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  1. This is a paper of mine on the subject of induction; I welcome your thoughts. -- The problem of induction asks, “How does one infer a general truth relating to a concept as such from the observation of a number of particular instances?” How does one establish that a property (by which I mean an attribute or causal implication of an attribute) is something all units of a concept have in common, or share, by virtue of their inclusion in the concept? How can one know that “Men are rational beings” — “Men are mortal” — “Men require self-esteem in order to live”? All of these statements are inductive truths, i.e. truths that assign a property to all units of a concept. An inductive truth is applicable universally to all units of that concept. But how does one determine that something is true of all instances of a concept based on a limited number of observations? There are two types of valid induction, that I will designate as ‘simple’ and ‘relational’. The first type, ‘simple’ induction, identifies a property that the units of a concept share by virtue of that which gave rise to the concept, i.e. the concept’s differentia. This type of induction involves an identification of a property of a concept informed by that which serves as the basis of the concept’s identity; it requires no further work than to look to the identification from which the concept was generated. “Spiders have eight legs”; “water has the chemical formula H2O”; “man is the rational animal”; are examples. Any organism one identifies as a spider will have eight legs; this is mandated in order for it to be identified as a ‘spider’. Any water will have the chemical formula H2O; this is mandated in order for it to be identified as ‘water’. Any man will have the capacity of reason; this is mandated in order for him to be identified as a man. In all cases, to identify a thing as a unit of the concept, is to identify that it possesses the attributes that were isolated and integrated when the concept was formed. The second form of induction I designate as ‘relational’ induction. This is the identification of a property that belongs to all units of a concept, not by virtue of the differentia, but by virtue of the nature of a wider group to which the concept belongs. The nature of the wider group informs the property for the narrower concept; it serves as an umbrella that informs the property for all that which comes within its scope. The famous relational inductive truth we will explore below is that which Aristotle applied to the case of Socrates, namely, “All men are mortal.” – ‘Relational’ induction begins with the observation that some units of a concept demonstrate a property and that the property cannot be established to characterize the units of the concept by virtue of the nature of the concept’s differentia – i.e., ‘simple’ induction is insufficient. Are men mortal? Let us consider the process of a hypothetical thinker. “What are Men? Men are living beings whose distinct means of survival is rational thought. “That they are beings of thought is the key differentia of the concept of man in relation to living things, and were I called upon to validate the induction, ‘Man is the rational animal,’ I could look to this. I can thus easily make the simple induction that all men are beings with the capacity of reason, for this is true on the basis of what is involved in identifying man as man. But this is wholly unrelated to the mortality of men. Is there any other aspect of man that as such can be related to the fact that men have the capacity of dying? What can I look to? “As the differentia is not helpful, let me then look to a genus of man, and see if that will help. “What is the genus of ‘Man’ related to the context here? Is there a genus of man relevant to the fact of mortality? “What is ‘mortality’? It is the capacity for the life of a living thing to end. Perhaps help can be found here. Is there something in the nature of life that implies mortality? “Life (I have observed) is a conditional state of self-generated, self-sustaining action. For all living things, a certain course must be pursued for life to continue, this course dictated by the nature of the living thing. It is conditional on following such a course of action, which one must pursue. An organism has no alternative. If it does not follow that course, its life will not continue. “Thus the key identification here in relation to ‘living thing’, the genus of ‘man’ I am investigating, is that it is conditional, and does not necessarily endure. Should a living thing not engage in the requirements of life dictated by its nature, its life in all cases will end. “Does this characterize life as such? Yes, it does. It is true of any living thing. The continued life of a living thing depends upon meeting the requirements of its existence in reality, these requirements dictated by its nature. “So then. “Living things are mortal. “All living things are mortal, by the nature of life. Men are living things. The syllogism is clear. Men are mortal.” What has our thinker done here? He has established (by means of independent thought) a quality relating to the nature of a wider group within which men are a narrower, valid grouping, that informs that quality for the narrower concept. Men are living things, and, by virtue of the nature of living things as such, men are mortal. And this quality is applicable to all men, as well as all valid narrower groupings within the concept ‘organism’ (i.e., that which subsumes living things). Everything that is alive is mortal – men, and dogs, and dolphins, and birds, and insects. To review: Induction is the process of identifying a truth relating to a concept. It identifies a property (whether an attribute or a causal implication of an attribute) that all units of a concept have in common, or share, by virtue of their inclusion in the concept. For example: “Men are rational beings” – “Men are mortal” – “Men require self-esteem in order to live.” There are two types of induction, ‘simple’ and ‘relational’. ‘Simple’ induction identifies a truth informed by an attribute true by virtue of the concept’s differentia. It relates to that which was isolated and integrated when the concept was formed. ‘Relational’ induction identifies a property shared by all units of a concept, not deriving from the concept’s differentia, but instead from a wider group to which the concept belongs, the nature of which informs that property for the narrower group. And it is a property shown by all things that come within its scope of the wider group. Thus a truth common to all units of a concept thus derives either (1) from the nature of the the concept qua the concept, i.e. by reference to the concept’s differentia, or (2) from a wider group, the nature of which informs the property for the narrower subgroup. Note that the units of a concept retain all of the properties of all of the wider groups to which the concept belongs. Again: Are all Men Mortal? Men are living things. All living things have the capacity of dying (this follows from the nature of life – see above). Therefore, men have the capacity of dying. Thus all men are mortal. As are all living things. And once we establish with certainty that all Men are Mortal, then given that we know (as Aristotle wrote) that Socrates is a Man, we can say with certainty that Socrates is mortal. This is the process of deduction – the application of an inductive truth to a given unit of the concept identified in that truth, establishing a property of that unit. Why is Socrates mortal? Because Men are mortal. Why are Men mortal? Because living things are mortal, by virtue of the nature of living things, a wider group within which men are contained. And a man stops here, once he, by means of his own reason, establishes that living things are mortal. And he is certain of his related convictions on every level from the point of the validated induction forward. Two final notes: (1) The widest categories – the Phyla, if you would, of the kingdom of reality – are existence and consciousness. All properties identified as belonging to each of these apply to all narrower categories within these groups. (2) In pursuit of an inductive truth, one first identifies that the units of a concept demonstrate a certain property. One can then look to the differentia of the concept, and see if the induction can be validated there (‘simple’ induction). If this offers no assistance, one then seeks the path of relational induction, and begins with the goal of identifying the relevant wider group the nature of which informs the property. How? There are two ways. First, to seek the relevant genus by seeking a genus that relates in some way logically to the attribute. E.g., if the issue is that of mortality, we can consider looking to the nature of life, for mortality is the capacity for life to end. Thus, perhaps there is something in the nature of life that causes life to the have the capacity of ending. Second, if we have no guidance from the first method, we can look for other concepts that share the attribute (e.g. mortality is shared by dolphins and men), then seek for a common, wider group they share to investigate. One then can inquire into the nature of that genus, and if all goes well establish the truth on its foundation (“Living things are mortal”). One can then go forward again, now with the confidence of certainty, and let that inductive truth inform all narrower concepts within that genus (“All men are mortal”, “All dolphins are mortal”, “Ants are mortal”), and all units of those concepts (“Socrates is mortal”, “This dolphin is mortal”, “This ant is mortal”). Also note that no matter how many instances of a given quality you witness, i.e. no matter how many men you see die, or apples you see fall, you do not achieve the certain belief that “All men are mortal” or that “All apples fall” until you yourself validate the induction by one of the two above described methods.
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