Logic and Critical Thinking


I. What is logic? Is Spock from Star Trek your idea of logic? Think of it this way, a carpenter needs to know how to build a cabinet with a saw or hammer. A mechanic needs knowledge of how a car works and best way to fix it with wrenches. A surgeon has to have a medical ability in order to use his scalpels and clamps properly.

But philosophy is the art of thinking, there are no tools except the tools of the mind. An untrained carpenter will make a cabinet that is not square, with poor fitting doors, and gaps in the seams. A cabinet will be made, but not well. The untrained thinker can think about a conceptual subject and come up with an answer that is a little crooked, with some gaps and poor fitting sections. A trained thinker will build a better cabinet of thought. Logic is that training, the tools needed, the understanding of how to use the tools of the mind.

Logic is usually a class of its own and you will see why. It is a vast area and we will just touch on the basics, such as the use of terms, their definitions, the types of statements, and the way to argue properly.

Logic that is based on language and the analysis of the way we think with words and phrases, is often called term logic or Aristotelian logic. This is what we are going to look at here, since it is the oldest and and most fundamental logic. There are other logical systems that try to reduce terms to symbols or other mathematical principles in order to remove some of the ambiguity or lack of precision of language.

Logic has various parts, since there are various ways the mind works and steps it goes through. We can divide these into three main parts.
1.    The mind initially knows a thing through its concept. The first part is then the logic of the concept, seeking to learn how to define a term, make an idea of an object that is unclear to be more distinct, and divided into its category. e.g. The idea of “triangle”
2.    Then the mind puts terms together in a statement and judges it to be a certain way, a phrase with a sense of true or falsity, “a triangle has three sides” - the logic of the statement.
3.    Then we put together statements in a sequence to form an rational argument or discourse, called a syllogism, or discursive reasoning – logic of the syllogism.
The main sources for term logic is a set of books by Aristotle called the Organon. Socrates in many ways was the father of logic, dedicating his life to leading people to define what they believed in, sometimes to their frustration. But he did not write a system of logic and Aristotle took it from there and developed it fully.


So first is the logic of the concept. Above all one must define the terms being studied. If we are looking at the issue at hand but you think the terms mean one thing an I think they mean something a little different, we may go around and around arguing, but may really agree, since we do not know what the other is saying. Or we will think we agree, but since the words mean one thing to me and something a little different to you, we do not actually agree. The word Define – comes from de-finis, to make limits.

1. The definition and the predicables.
A definition that is complete will consist of enough info to fully explain the term, the definition and the term should be interchangeable. There are five “predicables” that can be used to create a definition. They are called predicables because they are ways something is predicated, i.e said of another. 

These five are:
    as Genus,
    as Species,
    according to its Specific Difference,
    according to its Properties,
    according to its Accidents

The Genus is what is predicated when asked what is it? of many species, “a man is an animal”.

The Species is predicated when asked what is it of a subgroup of the genus, “Socrates is a man”.

The Specific Difference is that which essentially divides the genus into the various species, “man is a rational animal”.

A property is a trait that is always and only found with that species but is not essential, “humans can laugh”.

An accident is a trait that belongs to a thing, but not necessarily, and other things have it to, “Socrates is white.”

Another way of looking at the process of defining is mentioned in the book, by use of necessary and sufficient conditions. A necessary condition is that which must always be present for the concept being defined, like the specific difference and properties mentioned above. The sufficient conditions are the total set of necessary conditions needed for the concept to be completely defined.

2. The Categories:
These predicables and conditions are used to build proper philosophical definitions, they are the tools of working with concepts and terms. Aristotle also gives a set of categories that each thing fits into. The normal sets of categories consist of ten. Every concept one has, should move up through various genus and species until it reaches one of these categories, which are the highest level (the Summum Genus). 

The 10 are:
    Substance – concepts that answer what is it? the subjects of predicates and accidents.
    Quantity – concepts that answer the question how much? (five yards, many)
    Quality – concepts that answer the question what is it like? (redness, tall)
    Relation – concepts that are ordered to each other (superior, half)
    Place – concepts that answer where? (downtown)
    time – concepts that answer when? (yesterday, sundown)
    position – concepts that answer the question what form? (upside down, bent)
    outfit/habit – concepts that answer what is covering it? (armored, clothed)
    action – verbs or gerund verbs (to run, to stab, stabbing)
    being acted upon (passion) – receiving an action (being stabbed, being healed)
Only category Substance is for things, the others are for types of accidents mostly.

