Saturday, January 3, 2015

Ad hominem

The phrase "ad hominem" means, "to the man." In logic it refers to an informal fallacy where the person giving the argument is attacked instead of the argument itself. It is designed to deflect attention away from the weakness of the attacker's position or the strength of the defender's. This is common in politics, and is not always without merit.

If an environmentalist candidate flies exclusively in private jets, it is right to point out this hypocrisy, but hypocrisy doesn't affect the truth or falsity of his positions on global warming or other issues. Further, too often in politics and religion ad hominem attacks are used in lieu of valid reasoning skills.

For can you trust a draft-dodger's views on foreign policy? .... How can you believe in that religion with so many bad people leading it? ... That politician sleeps around and he wants to tell me what to do with my body? ... that man opposes gay marriage just because he's a homophobe...that person supports that bill because she's racist...

And so on. All of the above statements attack the person and not the idea. They may help us feel better but not think better.
posted from Bloggeroid

Categories again

Blogs are a good examples of how we use logic and categories.  Some blogging platforms have "Categories" and "Tags."  Others, like Blogger, have "Labels."  Bloggers who have the two use "Categories" to represent something broad like "fallacies," and "tags" to represent specifics such as "ad hominem" and "denying the antecedent."  Tags can be used any time a specific fallacy is mentioned, but categories keeps it general enough to avoid microprecision and clutter.

I use "Labels" like "Categories." I don't want to mention every fallacy every time, because there may be some I mention only once, and others I mention multiple times.  It's easier to stay broad and add more labels if I need to.

The point of this is that Blogging is a good example of the value of logic.

Denying the Antecedent

A logical condition has two parts: the antecedent and the consequent.  The antecedent (with the prefix ante-, meaning coming before, like anteroom or antebellum), indicates the first part of the condition.  If I say, "If P then Q" or "If it is raining, then the ground is wet" the antecedent is "P" or "it is raining."  The consequent is the other part of the condition, the Q, "the ground is wet."

There are two common fallacies: affirming the consequent and denying the antecedent.  If I affirm the consequent, I am saying that the ground is wet, so therefore it's raining, ignoring the possibility of the ground being wet for other reasons, such as a busted fire hydrant.  If I deny the antecedent, I say that since it is not raining, the ground cannot be wet, also ignoring the possibility of the ground being wet for other reasons.  Just because it is not raining does not mean the ground is dry.


Too many people today seem to have trouble dividing ideas and distinguishing things into categories.  A solid background in logic helps us to do this.  Logic has several mundane, practical applications such as helping people make lists, categories things and ideas, and organize their stuff and their plans.
Children learn logic primarily through games, such as sorting games and matching games.  There they learn how to create categories and systematically solve problems.  If a childhood is lacking in these games, the adult child will be lacking in logic skills.  We are by nature rational creatures, but neither our ideas nor our modes of thinking are wholly innate.  They must be learned.

Friday, January 2, 2015

Modus Tollens

The companion to modus ponens is modus tollens, the way of denying.

If I say something like, "if P is true, Q is true," and add, "however, Q is not true," I can conclude that P is not true, either.  In short: "If P, then Q. Q is not true, so neither is P."  I know this is so because if P were true, Q would be true.  But Q isn't true, so P can't be.

Here is an example: If it is raining outside, then there are clouds in the sky.  There are no clouds in the sky, so it is not raining.  The first sentence says there must be clouds for it to rain.  The second sentence tells me that there are no clouds, so how could it be raining?  It couldn't be raining, and it isn't raining!

Another example: In order for me to have stabbed the man, I must have been next to him.  However, I wasn't even in the same room.  Therefore, it couldn't have been me!  This example deviates from the grammatical syntax of the other, but follows the same logical form: If P (I stabbed the man), then Q (I was next to him).  Q isn't true (I wasn't in the room) therefore P isn't true (I didn't stab him).

Modus ponens & Affirming the Consequent

One of the most basic rules of validity is known as modus ponens, "the affirming way."  In short, it says that if I have a conditional statement and the first part of the statement is true, the second part must also be true.  This is often written as "If P, then Q.  P is true, so Q must be true."

Here are a few examples:

If it is raining, the ground is wet.  It is raining, so the ground is wet.

If you are human, you are also a mammal.  You are a human, therefore you're a mammal.

If you get 3 strikes, you're out.  You have three strikes, so you're out.

Each example follows the same logical structure.  If (something happens), then (something else will happen).  Since (the first thing happened), I know that (the second thing happens).  I know that the ground is wet because it is raining.  I know that I am a mammal because I am human.  I know that I'm out because I got 3 strikes.

Keep in mind that this does not work in reverse. I do not know that it is is raining just because the ground is wet (someone could be washing their car).  I do not know that I am human because I'm a mammal (I could be a horse).  I do not know that I got 3 strikes because I'm out (I could have hit a pop fly).  If I were to make an argument this way, I would commit the formal fallacy known as affirming the consequent.

The consequent is the Q part of "If P, then Q."  This fallacy effectively says, "If P, then Q.  I know that Q is true, so P must be true."  As shown in the examples above, this isn't true.  There could be other reasons Q is true without P being true.


When we construct an argument, our terms must be unambiguous.  Their meanings must be clear and known to all involved.  Politicians and sophists of various stripes love to exploit ambiguity.  This is a fallacy known as equivocation.

Consider the following bit of dialogue:

Are you aware that Jim is gay?
Really?  He doesn't seem that happy to me.

