Module 9B Flashcards
Inductive Arguments
Inductive arguments are employed not only when drawing conclusions about an entire group based on an observed portion but also when investigating the causes of events.
Purpose of Inductive Arguments:
Inductive arguments serve the dual purpose of making generalisations about a group and exploring the complexities of causation.
Complexity of Causation
The topic of causation is intricate and a frequent source of philosophical controversy, making it challenging to address all aspects in this unit.
The unit focuses on addressing specific issues related to inferences about causes due to the complexity of the causation topic, acknowledging that it cannot cover all philosophical controversies
Philosophical Controversy
Question: What characterizes the topic of causation in the context of inductive arguments?
The topic of causation is extremely complicated and a frequent source of philosophical controversy, introducing challenges in making definitive conclusions about causes.
Inferences about Causes
Question: What is the primary focus in the unit regarding the use of inductive arguments?
The unit primarily addresses specific issues related to inferences about causes using inductive arguments, recognizing the inherent complexity of the causation topic.
Causation in Philosophy
The topic of causation has been a challenge for philosophers throughout history.
Providing a precise analysis of the concept of cause is difficult due to its varied usage, covering different meanings.
Difficulty in Defining Cause
The concept of cause is challenging to define precisely because it is sometimes considered a sufficient condition, a necessary condition, or a set of necessary and sufficient conditions, as highlighted by Govier.
Intuitive Understanding of Causation
Intuitively, stating that A caused B implies that A brought about or contributed to B’s occurrence, and in some sense, A necessitated B or was part of the factors that necessitated B.
Challenges in Precision
Challenges arise when attempting to provide a more precise account of causation.
Defining what causes are essentially is not straightforward, although examples can be easily given, and criteria can often be established in many contexts.
Primary Knowledge of Causes
Our primary knowledge of causes comes from our actions, where we have control over our limbs and use implements like shovels, knives, and pens.
While this knowledge is crucial, there’s a desire to extend understanding to discover patterns, causal laws, and factors contributing to events of broader interest.
Extending Knowledge of Causes
The goal is to extend knowledge beyond personal actions to uncover patterns between events, identify causal laws, and understand factors contributing to various phenomena.
This includes exploring topics like bodily functions, health preservation, plant growth, and the construction and improvement of objects like boats, bridges, and engines.
Observation of Causal Patterns
A significant part of observing causal patterns involves discovering correlations between types of events, providing insights into the relationships and connections between different phenomena.
Correlation in Arguments
The concept of correlation is crucial, especially when evaluating arguments that utilize statistical premises.
It plays a significant role in interpreting statistical information and drawing meaningful conclusions.
Significance of Correlation
Correlation is vital for understanding relationships between different characteristics, particularly in cases where statistical data is used. It helps assess the strength and direction of connections between variables.
Alarming Statistics Example
Question: Why might a statistic like 66% of male alcoholics being married sound alarming?
The statistic is alarming only if there is a positive correlation between being married and being alcoholic. It’s important to consider the percentage of married men in the male population for context.
Application of Correlation
The concept of correlation finds wide application, especially in cases where relationships can be established between pairs of characteristics.
Examples include being male/female, dead/alive, alcoholic/non-alcoholic.
Concentration on Correlations
This unit focuses on cases where correlations can be drawn between pairs of characteristics, providing a deeper understanding of the relationships between various attributes, such as gender, life status, and drinking habits.
examples of Contrived Correlations
Question: Provide examples of correlations that might seem a bit contrived.
Examples include blue/non-blue, being older than 40/being 40 and under.
While somewhat contrived, these examples still serve a useful purpose in exploring the concept of correlation.
Division of Population
We focus on cases where the population under study can be divided based on two characteristics, A and B, creating groups of A’s and non-A’s, as well as B’s and non-B’s.
Positive Correlation
If a higher proportion of A’s than non-A’s are B’s, it indicates a positive correlation between being A and being B.
