Philosophical logic is just a tool for Philosophers to structure the arguments they want to make, so their argument can be easily followed, checked, and proven without the trappings of rhetoric and literary flare. The study of logic is really the study of operations of thought, allowing a Philosopher to conform her own thinking and ideas to proven methods and strategies to reduce the chance of error.
The biggest difference between a formal and an informal fallacy is the effect the fallacy has on an argument. An informal fallacy may invalidate an entire argument, but more commonly, an informal fallacy just weakens an argument or is immaterial to the actual argument itself and is discarded. Formal fallacies actually invalidate an entire argument when detected, so if a Philosopher is checking over a proof for an argument, and she detects an a formal fallacy, she can simply stop parsing the argument and state the argument is an error. Formal fallacies are always fatal to an argument, informal fallacies are not always fatal.
The study of formal logic usually begins with propositional logic, with the goal of translating English sentences into a language of formal logic, that allows the Philosopher to test the validity of an argument using operators and inferences. Propositional logic reduces ideas into a simple symbol (one that is hopefully intuitive) and breaks down complex arguments into simple parts, so it can be tested for validity. The concept is very similar in arithmetic and algebra, where certain signs ( + or - ) represent various mathematical operations and letters represent variables.
To start, let’s begin by analyzing this argument by Honorentheos:
honorentheos wrote:If Stak starts posting images, then we know he is having a meltdown. Oh look! Stak just posted an image of Dean Martin. I guess we can conclude he is having a meltdown.
If you notice in the first sentence, I bolded the words ‘if’ and ‘then’ to emphasize that this sentence is called a conditional statement. If you notice the word ‘Stak’ precedes the word ‘then’, that indicates ‘Stak’ is the antecedent (that which precedes). The word ‘meltdown’ comes after ‘then’ and is called the consequent (that which follows). The concept of a conditional is pretty simple, if X happens, then Y is the result.
I underlined the first letter in the words ‘Stak’ and ‘meltdown’ to help point out my strategy in symbolization. S will stand in for, “Stak is posting an image” and M will stand in for, “he is having a meltdown”.
Now we can get down to translating the first sentence in Honorentheos’ argument. We can see that it’s a conditional statement, and that S is the antecedent and M is the consequent. We’ll use the symbol “ ~>“ to represent the “if…then”, and this is what we get:
S ~> M
…which reads, “ If Stak is posting an image then he is having a meltdown”
The next sentence is pretty simple and can be symbolized as:
S
The last sentence is a conclusion, which is the point Honorentheos wants to drive home. We’ll use the symbol ‘.:.’ to represent the conclusion and it can be read as ‘therefore’:
.:. M
The entire argument can be summed up as this:
S ~> M, S, .:. M
S ~>M and S represent the data, and M is the inference Honorentheos drew from that data. How did he do so? From the handy rule of inference called “modus ponendo ponens” (the way that affirms by affirming) or simply Modus Ponens. Modus Ponens is a rule that simply states, “ X ~> Y, X .:. Y”. Since Honorentheos’ argument takes the exact form of Modus Ponens, we know straight away that it is valid and contains no formal fallacy.
It’s important to note that proposition logic is truth functional, meaning that it does not test the truth value of any premise, it’s just a way to test an argument to make sure the conclusion follows from the given premises. ‘S ~> M’ and ‘S’ are premises and can be challenged, but that leaves the venue of propositional logic.
In propositional logic, an argument is valid if a Philosopher can show how she drew her conclusion from the premises via rules of inference (like Modus Ponens), an argument is sound if all the premises are true and all the inferences are valid.
In my next installment, I’m going to cover a few more logical operators in propositional logic, so that we can begin to do some epistemology found in the Book of Mormon.