-Surah 12:4
Despite the frequency with which these terms are used, a lot of people don't really understand what is what. In fact, Sherlock Holmes has the ever-well known reputation for being a master of deductive reasoning, when it was in fact inductive reasoning that he used to solve various mysteries. Similar words, but drastically different meanings.
Deductive Logic and Reasoning:
Deductive logic is when you create a series of premises which then, without doubt, lead to a conclusion. This conclusion, if the premises are true, is inherently true. This is the form of logic used in formal mathematics; axioms make up the most basic premises, and are accepted as true. When a mathematician follows a series of steps, each building off of the previous, new formulas and proofs are created. Once something is proved in math, since it is shown to be true (as it is based off of entirely true premises), it is then accepted to be true universally. . A classic example of deductive logic is as follows:
P1: Socrates is a man.
P2: All men are mortal.
C1: Socrates is mortal.
If the two premises are true, then the conclusion is undeniably true, as it logically follows from the premises. Socrates is a man, and if all men are mortal, then by definition Socrates is mortal. No assumptions are made to connect the premises to the conclusion (although, as we will see, P2 was actually based upon inductive reasoning itself).
As a side note, the mathematical form of proof by induction is, in fact, deductive logic.
Inductive Logic and Reasoning:
Inductive logic is when you draw generalized conclusions from a collection of specific observations. What does this mean? Take, for example, the case of duct tape. For many underprivileged people, the only duct tape available to them is silver. It might seem reasonable to them to assume that, since they have only ever seen silver duct tape, duct tape is only made silver. Most of us, however, know this is not the case (this is a form of the Black Swan fallacy, which I will discuss in a later post). This presents the key issue with inductive logic; you are forced to make assumptions that could very likely turn out to be untrue. Another example, in syllogism form, is the basis for one of our premises above (note also that this and argument from ignorance, which I will also be making a post about):
P1: All things that die are mortal.
P2: Every man in recorded history has died.
C1: Therefore, all men are mortal
This clearly seems like a justified conclusion, and yes, induction is important and often true, though at the same time it often leads to false conclusions, as in the below example (note the argument from analogy):
P1: Every man is an animal.
P2: Every horse is an animal.
C1: Every man is a horse.
Because of the very nature of inductive logic, it cannot provide any proof, in any situation. The most inductive logic can do is provide evidence in support of something.
Correlation Does Not Imply Causation:
This is a fallacy which many people are subject to at one point or another. Whether this be with respect to lucky underwear, prayer to various gods, or shoe sizes affecting handwriting, they all are guilty of committing either the fallacy of cum hoc ergo propter hoc (at the same time as this therefore because of this) or post hoc ergo propter hoc, which translated literally means "after this therefore because of this." It bases itself on the assumption that because two things consistently occur together or because one thing often follows another, the first is the cause of the second.
As an example, there was once a teacher of students from grades 1-8 who graded a lot of writing work. What he noticed was that there seemed to be a correlation between the shoe size of the student and the neatness of his handwriting. He compiled a list of students' shoe sizes and gave them ratings based on the neatness of their handwriting, and found that the larger the shoe size, the neater the handwriting. He then concluded that big feet cause neat handwriting. He fallaciously assumed that one was the cause of the other, when most likely it was simply because, as a person gets older, their feet grow and their handwriting generally improves. This could be attributed to the cause of both, and so a correlation will inevitably exist. This is an example of inductive reasoning gone wrong.
Another example could be the following, cited from With Good Reason by S. Morris Engel:
Despite the frequency with which these terms are used, a lot of people don't really understand what is what. In fact, Sherlock Holmes has the ever-well known reputation for being a master of deductive reasoning, when it was in fact inductive reasoning that he used to solve various mysteries. Similar words, but drastically different meanings.
Deductive Logic and Reasoning:
Deductive logic is when you create a series of premises which then, without doubt, lead to a conclusion. This conclusion, if the premises are true, is inherently true. This is the form of logic used in formal mathematics; axioms make up the most basic premises, and are accepted as true. When a mathematician follows a series of steps, each building off of the previous, new formulas and proofs are created. Once something is proved in math, since it is shown to be true (as it is based off of entirely true premises), it is then accepted to be true universally. . A classic example of deductive logic is as follows:
P1: Socrates is a man.
P2: All men are mortal.
C1: Socrates is mortal.
If the two premises are true, then the conclusion is undeniably true, as it logically follows from the premises. Socrates is a man, and if all men are mortal, then by definition Socrates is mortal. No assumptions are made to connect the premises to the conclusion (although, as we will see, P2 was actually based upon inductive reasoning itself).
As a side note, the mathematical form of proof by induction is, in fact, deductive logic.
Inductive Logic and Reasoning:
Inductive logic is when you draw generalized conclusions from a collection of specific observations. What does this mean? Take, for example, the case of duct tape. For many underprivileged people, the only duct tape available to them is silver. It might seem reasonable to them to assume that, since they have only ever seen silver duct tape, duct tape is only made silver. Most of us, however, know this is not the case (this is a form of the Black Swan fallacy, which I will discuss in a later post). This presents the key issue with inductive logic; you are forced to make assumptions that could very likely turn out to be untrue. Another example, in syllogism form, is the basis for one of our premises above (note also that this and argument from ignorance, which I will also be making a post about):
P1: All things that die are mortal.
P2: Every man in recorded history has died.
C1: Therefore, all men are mortal
This clearly seems like a justified conclusion, and yes, induction is important and often true, though at the same time it often leads to false conclusions, as in the below example (note the argument from analogy):
P1: Every man is an animal.
P2: Every horse is an animal.
C1: Every man is a horse.
Because of the very nature of inductive logic, it cannot provide any proof, in any situation. The most inductive logic can do is provide evidence in support of something.
Correlation Does Not Imply Causation:
This is a fallacy which many people are subject to at one point or another. Whether this be with respect to lucky underwear, prayer to various gods, or shoe sizes affecting handwriting, they all are guilty of committing either the fallacy of cum hoc ergo propter hoc (at the same time as this therefore because of this) or post hoc ergo propter hoc, which translated literally means "after this therefore because of this." It bases itself on the assumption that because two things consistently occur together or because one thing often follows another, the first is the cause of the second.
As an example, there was once a teacher of students from grades 1-8 who graded a lot of writing work. What he noticed was that there seemed to be a correlation between the shoe size of the student and the neatness of his handwriting. He compiled a list of students' shoe sizes and gave them ratings based on the neatness of their handwriting, and found that the larger the shoe size, the neater the handwriting. He then concluded that big feet cause neat handwriting. He fallaciously assumed that one was the cause of the other, when most likely it was simply because, as a person gets older, their feet grow and their handwriting generally improves. This could be attributed to the cause of both, and so a correlation will inevitably exist. This is an example of inductive reasoning gone wrong.
Another example could be the following, cited from With Good Reason by S. Morris Engel:
"More and more young people are attending high schools and colleges today than ever before. Yet there is more juvenile delinquency and more alienation among the young. This makes it clear that these young people are being corrupted by their education."
This is a post hoc explanation for the rising crime rates. A correlation is seen between college students and delinquency, and therefore one is deemed the cause of the other, without taking the rising population into account. When two thing appear to have a relationship, be careful to assume that one is not causing the other, as this often leads to false conclusions.
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| xkcd.com |
