Philosophy 6: Logic in Practice

Los Angeles Pierce College

Department of History, Philosophy, & Sociology

 

 

 

 

 

Lecture Notes

 

 

 

 

 

 

Lecture Notes for "Chapter 10: Deriving Generalizations / Forming Hypotheses"

 

 

 

 

 

 

Generalizing & Describing

Generalizations can be used to justify a conclusion when those justifications are well founded. 

        

"knowledge would hardly be possible unless we made connections, saw similarities between things, and reached broad conclusions about them." 

        

 

 

 

Abstraction as a Mode of Generalization     

Individuals may have unique characteristics, but we can find common characteristics amongst them.   

 

And "sees similarities in the differences that allow a generalization to be made." 

        

 

 

 

 

 

 

 

Stereotyping     

Stereotyping happens when "each member of the group is treated as typical and assumed to possess all the group's features." 

        

 

 

 

 

 

 

 

 

 

 

Avoiding Stereotyping       

We are engaged in inductive generalizations, so remember, we are in the land of probabilities only

 

"Each person should be treated as an individual even though he or she will probably exhibit some characteristics of the group." 

        

 

 

 

 

 

 

 

 

 

 

Fair Generalizations

To have a fair generalization is to have one that attains an appropriate level of probability

 

A fair generalization attains an appropriate level of probability when it is well founded

        

 

 

Good Generalizations    

"The main problem in generalizing, therefore, is figuring out how to achieve reliability."

 

"in building a generalization into our argument we must be sure it is based on a fair sample." 

 

"This means one of sufficient size and randomness to make the generalization" reasonable or well-founded. 

 

"It must also be properly stratified." 

        

 

 

 

 

 

 

Size

"the number of cases we examine should be large enough to represent the whole." 

 

Judgment here is needed as the subject matter will determine the acceptable size of the sample

 

A "way to determine whether the sample is sufficiently large is to see what the generalization is about." 

        

 

 

 

 

 

 

 

 

 

 

 

Singular E.G.    

In some cases, we need a singular sample

 

"From the fact that we burn our hand in fire, we can conclude that fire burns." 

 

Small E.G.   Hardness of diamonds

        

Large E.G.   Hardness of wood

        

 

 

 

 

 

 

 

 

 

 

 

 

 

Sufficient Size  

"The moral of the story is that if we want to generalize in our argument we need a large enough sample on which to base it"

        

Problems

"we may not always know the subject well enough to determine in advance whether a large or small sample is needed." 

        

 

 

 

 

 

 

 

 

 

 

 

 

Hands-On Method     

"In this method we increase the sample size until the results begin to repeat themselves." 

 

"Then we can stop, knowing we have examined enough cases." 

 

"A hands-on experiment ... is the most reliable method of determining whether our generalization is based on an adequate sample size." 

        

 

 

 

 

 

 

 

 

 

 

 

Randomness     

Here we can thwart biased generalizations

 

"we must make sure that the sample studied represents the whole and does not bias our conclusion." 

 

"Unless our sample is random, our generalization will be distorted rather than fair." 

        

 

 

 

 

 

 

 

 

The Bias Danger        

"we tend to perceive and remember what we are seeking, and to ignore counter instances." 

        

 

 

 

 

 

 

 

 

 

 

 

 

Stratification    

"Here we want to include all strata or classes that could have an important effect on our generalization." 

 

"Every relevant group must be taken into account." 

        

 

 

 

 

 

 

 

 

 

 

 

 

 

Reliability

With those three steps completed, our generalization becomes more reliable

        

Steps to Fair Generalization       

 

Size

 

Randomness

 

Stratification

        

 

 

 

 

 

 

 

 

 

 

 

 

 

Steps to Fair Generalization / Step One / Size   

1) "Check for adequate size in terms of the nature of the subject matter." 

 

"In an experimental situation, take repeated samples until the results begin to repeat themselves." 

        

 

 

 

 

 

 

 

 

 

 

Steps to Fair Generalization / Step Two / Randomness       

2) "Be sure the generalization is random and free from bias in the sampling, so that each of the relevant elements has an equal chance of being chosen." 

 

 

 

 

 

 

 

        

Steps to Fair Generalization / Step Three / Stratification    

3) "Make certain the sample is stratified, which means that all relevant categories are included and none is excluded that would significantly affect the generalization." 

        

 

 

 

 

 

 

 

 

 

 

 

 

 

Hypotheses in Arguments

"A hypothesis can be defined as an explanatory principle accounting for known facts." 

 

"In hypothetical thinking we want to know why something is true, and we reason backward to find some explanation for the facts, one that makes sense of them."

 

"We use our imagination to find some reason why things are the way they are."  

 

 

 

 

 

 

 

 

        

Resonance w/ Analogical Arguments         

Just as we go from the known to the unknown in analogical arguments, by employing an hypothesis, we go from known facts to an unknown explanation.  

 

"the facts are known but the explanation for the facts is missing." 

 

(See what I did there?) 

        

 

 

 

 

 

 

 

 

 

 

 

Evaluating Hypotheses      

"How ... do we separate the genuine hypothesis from the fictional one?" 

 

"What separates a reliable hypothesis from an unreliable one or, more precisely, what features must a sound hypothesis possess?" 

        

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Developing an Adequate Hypothesis  

"We must pay attention to these five rules in order to develop sound hypotheses." 

 

1) Consistency

 

2) Plausibility

 

3) Comprehensiveness

 

4) Simplicity

 

5) Predictability

        

 

 

 

 

 

 

 

 

 

 

 

Measuring the Adequacy of Hypotheses / Consistency        

"Consistency with other hypotheses we accept." 

 

"A new hypothesis should be congruent with the bulk of hypotheses that we believe to be true." 

 

"It should fit in with the body of explanations that from our outlook on life." 

 

 

 

 

        

        

Consistency and Our Expectations     

"We should therefore demand consistency in any hypothesis we read about, and we should not except anyone to accept our novel hypothesis if it means that person must radically revise his or her beliefs." 

 

Really?

 

 

 

 

 

 

 

 

 

 

        

Measuring the Adequacy of Hypotheses / Plausibility

"any new hypothesis must be plausible according to common sense and traditional ideas." 

 

"Every event can be explained in any number of ways, so to determine which hypothesis should be accepted we must screen out the very unlikely ones." 

        

"we want to begin our inquiry with the most credible explanation and end up endorsing the hypothesis that is the most plausible." 

        

 

 

 

 

 

 

 

 

 

 

 

 

Measuring the Adequacy of Hypotheses / Comprehensiveness   

"Any hypothesis that we present should be the most complete explanation we can find." 

 

"Many hypotheses will provide a partial answer to the question we are investigating, but we want the most encompassing one that will not leave important parts unexplained." 

        

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Measuring the Adequacy of Hypotheses / Simplicity   

Ockham's Razor / Principle of Parsimony

 

"It states that 'entities should not be multiplied beyond what is required,' that is, as simple explanation is preferable to a complicated one." 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

        

Measuring the Adequacy of Hypotheses / Predictability      

"given the conditions described in our hypothesis, we can expect certain results to follow." 

 

"if nothing can be predicted on the basis of our hypothesis, this counts against its soundness, and we should hesitate to use it in our argument."