This suggests a connection between the two characteristics.
Negative Correlation
If a smaller proportion of A’s than non-A’s are B’s, it signifies a negative correlation between being A and being B.
This implies an inverse relationship between the two characteristics.
No Correlation
If the same proportion of A’s as non-A’s are B’s, it indicates no correlation between being A and being B.
This suggests that the presence or absence of A does not influence the likelihood of B.
Implications of Correlation Definitions
Positive correlation between A and B implies a negative correlation between non-A and B.
Additionally, if there is a positive correlation between A and B, there is also a positive correlation between B and A.
Correlation Symmetry
The definitions imply symmetry in correlations; if there’s a positive relationship between A and B, the same holds for B and A.
Similarly, if there’s a negative correlation between A and B, there is also a negative correlation between B and A.
Causal Relationships and Observation
Many causal relationships involve events we don’t directly observe or the exercise of relevant causal powers that are not directly witnessed.
Observations often focus on the relationships between events and patterns of association, providing evidence for potential cause and effect.
Evidence through Association
Repeated patterns of association between events of different types, such as C and E, suggest that the events are not accidentally related.
This association may indicate a causal relationship between the observed events.
Positive Correlation
Positive Correlation Example
Events A and B are positively correlated when the proportion of A’s that are B’s is greater than the proportion of non-A’s that are B’s.
For example, smoking (A) being positively correlated with lung cancer (B) suggests that smoking may be a cause of lung cancer.
Smoking (A) is positively correlated with lung cancer (B) because the percentage of smokers with lung cancer is higher than the percentage of non-smokers with lung cancer.
Negative Correlation
Negative Correlation Example
Events A and B are negatively correlated when the proportion of A’s that are B’s is less than the proportion of non-A’s that are B’s.
For instance, being inoculated with the cowpox vaccine (A) is negatively correlated with being a smallpox sufferer (B), suggesting that the vaccine may prevent smallpox.
Being inoculated with the cowpox vaccine (A) is negatively correlated with being a smallpox sufferer (B) because the percentage of those receiving the vaccine and still getting smallpox is smaller than the percentage who do not receive the vaccine and get smallpox.
Positive Correlation and Causal Link
Although a positive correlation may suggest a potential causal link, it is a common fallacy to directly argue from the presence of a positive correlation between A and B to the conclusion that A is the cause of B.
Fallacy in Causation Inference
The logic of correlations and causes explains why inferring causation directly from correlation is fallacious.
While ‘x is positively correlated with y’ is symmetric, implying ‘y is positively correlated with x’, the relation ‘x is a cause of y’ is asymmetric, implying ‘y is not the cause of x’.
Term: Symmetry in Positive Correlation
Question: What is a characteristic of the relationship expressed by ‘x is positively correlated with y’?
The relationship is symmetric, meaning ‘x is positively correlated with y’ entails that ‘y is positively correlated with x’.
Asymmetry in Causal Relation
Question: What characteristic distinguishes the relationship expressed by ‘x is a cause of y’?
The relationship is asymmetric, meaning ‘x is a cause of y’ entails that ‘y is not the cause of x’.
Correlations and Explanations
Relating correlations to inductive arguments involving inferences to the best explanation, consider a positive correlation between (A) drinking moderately and
(B) having a high wage.
Various explanations could exist, and proper inferences to causation require excluding alternative explanations.
Explanations for Positive Correlation
When observing a positive correlation between (A) drinking moderately and (B) having a high wage, potential explanations include:
1) Drinking moderately causally increases income.
2) Having a high income leads to moderate drinking.
3) Some third factor influences both moderate drinking and high income.
4) The correlation is coincidental and disappears when studying more populations.
Fallacy in Inferring Causation
It is fallacious to infer that A causes B solely based on a positive correlation between them.
Proper inferences to causation require eliminating alternative explanations, such as the second, third, and fourth possibilities mentioned.
