Dustin Arand's Blog - Posts Tagged "logic"
Justification, Theory, and Truth
We're all familiar with the Aristotelian syllogism, and its most famous exemplar:
MP: All men are mortal.
mp: Socrates is a man.
C: Socrates is mortal.
But notice that the major premise depends upon an inductive inference, based on the empirical observation that we have not yet met anyone who has survived beyond a certain age. It could be the case that Socrates will be the person who finally disconfirms this inference.
That is the vulnerability of all inductive knowledge. Consequently, the flaw in the syllogism is that it basically assumes that which it sets out to prove, since the claim that "all men are mortal" depends upon Socrates (among others) also being mortal.
Another way to put this criticism is to say that deductive syllogisms cannot produce information in their conclusions that is not already contained in their premises. But this seems to call into question Kant's distinction between "synthetic" and "analytic" statements, that is, between statements whose predicates explicate or illuminate the nature of their subjects, and those that merely state a definition (e.g. "A bachelor is an unmarried man.")
What difference is left between them if the supposedly synthetic statements are ultimately begging the question?
But this worry leads to another, for if all logical argument is analytic, what becomes of justification? Plato tells us that knowledge is justified true belief, but Wittgenstein retorts that, eventually, our spades will hit rock and be turned back.
All justifications must end somewhere, and if all justifications consist of analytic statements, then eventually they curl back on themselves, and knowledge is revealed to be a web of interconnected definitions, suspended in thin air. The only alternative is an infinite regress.
Is this good news for cynics, nominalists, and post-modernists?
Perhaps if there were only one possible web of interconnected definitions, the claim that knowledge was not ultimately justifiable would have some force.
But happily knowledge is a buyer's market. For any given set of empirical observations, there are an infinite number of theoretical explanations, some of which will clearly be better than others in the sense that they will fulfill more of needs, answer more of our questions, and suggest more avenues for further research.
We should think of knowledge not as a process of adding true statements to an ever increasing body, but as an endless series of creative re-imaginings of the entire web of definitions by which we divide up the world. It is therefore not statements per se that are true or false, but whole systems - theories - that are either already, or not yet, falsified. No system can be said to be true without reservations.
MP: All men are mortal.
mp: Socrates is a man.
C: Socrates is mortal.
But notice that the major premise depends upon an inductive inference, based on the empirical observation that we have not yet met anyone who has survived beyond a certain age. It could be the case that Socrates will be the person who finally disconfirms this inference.
That is the vulnerability of all inductive knowledge. Consequently, the flaw in the syllogism is that it basically assumes that which it sets out to prove, since the claim that "all men are mortal" depends upon Socrates (among others) also being mortal.
Another way to put this criticism is to say that deductive syllogisms cannot produce information in their conclusions that is not already contained in their premises. But this seems to call into question Kant's distinction between "synthetic" and "analytic" statements, that is, between statements whose predicates explicate or illuminate the nature of their subjects, and those that merely state a definition (e.g. "A bachelor is an unmarried man.")
What difference is left between them if the supposedly synthetic statements are ultimately begging the question?
But this worry leads to another, for if all logical argument is analytic, what becomes of justification? Plato tells us that knowledge is justified true belief, but Wittgenstein retorts that, eventually, our spades will hit rock and be turned back.
All justifications must end somewhere, and if all justifications consist of analytic statements, then eventually they curl back on themselves, and knowledge is revealed to be a web of interconnected definitions, suspended in thin air. The only alternative is an infinite regress.
Is this good news for cynics, nominalists, and post-modernists?
Perhaps if there were only one possible web of interconnected definitions, the claim that knowledge was not ultimately justifiable would have some force.
But happily knowledge is a buyer's market. For any given set of empirical observations, there are an infinite number of theoretical explanations, some of which will clearly be better than others in the sense that they will fulfill more of needs, answer more of our questions, and suggest more avenues for further research.
We should think of knowledge not as a process of adding true statements to an ever increasing body, but as an endless series of creative re-imaginings of the entire web of definitions by which we divide up the world. It is therefore not statements per se that are true or false, but whole systems - theories - that are either already, or not yet, falsified. No system can be said to be true without reservations.
