Wednesday, July 8, 2015

Abductive Arguments (Inference to the Best Explanation)

An abductive argument (also known as an inference to the best explanation) is an argument in which a hypothesis is inferred from some data on the grounds that it offers the best available explanation of that data.1 Though it may appear as a special type of induction, many philosophers view it as a separate type of inference.

The following example is useful in drawing the distinction between deduction, induction and abduction:

Deductive Reasoning: Suppose a bag contains only red marbles, and you take one out. You may infer by deductive reasoning that the marble is red.

Inductive Reasoning: Suppose you do not know the color of the marbles in the bag, and you take out a handful and they are all red. You may infer by inductive reasoning that all the marbles in the bag are red.

Abductive Reasoning: Suppose you find a red marble in the vicinity of a bag of red marbles. You may infer by abductive reasoning that the marble is from the bag.

Hence we can say that with a deductively valid inference, it is impossible for the premises to be true and the conclusion false. With an inductively strong inference, it is improbable for the premises to be true and the conclusion false. In an abductively weighty inference, it is implausible for the premises to be true and the conclusion false.

Abduction is essentially a kind of guessing by forming the most plausible explanation for a given set of facts or data. It's inference comprises of three steps. First, it begins with the observation of the data, evidence, facts, etc. Second, it forms various explanations that can be given to explain the observations in the first step. Third, it selects the best explanation and draws the conclusion that the selected explanation is acceptable as a hypothesis. Here is the process in standard form:

P1. D exists.
P2. H1 would explain D. 
P3. H1 would offer the best (available) explanation of D. 
C. Therefore, probably, 4. H1

Abductive arguments are commonly used in many areas including law, archaeology, history, science and medical diagnosis. A medical example would include when a doctor examines a patient with certain symptoms and tries to reason from those symptoms to a disease or condition that would explain them. A legal example would be when a police detective gathers evidence then forms a hypothesis as to who committed a crime.

Evaluating Abductive Arguments
The strength of an abductive argument depends of several factors.
1. how decisively H surpasses the alternatives.
2. how good H is by itself, independently of considering the alternatives (we should be cautious about accepting a hypothesis, even if it is clearly the best one we have, if it is not sufficiently plausible in itself)
3. judgments of the reliability of the data
4. how much confidence there is that all plausible explanations have been considered (how thorough was the search for alternative explanations)

Additional factors to consider are:
1. pragmatic considerations, including the costs of being wrong, and the benefits of being right 
2. how strong the need is to come to a conclusion at all, especially considering the possibility of seeking further evidence before deciding.

1. A Practical Study of Argument

2. Abductive, presumptive and plausible arguments

Tuesday, July 7, 2015

Bradford Hill Criteria for Causation (epidemiology)

The Bradford Hill criteria for causation are a group of criteria or guidelines used to help determine if an observed association is potentially causal. They were established in 1965 by the English epidemiologist Sir Austin Bradford Hill.

Research to determine the cause of disease is a principal aim of epidemiology. As most epidemiological studies are observational rather than experimental, a number of possible explanations for an observed association must be considered before a cause-effect relationship can be inferred. In his 1965 paper The environment and disease: association or causation, Hill proposed the following nine guidelines to help assess if a causal relationship exists:


1. Strength: (effect size): A small association does not mean that there is not a causal effect, though the larger the association, the more likely that it is causal.

2. Consistency: (reproducibility): Consistent findings observed by different persons in different places with different samples strengthens the likelihood of an effect.
3. Specificity: Causation is likely if a very specific population at a specific site and disease with no other likely explanation. The more specific an association between a factor and an effect is, the bigger the probability of a causal relationship.

4. Temporality: The effect has to occur after the cause (and if there is an expected delay between the cause and expected effect, then the effect must occur after that delay).

5. Biological gradient: Greater exposure should generally lead to greater incidence of the effect. However, in some cases, the mere presence of the factor can trigger the effect. In other cases, an inverse proportion is observed: greater exposure leads to lower incidence.

6. Plausibility: A plausible mechanism between cause and effect is helpful (but Hill noted that knowledge of the mechanism is limited by current knowledge).

7. Coherence: Coherence between epidemiological and laboratory findings increases the likelihood of an effect. However, Hill noted that "... lack of such [laboratory] evidence cannot nullify the epidemiological effect on associations".

