accept such assumptions? (c) Should these assumptions be accepted?

Exercise

https://philosophy.hku.hk/think/arg/hidden.php

Analogical Arguments

To argue by analogy is to argue that because two things are similar, what is true of one is also true of the other. Here are some examples :

• There might be life on Europa because it has an atmosphere that contains oxygen just like the Earth.

• This novel is supposed to have a similar plot like the other one we have read, so probably it is also very boring.

• The universe is a complex system like a watch. We wouldn't think that a watch can come about by accident. Something so complicated must have been created by someone. The universe is a lot more complicated, so it must have been created by a being who is a lot more intelligent.

Evaluating analogical arguments

So how should we evaluate the strength of an analogical argument that is not deductively valid? Here are some relevant considerations :

• Truth : First of all we need to check that the two objects being compared are indeed similar in the way assumed. 

• Relevance : Even if two objects are similar, we also need to make sure that those aspects in which they are similar are actually relevant to the conclusion. 

• Number : If we discover a lot of shared properties between two objects, and they are all relevant to the conclusion, then the analogical argument is stronger than when we can only identify one or a few shared properties. 

• Diversity : Here the issue is whether the shared properties are of the same kind or of different types. If the objects have many different types of shared properties, they are more likely to be similar, than if they have shared properties of only one kind.

• Dis-analogy : Even if two objects X and Y are similar in lots of relevant respects, we should also consider whether there are dissimilarities between X and Y which might cast doubt on the conclusion. 

Exercise

Some exercises on Analogical arguments: https://philosophy.hku.hk/think/arg/analogy.php

Good Arguments

A good argument is an argument that is either valid or strong, and with plausible premises that are true, do not beg the question (1), and are relevant to the conclusion.

Note (1): "Begging the question" in philosophy refers to a logical fallacy where an argument assumes the truth of its conclusion within its premises, essentially using the point you are trying to prove as evidence for itself, creating a circular reasoning loop.  Despite the name, "begging the question" in philosophy does not mean to invite an obvious question, which is the more common definition.

Exercise

Some exercises on good arguments: https://philosophy.hku.hk/think/arg/goodarg.php

Logical reasoning (Arguments)

Introduction

There are different ways of thinking.  People in everyday life often do not think critically, and they think or decide things based on: 

1. traditions or customs,
2. emotions, 
3. religious beliefs,
4. popular opinions, or
5. ideology, etc.

Critical thinking is an approach to think clearly and rationally about what to do or what to believe mostly about the physical world.  Critical thinking can include different thinking methods or approaches.  A crucial part of critical thinking is to identify, construct, and evaluate arguments.

It should be noted that there are mental processes other than thinking and reasoning.  These processes include sensation, perception, memory, emotion, creativity, interaction with the body etc. 

What is an argument?

In everyday life, people often use "argument" to mean a quarrel between people. But in logic and critical thinking, an argument is a list of statements, one of which is the conclusion and the others are the premises or assumptions of the argument.

For present purposes, we shall take a statement to be any declarative sentence. A declarative sentence is a complete and grammatical sentence that makes a claim. So here are some examples of statements in English :

Snow is white.

The moon is made of green cheese.

Everyone is here.

As you can see, statements can be true or false, and they can be simple or complex. But they must be grammatical and complete sentences.

To give an argument is to provide a set of premises as reasons for accepting the conclusion. To give an argument is not necessarily to attack or criticise someone. Arguments can also be used to support other people's viewpoints.

Here is an example of an argument:

If you want to find a good job, you should work hard. You do want to find a good job. So you should work hard.

The first two sentences here are the premises of the argument, and the last sentence is the conclusion. To give this argument is to offer the premises as reasons for accepting the conclusion. [1]

The standard format

Presenting arguments in the standard format [2]

When it comes to the analysis and evaluation of an argument, it is often useful to label the premises and the conclusion, and display them on separate lines with the conclusion at the bottom :

Premise 1:  If you want to find a good job, you should work hard. 
Premise 2:  You do want to find a good job.
Conclusion:  So you should work hard.

Let us call this style of presenting an argument a presentation in the standard format. Please rewrite the following two arguments using the standard format:

1. We should not inflict unnecessary pain on cows and pigs. After all, we should not inflict unnecessary pain on any animal with consciousness, and cows and pigs are animals with consciousness.
2. If this liquid is acidic, the litmus paper would have turned red. But it hasn't, so the liquid is not acidic.

See answers here. 