Proper Inferences from Correlation to Cause
Inferences from correlation to cause must be supported by reasons for excluding alternative explanations.
Merely observing a positive correlation is insufficient; careful consideration of potential causal relationships and eliminating other possibilities is necessary.
Eliminating Possible Explanations
Eliminating the second possible explanation of a correlation becomes easier when knowing the temporal order of events.
If the later event occurs after the earlier one, it cannot be the cause.
Lack of knowledge about temporal order may complicate the elimination of the possibility that B causes A.
Temporal Order in Elimination
Knowing which type of event occurs first in time helps eliminate the possibility that the later event is the cause of the earlier one.
Temporal order clarification is crucial in assessing causation.
Background Knowledge in Elimination
Eliminating the third possible explanation requires consulting background knowledge about whether common causes of A and B are likely.
In cases where knowledge is insufficient, sophisticated research may be necessary for a thorough elimination.
Common Causes and Elimination
To eliminate the third possible explanation, assessing common causes of A and B is essential.
Limited background knowledge may necessitate further research for a comprehensive elimination.
Limitations in Elimination
The fourth possibility, that the correlation is coincidental, cannot be conclusively eliminated through scientific reasoning.
The longest a correlation persists, the more reasonable it is to assume it’s not accidental, but certainty remains elusive.
Persistence and Accidental Correlation
Scientific reasoning cannot definitively eliminate the fourth possibility of accidental correlation.
The longer a correlation persists, the more likely it is not accidental, but absolute certainty is challenging to achieve.
Hasty Generalization
Hasty Generalization is a fallacy where conclusions are drawn based on insufficient inductive evidence, often leading to unjustified inferences about other social groups.
The weakness lies in the small evidence base, making the support for the generalization weak.
Trouble in Hasty Generalization
The issue is not with reaching generalizations, as many are well-justified and true.
The problem arises when the evidence is too small, compromising the strength of the support for the generalization.
Faulty moral conclusions may result from hasty generalizations that highlight differences between certain groups.
Post Hoc Fallacy
he Post Hoc Fallacy involves concluding that A causes B simply because A occurred before B.
Treating the temporal sequence as a sufficient condition for causation is the fallacy, ignoring other necessary conditions.
Necessary vs. Sufficient Conditions
Happening before B is a necessary condition for A causing B.
However, the Post Hoc Fallacy wrongly treats this necessary condition as though it were a sufficient condition for establishing A causing B.
Objectionable Cause
The Objectionable Cause fallacy occurs when causal conclusions are drawn based on scanty evidence.
Typically, the evidence fails to rule out other potential explanations for the observed correlation, making the inference weak and objectionable.
Weakness in Objectionable Cause
The weakness in the Objectionable Cause fallacy lies in the lack of evidence that rules out alternative explanations for the observed correlation.
Causal conclusions drawn from insufficient evidence are objectionable due to their limited support.
“A positive correlation between A and B is some evidence that there is a causal link between A and B.”
True
Good. But don’t confuse “some evidence that there is a causal link between A and B” with “A caused B.” These are very different.
“A population is analysed with respect to the categories A, non-A, B and non-B. If a higher proportion of A’s than non-A’s are B’s, then there is a positive correlation between being A and being B.”
true
“If there is a positive correlation between A and B, then there is a negative correlation between non-A and B.”
true
“If there is a positive correlation between A and B, then there must be a causal link between A and B.”
False
Might be, sure. Must be? No. Correlation is not causation.
“Inductive arguments with biased samples are worthless.”
false
“The only perfectly representative sample is a randomly selected sample.”
false
“The relation of causation is an asymmetric relation.”
True
Symmetric relation: Where X bares the F-relation to Y, Y bares the F-relation to X.
Asymmetric relation: Where X bares the F-relation to Y, it is not the case that Y bares the F-relation to X.
Causation: Where X caused Y, it is not the case that Y caused
“The relation of positive correlation is a symmetric relation.”
True