8. Experiment: "Occasionally it is possible to appeal to experimental evidence".

9. Analogy: The effect of similar factors may be considered.


Friday, June 19, 2015

Mill's Methods

Mill's Methods
The nineteenth century philosopher John Stuart Mill devised five methods for reasoning about cause and effect. Though they have serious limitations, they are still useful and widely taught today.

1. The Method of Agreement - Mill wrote "If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or the effect) of the given phenomenon." In other words, if there is a single circumstance that is present in all positive instances, then we can conclude that this circumstance was the cause of the phenomenon. Note that in textbooks this is often referred to as the direct the method of agreement and only looks at positive instances of the effect in question.

For example, lets say four students dined together at the cafeteria and two of them became ill with food poisoning. The students were questioned about what they ate which resulted in the following list:

STUDENT   STEAK?   FRIES?   PASTA?   BEANS?   FOOD POISONING?
Carla            No             Yes          Yes           Yes            Yes
John             Yes            No           No            Yes             Yes
Tom             Yes            Yes          No            No              No
Mary            No             Yes          Yes           No              No

Based on the above information, we can conclude that it was the beans that gave Carla and John food poisoning as this was the only potential cause that was present in both instances.

Though not listed by Mill, some textbooks also refer to what is called the Inverse Method of Agreement (or Negative Method of Agreement). The Inverse Method of Agreement allows one to conclude that a certain circumstance is the cause of the phenomenon under investigation if this circumstance is the only circumstance (of those considered) that is absent in all negative instances.

Using the above example, the inverse method of agreement would lead us to look at the negative instances of Tom and Mary not getting food poisoning. Here we find the beans to be only potential cause which were absent in both cases and can thus conclude them to be the cause.

2. The Method of Difference - "If an instance in which the phenomenon under investigation occurs and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former, the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon." In other words, if there is a positive and a negative instance where the presence or absence of all possible causes are the same except one cause which is present in the positive instance and absent in the negative instance, then it can be concluded to be the cause of the phenomenon. Note that the method of difference looks at both  positive and negative instances of the effect in question.

Using the food poisoning example above there are two relevant instances where the method of difference can be applied:

STUDENT   STEAK?   FRIES?   PASTA?   BEANS?   FOOD POISONING?
Carla            No             Yes          Yes           Yes            Yes
Mary            No             Yes          Yes           No              No

Since the only potential cause in which they differ is present in the positive instance and absent in the negative instance, we can conclude it was the beans that caused the food poisoning.

3. The Joint Method of Agreement & Difference - "if two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance; the circumstance in which alone the two sets of instances differ, is the effect, or cause, or a necessary part of the cause, of the phenomenon."  There seems to be a fair amount of controversy over this method among those scholars that examine such things. The biggest criticisms seem to be that The joint method/indirect method is not really a combination of the method of agreement and method of difference. Also, the definition above as provided by Mill is restrictive in that it does not allow full achievement of the intended purpose of the joint method. A more usable amended joint method of agreement & difference is provided by Skorupski:

"If two or more instances in which the phenomenon occurs have a circumstance in common, while in two or more instances in which the phenomenon does not occur that circumstance is absent, and if there is no other circumstance or combination of circumstances which is present in all the instances in which the phenomenon occurs, and absent in all the instances in which it does not occur, then the given circumstance is the effect, or the cause, or an indispensable part of the cause, of the phenomenon."

This can be summarized as the circumstance which alone is present in all the positive instances and absent in all the negative instances.

Here is a modified version of the food poisoning example which demonstrates the amended joint method:

STUDENT   STEAK?   FRIES?   PASTA?   BEANS?   FOOD POISONING?
Carla            No             Yes          Yes           Yes            Yes
Ann              Yes            Yes          No            Yes            Yes
Doug            Yes            No           No            No              No
Byron           No             Yes          No            No              No

With this example, the method of agreement does not give a unique answer since there are two positive circumstances (fries and beans) present in both positive instances. The method of difference also does not provide an answer since there is not a positive and negative instance where all causes are the same except a single cause which is positive in one instance and negative in the other. However, using the amended joint method we find that the beans are the cause as they are the only circumstance which is present in all positive instances and absent in all negative instances.