The ambiguous term gay here is exploited by the meanings homosexual and happy, carefree.

Another example in the form of a syllogism:

God is love.
Love is blind.
Therefore God is blind.

This argument is valid, but is not sound because the terms love and blind are ambiguous.  Their meaning changes throughout the syllogism, and the multiple meanings of the words are exploited.  The first love refers to love of a self-sacrificing the nature, the second to erotic love or sacrificial love, depending on whom you're talking to.  The first blind is metaphorical, whereas the second is literal.  Arguments like this are sound and fury signifying nothing.

Thursday, January 1, 2015


Logic need not be complicated.  It is not merely for the pseudo-vulcans of the academy.  Children must be taught logic if we are to have an educated citizenry of the future.  Children who are taught logic will read better, write better, understand the concepts of math, science, and social studies better.  Children who are taught logic will become more virtuous adults.

The foundation of logic is common sense.  Let us learn how to think again.


Gregory of Nazianzus, to Sophronius, for his son:

Gold is changed and transformed into various forms at various times, being fashioned into many ornaments, and used by art for many purposes; yet it remains what it is— gold; and it is not the substance but the form which admits of change. So also, believing that your kindness will remain unchanged for your friends, although you are ever climbing higher, I have ventured to send you this request, because I do not more reverence your high rank than I trust your kind disposition. I entreat you to be favourable to my most respectable son Nicobulus, who is in all respects allied with me, both by kindred and by intimacy, and, which is more important, by disposition. In what matters, and to what extent? In whatever he may ask your aid, and as far as may seem to you to befit your Magnanimity. I on my part will repay you the best I have. I have the power of speech, and of proclaiming your goodness, if not nearly according to its worth, at any rate to the best of my ability.


Given that everything that is, is, something cannot both be true and false at the same time under the same circumstances.  Either A or not A.  Either I am married or I am unmarried.  Either I am alive, or dead.

This idea forms the second and third laws of thought: noncontradiction and the excluded middle.

Identity says that everything is itself; whatever is, is.  Noncontradiction says that it is itself and not something else; whatever is, cannot not be.  The law of the excluded middle says that no third way is possible; everything either is or is not.

The rules include things that are mutually exclusive of one another, but not do not include either/or statements that admit other possibilities.

For example, I have a glass of something to drink.  It is either water or something else.  Water or not water.  I can say that about any liquid: this liquid, or not this liquid.  But under the LNC, I cannot say "it is water or milk."  I may be able to make that assertion if someone poured a drink for me and the only drinkable liquids in my house are water and milk.  In that case, I have eliminated all other possibilities.   However, it does not follow from the LNC that my drink is either water or milk.  Water and milk do not logically contradict.

To attempt to say logically that my drink is either milk or water is to commit the fallacy of the excluded middle, i.e. to say that there is no third way when there actually is.


There are either absolutes or there are not absolutes.  If I assert that there are no absolutes, my assertion is itself an absolute; therefore, there are absolutes.

One such absolute is that everything that is, is.  Everything is itself.  Desiring, wishing, willing, or positive thinking alone will not change something from one thing to another.

This is sometimes phrased as "A is A."  In math we use the word "equals."  Everything is the same as itself.  A word always rhymes with itself.  A number is always equivalent to itself.

This principle is known as the Law of Identity and is the most fundamental law of thought.


"Your argument is invalid!" Perhaps you've heard this phrase before.  Perhaps you've used it yourself.

To most people, invalid is synonymous with wrong (i.e. false, not true) and it is wrong because I said so.  However, an invalid argument is not necessarily a false one.  By that I mean that the conclusion may be true even if the argument is invalid.  Likewise, an argument may be valid but have a false conclusion.

Consider an example of the first possibility:

1. All men are mortal.
2. Churchill is mortal.
3. Therefore, Churchill is a man.

Every one of these statements are true.  But the argument is not valid.  There is nothing about the first two statements that leads me to believe the third.

Consider an example of the second possibility:

1. All men are immortal.
2. Churchill is man.
3. Therefore, Churchill is immortal.

Since the first premise is not true, but the argument is valid, my conclusion is false as a result.  If all men were immortal, Churchill, being a man, would be immortal.  But not all men are immortal, and in fact, all men are mortal.

What is a valid argument?  A valid argument is one where if the premises are true and the terms unambiguous, the conclusion must be true.  Your choice is to believe the conclusion or be illogical.  Validity has to do with the form of an argument.  The structure of some arguments force you to believe the conclusion, just as the structure of some buildings force you to enter and leave a particular way (such as through a door rather than a window). We need valid arguments in order to think, debate, and reason clearly.  Otherwise, we are blindly stumbling looking for truth.

In the first example above, we see that all men are mortal and that Churchill is mortal.  But I do not know anything else about Churchill.  I can't conclude anything about him.  Churchill may be the name of my pet British bulldog, and hence not a man, rather than the British leader nicknamed the British Bulldog.  In the second, my knowledge of the first two statements leads me to my knowledge of the third.  I know that Churchill is mortal because he is a man and all men are mortal.

Consider a third possibility where an argument is valid and the conclusion true:

1. All men are mortal.
2. Churchill is man.
3. Therefore, Churchill is mortal.

When the structure, or form, of an argument is valid; the terms are unambiguous, for example, we know what mortal and men mean; and the premises are true; we must believe the conclusion.  We call this a sound argument.  It is impossible to disbelieve a sound argument and remain a rational thinker.