Causal Inductive Arguments

A causal inductive argument is an inductive argument in which the conclusion claims that one event(s) causes another.

Causality
Causality is the relationship between an event (cause) and a second event (effect), where the second event is understood to be the consequence of the first. Intuitively,


Types of Causes
The term "cause" can be used in several different ways:

1. Necessary Cause - A necessary cause (or condition) is one that is required to be present for the effect to occur. This relationship can be written as, C is the cause of E in the sense that C is a necessary condition of E. That is to say, without C, E will not occur. This relationship implies that the presence of E necessarily implies the presence of C. The presence C, however does not imply that E will occur.

For example, if a professor says that one can pass his class only by completing all the assignments, then completing the assignments is a necessary cause of the effect of passing the class. It should be noted that completing the assignments won't guarantee passing as there are other things (causes) that must happen such as having scores that average out to a passing grade.

2. Sufficient Cause - A sufficient cause is one that by itself is enough for the effect to occur. This relationship can be written as, C is the cause of E in the sense that C is a sufficient condition of E. That is to say, given C, E will occur. However, another cause may alternatively cause E. Thus the presence of E does not imply the presence of C.

For example, boiling a potato is a sufficient condition for cooking a potato, but it is not a necessary condition since there are many ways of cooking potatoes, such as baking or frying them.

3. Necessary & Sufficient Cause - A necessary and sufficient cause leads to an effect that always occurs when the condition is met and never occurs unless the condition is met. This relationship can be written as, C is the cause of E in the sense that C is a necessary and sufficient condition of E. That is to say, without C, E will not occur, and with C, E will occur.

For example, being a male sibling is necessary and sufficient for being a brother.

4. Contributing Cause - Commonly, when we speak of one event causing another we are referring to it being a contributing cause. This relationship can be written as, C is causally relevant to E. It is a condition that makes E more likely to occur than it would be were C not there.

A Contributing cause is neither necessary nor sufficient in and of itself to bring about a certain effect.

For example, being physically inactive is a general contributing causal factor to being overweight. It is not a necessary condition as some overweight people are physically active. Nor is it a sufficient condition as some physically inactive people are not overweight. Nevertheless, it is causally relevant being one of a number of contributing factors.


Distinguishing Between Correlation and Causation
A correlation is an association of two variables. When judging an association between variable, three possibilities exist:

1) Positive correlation - if a higher proportion of Qs than non-Qs are H, then there is a positive correlation between being Q and being H. In other words, Q and H increase and decrease in synchrony (parallel).
2) Negative correlation - if a smaller proportion of Qs than non-Qs are H, then there is a negative correlation between being Q and being H. In other words, Q tends to increase when H decreases and vice versa.
3) No correlation - if about the same proportion of Qs as non-Qs are H, then there is no correlation between being Q and being H.

The phrase 'correlation does not imply causation' is commonly used in science and statistics to emphasize that a correlation does not necessarily imply that one event causes the other. The reason for this is that a positive correlation generally allows for the existence of four possibilities:

1. Q is a cause of H. 

2. H is a cause of Q. 

3. The positive correlation of Q and H is a coincidence. 

4. Some other factor, X, is a cause of both Q and H

To automatically infer that a positive correlation between Q and H means that Q causes H is to disregard the other three possibilities. This is why correlation alone is generally thought to be insufficient grounds to establish cause.

Though a correlation alone is not enough evidence to establish causation, the absence of a correlation does establish the absence of a causal relationship.  This is true since correlation is a necessary aspect of causation even though it is not sufficient for it. The general form of this argument is:

P1. If Q is a cause of H, Q must be positively correlated with H. 

P2. It is not the case that Q is positively correlated with H. 

C. Therefore, It is not the case that Q is a cause of H.

Cogent Causal Arguments
We've established that correlation is a necessary condition of arguing for causality yet alone is not sufficient evidence. To establish a cogent causal argument, premised on a positive correlation, it is necessary to provide evidence which seeks to exclude the other possibilities which correlation allows for. There are various methods from diverse fields of science and philosophy available to help investigate causal claims, some of which are listed below.

1. Mill's Methods
2. Bradford Hill criteria for causation




A Practical Study of Argument

Logical Reasoning

Khan Academy: Fundamentals: Necessary and Sufficient Conditions

A Preferred Treatment of Mill's Methods

Mill (Arguments of the Philosophers)

The Logic of Causal Conclusions: How we know that fire burns, fertilizer helps plants grow, and vaccines prevent disease

Causality and Causation: The Inadequacy of the Received View
A Short History of ‘Causation’
Causation

http://changingminds.org/explanations/research/conclusions/inferring_cause.htm

http://psych.cf.ac.uk/home2/white/white%20bjsp%202000.pdf

http://www.skeptic.com/insight/the-logic-of-causal-conclusions-how-we-know-that-fire-burns-fertilizer-helps-plants-grow-and-vaccines-prevent-disease/

http://science.jrank.org/pages/8545/Causality-Inus-Conditions.html

http://see.library.utoronto.ca/SEED/Vol4-2/Hulswit.htm

https://en.wikipedia.org/wiki/Bradford_Hill_criteria

https://en.wikipedia.org/wiki/Causal_reasoning

http://www.skepticalob.com/2011/02/if-correlation-is-not-causation-what-is.html

https://books.google.com/books?id=vaU0AAAAQBAJ&pg=PA189&dq=douglas+walton+causation&hl=en&sa=X&ei=v6iSVeuBMMimNpKAgvgF&ved=0CEAQ6AEwBg#v=onepage&q=douglas%20walton%20causation&f=false