4. The Method of Residue - "Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents."

5. The Method of Concomitant Variation - "Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation." 

Friday, June 12, 2015

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

Thursday, June 4, 2015

Appeal to Authority

An appeal to authority is an argument that something is true because someone of authority says it is true. The basic form of the argument is:

P1. Person X has asserted claim P
P2. Person X is an authority on subject K
C. Therefore P is acceptable

A few internet sources (especially the Wikipedia entry) would lead one to believe that appeals to authority are always fallacious. In actuality, there are many instances where it is reasonable to accept inductive arguments where an authority is used to to support a claim. This is something I believe most would find intuitively true given that we rely on the advice and counsel of experts all the time.

The difference between a legitimate appeal to authority versus one which is fallacious generally dependent on whether the authority being cited is an expert on the matter under consideration and whether there is general agreement among experts in the area of knowledge under consideration.

Govier provides the following form of an acceptable appeal to authority:

1. Expert X has asserted claim P
2. X is a reliable and credible person in this context 
3. P falls within area of specialization K
4. K is a genuine area of knowledge
5. X is an expert, or authority, in K. 
6. The experts in K agree about P 
Therefore, 
7. P is acceptable

Given that the above guidelines provide for acceptable appeals to authority, then a violation of one or more of these conditions would lead to what is commonly referred to as a fallacious appeal to authority. Some ways an appeal to authority can go wrong or be weakened include:

1. The authority cited is not really an expert or is not an expert in the area pertaining to the issue at hand.
2. The authority is an "expert" in an area which is not a genuine area of knowledge (An "expert" in homeopathy promoting a treatment does not carry weight as homeopathy is not a genuine area of knowledge).
3. The authority's opinion is unrepresentative of what the majority of experts believe to be true about the subject.
4. There is widespread disagreement among experts on the subject.


Introduction to Logic and Critical Thinking 
A Practical Study of Argument
Fallacy Files: Appeal to Authority

To review later:
http://www.dougwalton.ca/papers%20in%20pdf/89reasoned.pdf

Thursday, May 28, 2015

Statistical Syllogism

A statistical syllogism is an inductive argument in which a statistical generalization is applied to a particular case. For example:

Most surgeons carry malpractice insurance.
Dr. Jones is a surgeon.
Therefore, Dr. Jones likely carries malpractice insurance.

This sort of argument can be written in the general form:

P1. Most A's are B
P2. x is an A
C. Therefore, probably x is a B

When the proportions are known the form can be written as:

P1. Z percent of A's are B
P2. x is an A
C. Therefore, it is probable to the .Z degree that x is B

In the general forms presented above, A is called the reference class,  B the attribute class and x is the individual object.

We often use informal versions of the statistical syllogism in everyday reasoning. For instance, if you read in the New York times that the President is visiting China and you believe it to be true, on what basis do you justify this belief? Most people understand that you can't believe everything you read in a newspaper but recognize that certain kinds of reports published in certain newspapers tend to be true. This is one of those kind of reports so it is likely true.

Strength/Weakness of a Statistical Syllogism
There are two primary standards which determine the strength of a statistical syllogism. First is the strength condition which is, the closer to 100% the reference class is to the attribute class the greater the confidence in the truth of the conclusion. Conversely, the closer to 0% the weaker the argument.

Second is the available evidence condition (also called the rule of total evidence) which requires using all available evidence in constructing or assessing such arguments. With statistical syllogisms this essentially means questioning if there is additional relevant information available concerning the individual object (x) that has not been included in the premises? Another way of saying this is that the individual object must be included in the reference class most specifically relevant to the conclusion. Failure to use all available evidence is commonly referred to as the Fallacy of Incomeplete Evidence.

For example:

P1. Sixty percent of students at the University believe in God.
P2. Fred is a student at the University.
C.  It is sixty percent probable Fred believes in God.

But if we also know that Fred is a history major and that only forty percent of history majors believe in God then it would not be appropriate to use the reference class in the example since it excludes this relevant information.

Due care must be taken when judging individuals using statistical syllogisms as their misuse can contribute to stereotyping and prejudice.


A Practical Study of Argument

Critical Thinking: An Introduction to Basic Skills

Critical Reasoning and Philosophy: A Concise Guide to Reading, Evaluating and Writing Philosophical Works