Types of arguments

Deductive argument 

Deductive argument offers the strongest support: the premises ensure the conclusion, meaning that it is impossible for the conclusion to be false if all the premises are true. Such an argument is called a valid argument, for example: 

All men are mortal.

Socrates is a man. 

Therefore, Socrates is mortal. 

For valid arguments, it is not important whether the premises are actually true.  However, if they were true, the conclusion could not be false. Deductive reasoning plays a central role in formal logic and mathematics.

Non-deductive argument [3]

For non-deductive arguments (or logical reasoning), the premises make their conclusion rationally convincing without ensuring its truth. This is often understood in terms of probability: the premises make it more likely that the conclusion is true and strong inferences make it very likely. Some uncertainty remains because the conclusion introduces new information not already found in the premises. Non-deductive reasoning plays a central role in everyday life and in most sciences. 

Often-discussed types are:

inductive, 

abductive, and 

analogical reasoning. 

 

Inductive argument is a form of generalisation that infers a universal law from a pattern found in many individual cases. It can be used to conclude that "all ravens are black" based on many individual observations of black ravens. 

Abductive argument, also known as "inference to the best explanation", starts from an observation and reasons to the fact explaining this observation. An example is a doctor who examines the symptoms of their patient to make a diagnosis of the underlying cause. 

Analogical argument compares two similar systems. It observes that one of them has a feature and concludes that the other one also has this feature. [4]  The structure or form may be generalised like so:

P and Q are similar in respect to properties a, b, and c.

P has been observed to have further property x. 

Therefore, Q probably has property x also.

 

Analysis of deductive arguments

If an argument is valid, and all the premises are true (then by definition the conclusion is necessarily true) then the argument is called a sound argument.

Validity

An argument is valid if and only if there is no logically possible situation where all the premises are true and the conclusion is false at the same time.

Validity and Truth

Note the following situations:

The premises and the conclusion of an invalid argument can all be true.

Adam loves Beth. 
Beth loves Cathy. 
So Adam loves Cathy.

This argument is not valid, for it is possible that the premises are true and yet the conclusion is false. Perhaps Adam loves Beth but does not want Beth to love anyone else. So Adam actually hates Cathy. The mere possibility of such a situation is enough to show that the argument is not valid. 

The premises and the conclusion of a valid argument can all be false.

All pigs can fly. 

Anything that can fly can swim. 

So all pigs can swim.

Although the two premises of this argument are false, this is actually a valid argument. To evaluate its validity, ask yourself whether it is possible to come up with a situation where all the premises are true and the conclusion is false. (We are not asking whether there is a situation where the premises and the conclusion are all true.) Of course, the answer is 'no'. If pigs can indeed fly, and if anything that can fly can also swim, then it must be the case that all pigs can swim.

A valid argument with false premises can still have a true conclusion.

All pigs are purple in colour. 
Anything that is purple is an animal. 
So all pigs are animals.

 

Some exercises

Some exercises on Validity (we can consider the Soundness of the arguments as well):  https://philosophy.hku.hk/think/arg/valid1.php

Some exercises on Analogical arguments: https://philosophy.hku.hk/think/arg/analogy.php

Some exercises on good arguments: https://philosophy.hku.hk/think/arg/goodarg.php

References:

1. [A01] What is an argument?  Critical Thinking Web, Maintained by Joe Lau, Philosophy Department, University of Hong Kong.  https://philosophy.hku.hk/think/arg/arg.php
2. [A02] The standard format.  Critical Thinking Web, Maintained by Joe Lau, Philosophy Department, University of Hong Kong.  https://philosophy.hku.hk/think/arg/standard.php
3. Logical reasoning, Wikipedia. https://en.wikipedia.org/wiki/Logical_reasoning
4. Argument from analogy, Wikipedia. https://en.wikipedia.org/wiki/Argument_from_analogy#:~:text=Argument%20from%20analogy%20is%20a,the%20world%20and%20make%20decisions.

Plato's Lysis (a dialogue on friendship)

Lysis (Friendship) By Plato Dramatized Audiobook - Audiobooks Dimension

The Text - Translation by Benjamin Jowett (1817 - 1893)

The following is a link to a pdf file of the dialogue. https://drive.google.com/file/d/1OA8uC-hIAl6Dl2qmNZFXAHKtk8bysdVq/view?usp=drive_link

The following is a link to the The Project Gutenberg EBook of Lysis, by Plato on the internet.

