Generalities and Specificities in Inference
Saturday, 24. June 2006, 14:38:52
On one hand, the inference engine behind many deductive arguments is the notion that if a characteristic or set of characteristics is known for all members of a group then that characteristic or set of characteristics applies to any particular member of that group. The manner in which an inference from a general statement to a particular statement is disproved is by finding at least one exception: in particular, finding at least one individual of the group without the stated characteristic or set of characteristics.
Of course, if the group is defined in terms of that characteristic or characteristics, finding an exception would be impossible. This tautological aspect is part of the explanation of the (necessary) validity of deductive arguments.
On the other hand, if one argues from the truth of a general statement about individuals having specific characteristics to a different particular kind of thing (i.e., instead, a particular thing having properties outside the scope of the application of the generalization), then the fallacy of Accident occurs.
An argument-look-alike to the fallacy of Accident is the often-mistaken inference based on the notion that if a characteristic is true of the group itself (not the members of the group, i.e., a so-called meta-property) then that characteristic is also claimed to be true of any particular member of a group. This sort of argument is invalid and is termed "the fallacy of Division."
Converse inference processes involve, respectively, most inductive arguments and the fallacy of Composition.
The inference engine behind many (but not all!) inductive arguments is the claim that whatever characteristic or characteristics are true of a representative sample of a group are also probably true for all of the members of that group.
Of course, the logical force of the argument depends entirely on how representative the sample is. If the representation of the sample to the group were to be exactly the same, then, in reality, the argument would be deductive because, in effect, no two things can be observationally identical. By definition, two different things cannot coexist in space and time--this is a basic presumption of the principle of identity upon which any principle of individuation must be built. Exact representation is the strict sense is definitional, à priori, or ideal.
Finally, if the sample proves not to be particularly representative of the group, then the fallacy of hasty generalization or Converse Accident occurs.
Of course, if the group is defined in terms of that characteristic or characteristics, finding an exception would be impossible. This tautological aspect is part of the explanation of the (necessary) validity of deductive arguments.
On the other hand, if one argues from the truth of a general statement about individuals having specific characteristics to a different particular kind of thing (i.e., instead, a particular thing having properties outside the scope of the application of the generalization), then the fallacy of Accident occurs.
An argument-look-alike to the fallacy of Accident is the often-mistaken inference based on the notion that if a characteristic is true of the group itself (not the members of the group, i.e., a so-called meta-property) then that characteristic is also claimed to be true of any particular member of a group. This sort of argument is invalid and is termed "the fallacy of Division."
Converse inference processes involve, respectively, most inductive arguments and the fallacy of Composition.
The inference engine behind many (but not all!) inductive arguments is the claim that whatever characteristic or characteristics are true of a representative sample of a group are also probably true for all of the members of that group.
Of course, the logical force of the argument depends entirely on how representative the sample is. If the representation of the sample to the group were to be exactly the same, then, in reality, the argument would be deductive because, in effect, no two things can be observationally identical. By definition, two different things cannot coexist in space and time--this is a basic presumption of the principle of identity upon which any principle of individuation must be built. Exact representation is the strict sense is definitional, à priori, or ideal.
Finally, if the sample proves not to be particularly representative of the group, then the fallacy of hasty generalization or Converse Accident occurs.
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