4. Propositional Logic and Black on Black Violence

 

 

Abstract. This lesson is an attempt to apply of Propostional Logic to fallacious statements (largely implications) about black and black violence and police brutality. 1. Applying the fallacy of denying the antecedent to a Rudy Guilaiani quote. 2. A brief summary of Propositional Logic. 3. Evidence both public and person of black people decrying black on lack violence in music and the church. 4. The normalization of black on black violence with the metaphor to breathing. 5. The fallacy of Affirming a disjunct and the fact that someone can protest police violence and black on black violence. 6. Affirming the consequent or the fallacy of more police.

 

 

1       Applying the fallacy of denying the antecedent to a Rudy Guilaiani quote

 

“Black Lives Matter never protests when, every 14 hours, somebody is killed in Chicago, probably 70 to 80 percent of the time a black person..” Rudy Guiliani

 

This statement implies that you should only protest police violence if you are willing to protest black on black violence. Statements like this annoy me. Because as a black person who has grown up on hip hop and in the church I can honestly say that there have been many rap songs, sermons, marches and movies that have openly denounced black on black violence and posed solutions. When that statement “Black Lives Matter never protests when, every 14 hours, somebody is killed in Chicago, probably 70 to 80 percent of the time a black person..” is rewritten with its implication it could look like the example below:

 

 

You should only protest police violence if you are willing to protest black on black violence.

You don’t protest for black on black violence

Therefore you shouldn’t protest police violence

 

When it is written in this way one can see it for what it is a propositional logic fallacy. This is the fallacy known as denying the antecedent. This occurs when one infers the opposite of the original statement.

If P, then Q.

Therefore, if not P, then not Q.

which may also be phrased as

{\displaystyle P\rightarrow Q} (P implies Q)

{\displaystyle \therefore \neg P\rightarrow \neg Q} (therefore, not-P implies not-Q)

 

This argument form does not give good reason to establish its conclusions, even if its premises are true.

If you are a line cook, then you know how to cook.

You are not a line cook

Therefore, you can’t cook.

 

 

2       A brief summary of Propositional Logic

Putting this statement is the Propositional Logic form helps to illustrate the irrationality of these statements. In Algebra letters represent numbers while in Propositional Logic - letters represent statements or sentences. The common letters used in Algebra are x, y, and z. The common letters used in Propositional Logic are p, q, r, and s. And each letter represents a statement. It represents a sentence (Subject and a predicate). Propositional Logic is Macro Logic

We are not concerned with what is in the sentence, but how the sentence is said to relate to others. Propositional Logic only worries about those statements that are already sentences by themselves. So we might list them in one single sentences but those parts that can be broken out as separate sentences are what we are concerned with.

 

Example

1.                If it is raining outside

2.                then I will bring an umbrella

3.                It is raining outside,

4.                therefore I will bring an umbrella.

 

These are sentences on their own.

So we are concerned with them in Propositional Logic and we can replace these sentences with letters.

 

 

“1. If it is raining outside” Can be replaced with “P”

“2. then I will bring an umbrella” Can be replaced with “Q”

 

When we do this we have the sentence

 

If P then Q

 

Truth Tables – is a table, where if you make a statement you can then list all the possible outcomes of that statement. The statements are represented by letters. The statement “It is raining” is represented by the letter “P”. And the statement is either TRUE or FALSE.

 

Statement “P”:

Either it is raining or it is not raining

“It is raining” is either T (TRUE) or F (FALSE)

You have two possible outcomes with this statement.

If you have two statement

“It is raining” and “I have an umbrella”

 

We have four different outcomes

“T” - It is raining and I have an umbrella - “F”

“T” - It is raining and I do not have an umbrella - “F”

“F” - It is not raining and I have an umbrella - “T”

“F” - It is not raining and I don’t have an umbrella - “F”

 

We have there statements we have eight different outcomes. And with four we’d have sixteen.

 

It is possible that an argument that denies the antecedent could be valid if the argument instantiates some other valid form. If the first premise of a new argument was "If I listen to enough rap music, then I will come across a song that decries black on black violence.” This claim is now modus tollens, and thus valid.

 

If I listen to enough rap music, then I will come across a song that decries black on black violence.

I don’t listen to enough rap.

Therefore, I have not come across a song that decries black on black violence

 

 

 

5       The fallacy of Affirming a disjunct and the fact that someone can protest police violence and black on black violence

Affirming a disjunct is the fallacy of concluding that one disjunct must be false because the other disjunct is true. Eventhough both statements may both be true because "or" is defined inclusively rather than exclusively. It is a fallacy of equivocation between the operations OR and XOR. Affirming the disjunct should not be confused with the valid argument known as the disjunctive syllogism.

The action is illegal, or it is not subject to a penalty.

The action is not illegal.

Therefore, it is not subject to a penalty.(This is the valid form) Below this disjunctive syllogism is the invalid form.

 

A or B

A

Therefore, not B

 

The following argument indicates the unsoundness of affirming a disjunct:

You can protest police violence or you can protest black on black violence.

You are protesting police violence.

Therefore, you can’t protest black on black violence.

 

This inference is unsound because you can protest both.

 

To be the president one must be an idiot or very ugly.

The president is an idiot.

Therefore, this idiot is not very ugly.

 

This is fallacious because the president could be both.

 

 

 

6       Affirming the consequent or the fallacy of more police

Anyway many of our problems (the 22 percent of us who are poor, BECAUSE ALL BLACK PEOPLE ARE NOT POOR) stem from poverty and politicians, and some older black people, present more cops as the solution. This presents us with the fallacy of affirming the consequent (also a predicate logic fallacy). This fallacy occurs when on takes a true conditional statement and invalidly infers its converse even though the converse may not be true. If my window is busted someone broke in. Someone broke in so my window is busted.

 

If we have more police there will be less crime.

There are more police

Therefore, there is less crime.

 

More police is not the only reason for reductions in crime. Many other things reduce crime, elderly people commit less crime, and employed people may commit less violence rime. Also when we get more police we get more racialized policing where officers are often more brutal on black bodies. Cops won’t protect you if you report a crime, they may even end up killing you if and getting away with it if you are black.

We can’t resolve unemployment, poverty and crime in the black community or any community with more police. This is obvious. We also can’t continue to use black on black violence, which is a result of years of racist police/police, etc, to undermine people protesting racist criminal justice norms and policies. So stop it.