Perseus Digital Library text on Lysis: https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0176%3Atext%3DLysis

Some resources

Wikipedia: Lysis (dialogue)

Wikipedia: https://en.wikipedia.org/wiki/Friendship

Some questions relating to friendship

(Extract from the Introduction section of the Benjamin Jowett translation of Lysis)

The subject of friendship has a lower place in the modern than in the ancient world, partly because a higher place is assigned by us to love and marriage. The very meaning of the word has become slighter and more superficial; it seems almost to be borrowed from the ancients, and has nearly disappeared in modern treatises on Moral Philosophy. 

We may ask the following:

1. What are the different type of friendships?
2. Why do people want to have friends?
3. What are the characteristics or personalities that enable one to have more friends?
4. Why do some people have a few good and close friends, some have many acquaintances, and some people are lonely?
5. Is friendship between humans only? Could there be friendship between: a) human and pet/animal, b) animal and animal,  c) human and subject (e.g. philosophy, mathematics, science), d) human and activities (e.g. work, sports, art)?
6. Philosophy means "love of wisdom".  Is that one of the most important type of friendship?
7. What is friendship? (Please see for information the Wikipedia page on friendship.)
8. What are the main themes explored in Lysis and what are some questions related to those themes? (See Wikipedia page on Lysis.)

Introduction to Philosophy

What is Philosophy?

Philosophy is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, value, mind, and language. It is a rational and critical inquiry that reflects on its methods and assumptions.

Historically, many of the individual sciences, such as physics and psychology, formed part of philosophy.  However, they are considered separate academic disciplines in the modern sense of the term. [1]

What does the word "philosophy" mean? 

The word "philosophy" literally means "love of wisdom".  The word philosophy comes from the Ancient Greek words φίλος (philos) 'love' and σοφία (sophia) 'wisdom'. [1]

What are the branches of Philosophy?

Let's have a look at the following Wikipedia pages:

Portal: Philosophy
https://en.wikipedia.org/wiki/Portal:Philosophy

Outline of Philosophy

https://en.wikipedia.org/wiki/Outline_of_philosophy

Some Questions for Discussion

1. Why do people study and practise philosophy?
2. Is philosophy or the pursuit of wisdom a good thing? 
3. Is having wisdom sufficient for a person to be a good person?
4. Is the pursuit of wisdom sufficient for a person to live a meaningful life?
5. Can the study and the practice of philosophy help to improve the world?
6. What is or are the aims of studying and practising philosophy?

Note:

1. Wikipedia: Philosophy page.

Welcome to first class of 2025

 At this class, we will briefly introduce ourselves, and then have a look at the following:

• Emergency and evacuation procedures

• WhatsApp discussion group

• The Philosophy Phor Phun Discussion Blog

• Guidelines for respectful, constructive, and inclusive philosophical discussion

• Political Discussion and Philosophical Discussion

Record of 2024 Discussion Topics

Year 2024

Term 1 started on Wednesday 7th February 12:30 - 1:30 PM in Meeting Room 5 at the Hub.

Term 1 discussion topics

Class	Dates	Discussion Topics
1	7/2/2024	What is Philosophy?
2	14/2/2024	What is Philosophy? Prof. Kaplan
3	21/2/2024	What is Philosophy?  Karl Jaspers
4	28/2/2024	What is Philosophy?  Karl Jaspers
5	6/3/2024	Sources Philosophy, K Jaspers
6	13/3/2024	The Comprehensive, K Jaspers
7	20/3/2024	Aristotle's Ethics (Helen to take class)
8	27/3/2024	Peter Singer (Helen to take class)

Term 2 discussion topics

Class	Dates	Discussion Topics
1	17/4/24	Critical Thinking
2	24/4/24	Predicament of Existence
3	1/5/24	Myth we need to survive - Yuval Noah Harari
4	8/5/24	Myth we need to survive - Yuval Noah Harari (cont.)
5	15/5/24	Critical Thinking (cont.)
6	22/5/24	Critical Thinking and Schrödinger's Cat
7	29/5/24	Schrödinger's Cat and Double Slit Experiment
8	5/6/24	Schrödinger's Cat and Critical Thinking
9	12/6/24	Critical Thinking
10	19/6/24	Smell the glove is here

Term 3 discussion topics

Class	Dates	Discussion Topics
1	17/7/24	Socrates
2	24/7/24	Socratic method
3	31/7/24	Plato's dialogue - Euthyphro
4	7/8/24	Plato's dialogue - Euthyphro
5	14/8/24	Plato's dialogue - Euthyphro
6	21/8/24	Euthyphro Dilemma
7	28/8/24	Euthyphro Dilemma / Introduction to Ethics
8	4/9/24	Free will and determinism
9	11/9/24	Free will and determinism / Normative Ethics - Consequentialism
10	18/9/24	Lunch and chat at Canteen