3. Concepts and Words
Lastly, the relation between the concept and the word. The concept is the sign of the object in our thought. The word or term is a sign of the concept. By means of a term I pass to a listener the concept I have in mind. I say dog, you think of dog. The concept is a sign of the object, so a word has an indirect link to the object by means of the concept.
Now words are not a precise as concepts, since I have a separate idea of each thing, but terms are not always so clear. The same term can be used for different concepts, such as Atlas the book of maps, and Atlas the constellation, and Atlas the mythical giant. Each has a different concept with the same word. This leads to three ways of using terms:

First is called equivocal terms, these have the same term with various meanings, such as "Atlas".

Second is called univocal terms, these are used with only one corresponding concept, such as “desk” – it is what it is, the term is pretty much used the same way whenever it is used.

A third way is included by many, this is analogy. Analogy is an important third way (sort of a middle way between uni- and equivocal). This is when a term is spoken of many different things in a way that is different for each one, but all related to one common meaning. Such as “healthy”, we say healthy apple, healthy person, healthy skin tone, healthy attitude, etc. It means slightly different things in each case, but all related to the health of the person. Some claim it is just another case of equivocal use. Some want to try to figure a way to overcome it and not use it since it is an unclear part of logic, they say an ideal language would have a different term for each concept. But philosophers do not create the way we speak (thank goodness).

Most see analogy as an important part of our knowledge, since we know some things well, and others vaguely, we can use analogy to learn slivers of knowledge about things we do not know, by referring them to things we do know.


1. What is a statement.
The logic of our statements is the next activity of the mind, and the next part of logic. A statement is used to transmit our judgments to others. If I just say a word, you will think of it, but you will not know what I mean, it is an incomplete communication. To just use a term no judgment of truth or falsity is made. “Dog” just is the idea of a dog, but to say “the dog is red” has truth or falsity to it, truth or error is only found in a composed phrase – two or more concepts put together. A statement is the combining of multiple concepts with a verb to express a truth. Not every sentence is a statement (also called a proposition or declaration), only those inviting truth or falsity. A request or a command is not a statement.

2. Opposition of Statements.
The statement divides into various types: it can be either a positive affirmation (some people are wise), or a negative denial (some people are not wise). It can also be universal (all dogs bark) or particular (that dog barks). 

One can go up and down the levels of universality. To say “Socrates is tan” means I can also say “some men are tan”, but does not mean I could say “all men are tan”. To say “all men are rational”, means I can also say “some men are rational” or Socrates is rational”. In philosophy one deals mainly with the universal, so as to be able to apply it to every particular example contained in the universal concept.
There is a chart to organize these statements:

A = universal affirmative       < contraries >        E = universal negative / denial
                l                       \                         /                      l  
        subalterne                     Contradictory                    subalterne
                l                       /                         \                      l
I = particular affirmative      < subcontraries >    O = particular negative / denial

The forms of statements are traditionally labeled A, E, I, O, and all oppose each other in different ways, as shown by the arrows and lines. By use of the chart one can see, that if an I statement is true, the same terms in a E statement must be false because they are contradictory.

Contradictory statements are those opposites of different quantity and , they have no middle ground, if one is true the other must be false.

Contrary statements have same quantity (both universal) and exclude each other as being true, but both could be false, a middle ground exists.

Sub-contrary statements have the same quantity (both particular), and can both be true, but not both false.

There are many rules for converting statements, negating statements, adding possibility to them, adding necessity to them... way more than is for this class.


1. The argument is the next act of the mind. The mind seeks knowledge by putting together statements of truth or falsity that relate to each other in order to come to a conclusion. The is called an argument, or in philosophy a syllogism. It is also called the process of deduction, or the reasoning process.

It has nothing to do with the emotional fights people have with family or friends that we call arguments. Philosophical arguments seek to appeal to the intellect, to prove a point. Fancy talk to sway feelings is for advertisers and politicians – this can move people, but temporarily. A logical intellectual proof moves someones ideas more permanently. But no one is immune from giving up what they know by rational proof to be true, and to follow their emotions and desires which are very powerful if not under control. So a perfect real world argument uses logic proofs, mixed with motivations based on emotion as well to supplement the reasoning. But here in philosophy we look at the logical side. In a class of rhetoric or public speaking you should learn the ways to motivate other by speech that addresses the emotions.

