Formal and Informal Fallacies
- A valid argument is the one where if the premises are true, the conclusion must be true. it has a correct formal structure.
- A sound argument is in addition to being a formally correct argument, also contains true premises.
Ideally, the best kind of formal argument is a sound, valid argument. Formal logic checks only argument validity, not soundness, so can not solely be used to determine whether or not an argument is true.
There are only Formal Fallacies in this list.
Affirming the consequent
When there is a simple conditional statement, where condition or precursor (antecedent) results in consequent and they are swapped in their places, for example, source true statement:
Caution! When it’s raining, then the road is slippery.
If swap antecedent (When it’s raining) and consequent (the road is slippery) - that converse switch is called Affirming the consequent.
It is a type of non sequitur reasoning also called fallacy of the converse, converse error, or confusion of necessity and sufficiency.
When the road is slippery - it’s raining.
That is especially clear if there are several reasons (antecedents) for a consequent. The road can be slippery because of the snow or machine oil spilt. These types of converse errors are common in everyday thinking and communication and can result for example from communication issues or failure to consider other possible reasons for the event.
The opposite statement with converse switch, denying the consequent, is a correct form of argument, for examle
If the road is not slippery then it’s not raining.
Denying the antecedent
Also called inverse error or fallacy of the inverse, is a formal non sequitur fallacy of inferring the inverse from the original statement. It’s happening when both antecedent and consequent of logical statement are netaged, for instance for the original example above about the rain and road:
When it’s not raining, then the road is not slippery.
The reasoning is not valid and it is a logical fallacy because there could be other reasons for the road to become slippery.
Obvious absurdity of this fallacy can be demonstrated on generalizational conditions, if we have original statement
If it’s a dog then it’s a mammal.
Denying both both antecedent and consequent would result in
If it’s not a dog then it’s not a mammal.
Cats and horses don’t express any agreement with this kind of logic.
Affirming a disjunct
Also called the fallacy of the alternative disjunct or a false exclusionary disjunct occurs when a in a statement with a disjunct this is supposed to meen exclusive or (either … or…) instead of literal inclusive. It is a Fallacy of Equivocation between the operations OR and XOR. For example
Leave the door open! There are cats or dogs still outside.
The Affirming a disjunct example:
Both cats are inside we can close the door now, no one outside.
The fallacy lies in supposing and expressing that if one disjunct is true then another must be false; actually they may both be true. There is a valid argument disjunctive syllogism, that looks similar but must be diffirentiated.
Denying a conjunct
Very similar to False Dichotomy. It suggests assumption that if to conditions are exclusive then one of them must be true.
Are you paying by cash or by card?
Even if we can not pay using both methods (Denying a conjunct), that doesn’t meen we have to pay using one of them. In reality see false dilemma fallacy, there is still possibility of the third or fourth or option of not buying now at all.
Fallacy of the undistributed middle
This non sequitur also called non distributio medii is a type of formal fallacy that is committed when the middle term in a categorical syllogism (logical conclusion based on two premises of groupping) is not distributed. It is thus a syllogistic fallacy. For example:
- All cats are animals.
- Lion is a animal.
- Therefore, lion is a cat.
If in sentense above in first raw those sets (cats and animals) are swapped then the argument would be valid. Though not very sound.
This Fallacy of the undistributed middle example, called the Politician’s Syllogism, politician’s fallacy or politician’s logic is shown in “Yes, Prime Minister” TV series on BBC:
- We must do something
- This is something
- Therefore, we must do this.
Fallacy of Four Terms
This formal syllogistic fallacy also called quaternio terminorum, occurs when a syllogism has four (or more) terms rather than the requisite three,
For example here, the three terms are: “goldfish”, “fish”, and “fins”:
All fish have fins.
All goldfish are fish.
Therefore, all goldfish have fins.
Using four terms invalidates the syllogism:
All fish have fins.
All goldfish are fish.
Therefore, all humans have fins.
In everyday reasoning, the fallacy of four terms occurs most frequently by equivocation: using the same word or phrase but with a different meaning each time, creating a fourth term even though only three distinct words are used:
Nothing is better than eternal happiness.
A ham sandwich is better than nothing.
A ham sandwich is better than eternal happiness.