Term 4 discussion topics

Class	Dates	Discussion Topics
1	9/10/24	John Rawls - Helen took the class
2	16/10/24	Isaiah Berlin - Two Concepts of Liberty
3	23/10/24	Some questions on the two concepts of liberty
4	30/10/24	Value Pluralism
5	6/11/24	US election news / Value pluralism (cont.)
6	13/11/24	TBD (US news / Some terminology of meta ethics / Liberalism?)
7	20/11/24	Lunch at Blackburn Hotel

The Problem of Evil

 

The Problem of Evil: Crash Course Philosophy #13

Introduction

The problem of evil is the philosophical question of how to reconcile the existence of evil and suffering with an omnipotent, omnibenevolent, and omniscient God.  

The above video from Crash Course Philosophy gives an introduction to the problem of evil.  The following are some other videos that introduce the problem of evil:

• Philosophy Vibe - The problem of evil (and the existence of God) 
• https://youtu.be/FfjrJH9PNPA?si=VCrEqsmZq7v40kyG
• This video presents the following defences or theodicies:
• The Augustinian Theodicy
• Irenaean (Soul Making) Theodicy
• The Free Will Defence Argument

Theodicies

The following videos present different defences or theodicies:

• Alex O'Connor - Free Will (defence), Souls, and the Problem of Evil | Richard Swinburne
• https://youtu.be/8Y3PtkyhOiU?si=0EhzNayO5dQckq3L
• Philosophy Vibe - Free Will Defence - Does it Solve the Problem of Evil?
• https://youtu.be/bIoN-CTwjAU?si=K0QeQyQA-zPepBEJ
• Philosophy Vibe - Leibniz - Best of all Possible Worlds Argument (Explained and Debated) 
• https://youtu.be/K8PNhJZrDlY?si=demit9KdbC6Vxylf
• Untangle Philosophy - John Hick & the Soul-Making Theodicy
• https://youtu.be/FUDmovWczng?si=5LsIo-O3oOm4Ze4g
• Untangle Philosophy - Augustine’s Theodicy | Free Will, Fallen Angels & Original Sin 
• https://youtu.be/fQZ9soVdcq0?si=OGOEhU_Ip0swOSzC
  

The arguments

The following videos present the arguments relating to the problem of evil.

• Wireless Philosophy - Philosophy: the problem of evil part 1
• https://youtu.be/V4z9Y2u30Qs?si=O2VQrqAN0Eku6MEb
• Wireless Philosophy - Philosophy: the problem of evil part 2
• https://youtu.be/prWSGbDW3LU?si=qDCNY1qOS3RIf0yM
• Wireless Philosophy - Philosophy: the problem of evil part 3
• https://youtu.be/L67dlpMgDa4?si=AT7tqTNULYwcy52U
  

Further readings

1. Internet Encyclopedia of Philosophy - Logical Problem of Evil - https://iep.utm.edu/evil-log/
2. Stanford Encyclopedia of Philosophy - The Problem of Evil - https://plato.stanford.edu/entries/evil/
3. Wikipedia - The problem of evil - https://en.wikipedia.org/wiki/Problem_of_evil
4. Wikipedia - Theodicy - https://en.wikipedia.org/wiki/Theodicy

Some Questions

1. Free Will is one of the explanations for the problem of evil.  Is evil necessary for the existence of free will?  Can't one choose between different good options?  
2. Christians believe there is no evil or suffering in heaven.  Since God allows people to have Free Will, Free Will must be good.  If Free Will is good, people would have Free Will in heaven.  Since it is possible to have Free Will in heaven where there is no evil and suffering, then evil and suffering and Free Will can co-exist.  Does that mean Free Will is not a good defence for the problem of evil?
3. One explanation of the existence of evil and suffering on earth is that Adam and Eve disobeyed God and therefore God allows evil and suffering to exist on earth.  If the reason for evil and suffering is because God wishes to punish humans, then why are there so much evil and suffering?  The punishment does not seem to be proportional to the misdemeanour.
4. One explanation of the existence of evil and suffering on earth is that they are caused by Satan, a fallen angel.  However, since God is omnipotent, why does God allow Satan to exist?
5. A defence of the existence of evil and suffering is that humans are not able to understand God's reasons for allowing evil to exist.  It appears that God had created a universe with natural laws and God does not interfere with the day to day running of the world.  If that is the belief, is it still reasonable to believe in an omnipotent, omnibenevolent, and omniscient God who is in control of all things on earth?