2. Structure of a syllogism.
The reasoning process is a series of statements, the first two are the premises, the third is the conclusion, a result of the first two.  A=B, and B=C, therefore A=C is the basic structure. For example, “I (A) am a teacher (B), teachers (B) are underpaid (C), therefore I (A) am underpaid (C)” The premises should lead necessarily to the acceptance of the conclusion.

To be a convincing argument the premises must be true, and the structure must be valid. If an argument is validly structured, but a premise is not true, it it is false. For example, "All dogs are animals, the hound is not an animal, therefore the hound is not a dog" (incorrect since a hound is an animal). Or it could have true premises, but a faulty structure, and thus does not work either. For example, “All dogs are animals, all cats are animals, therefore all dogs are cats” (the middle term is predicate in both premises.)
The key to the syllogism is the use of the middle term. One term should be the subject of one premise, and predicated of the other. There are 14 forms of the syllogism based on position of the middle term, and whether the statements are universal or particular. Each of these has its own rules to convert it to a basic syllogism, but that is beyond this class. In the middle ages Latin songs were written to help remember the types of syllogism forms.

3. Other types.
Arguments can be dialectic as well (asking questions), syllogisms of probables (A is probably B, B is C, therefore A is probably C), or can be inductive instead of deductions like syllogisms. An induction is to argue to a universal generalization, based on individual examples, for example, This computer runs on electricity, your computer runs on electricity, therefore all computers run on electricity.” It often works, but does not provide solid proof, for example, “I can speak English, John can speak English, Jane can speak English, therefore all people can speak English.” Induction only provides a probable argument.


There are many common distortions of logical principles, they are seen everyday in news stories and poorly written articles or books. Many appear wise without reality of wisdom. We will cover some common ways of arguing improperly by use of the fictional argument in White pg 28: 
1. Use of ambiguous terms – not defining first the concepts your talking about. 
2. Skipping the middle term - missing a premise, resulting in an incomplete argument. 3. Ad Hominem attack - fighting the arguer, not the argument, poisoning the source. 
4. Improper association of cause, post hoc ergo propter hoc assuming something is caused by another simply because it follows it. Opposite can also be wrong, denying the antecedent. 
5. Posing a hypothetical contrary to fact 
6. Appeal to authority - Sometimes valid to establish probability, but not allowed in strict argument. Allowed if one is arguing the details of an authoritative pronouncement (I.e the constitution, or bible study). Logic can also be used to establish authority, for example, Jesus (or Moses, or other holy person) did miracles, miracles are from the divine, thus Jesus is from the divine, that from the divine cannot be wrong, Jesus is from the divine, thus Jesus cannot be wrong. Or Aristotle's theories are often good explanations, good explanations are a sign of wisdom, thus Aristotle shows wisdom. 
7. Improper analogy – the various terms of the analogy must have a true relation to the one unifying meaning. 
8. The All-or-Nothing, or False Dilemma – the error of reducing the available options to an either-or even though more options exist. Making black and white what is not. 
9. Emotional appeal – bypassing reason to sway feelings. 
10. Unsubstantiated Generalization – an improper induction, making an Unsubstantiated leap from the individual to the universal. 
11. Emotionally charged terms or name calling – similar to ad hominem 
12. Statistical error – using an unrepresentative example, appealing to the authority of the crowd, and improper induction all follow from this. 
13. Straw-man argument, or red herring – arguing against a position similar to your opponents, that is easier to refute. 
14. Circular reasoning – also called begging the question. Using a premise that relies on something very similar to the conclusion, for example, “Are my friends brainwashed by the enemy? No, since they say they are still your friends, and friends would not lie to you, therefore, they are still your friends.”

So why do people fall into such false logic so often?

For many it is force of habit and poor education, laziness and lack of mental discipline, since it is hard work to create a good argument. Fear of change is also a big cause. Some questions are so important that to “lose” the argument means changing one's views and this is a scary idea for many.

Politics is a good example. If I lose, the other party may enact their laws which will lessen my power. To not have the power is a scary idea for a politician.

Secret desires are powerful as well, we want what we want and others may stand in the way, we will create an argument no matter how illogical in order to obtain what we want.
A  good critical thinker, who wishes to argue properly, needs to be in control of their emotional urges and desires and fears. One sees in the history of thought so many philosophers that lived a disciplined and austere life in order to think better.