Analytic vs synthetic
A true sentence is
analytic if it true in virtue of the meanings of the terms in the sentence. Anyone who understands an analytic sentence knows that it is true.
Example: A bachelor is an unmarried male.
A true sentence is
synthetic if it is not analytic. Truths about the world are synthetic.
Example: Isaac Newton was a bachelor.
A priori ("before") vs a posteriori ("after") This distinction is not the same as the analytic–synthetic distinction, but they have often been mixed up.
A true sentence is true
a priori if it can be known to be true without looking at the world.
A true true sentence is true
a posteriori if knowing that it is true requires looking at the world.
This distinction is about whether knowledge of the world is required. It doesn't mention definitions, like the analytic–synthetic distinction.
This
may be an example of an a priori truth that is
not analytic:
I think, therefore I am.
Kant thought that most of mathematics was a priori, but not analytic.
I purposefully, just vaguely said, knowledge of the "world." What does that mean? Almost always, and certainly for our purposes, "knowledge of the world" is the sort of thing empiricists think is knowledge.
Deductive vs Nondeductive Confirming reasoning (induction, ...)
Deductive reasoning is reasoning that connects premises to a conclusion that follows from them necessarily or with certainty.
Examples:
Isaac Newton was a bachelor.
Therefore,
Isaac Newton was a bachelor.
Isaac Newton was a bachelor and New Orleans is a mess.
Therefore,
Isaac Newton was a bachelor.
All philosophers are mortal.
Socrates was a philosopher.
Therefore,
Socrates was mortal.
Isaac Newton was a bachelor.
Therefore,
Isaac Newton was unmarried.
All reasoning in mathematical proofs is deductive reasoning and that is a sort of paradigm of deductive reasoning. That is even true of what is called mathematical "induction."
The first three of our arguments were true in virtue of their form:
A, therefore A.
A and B, therefore A.
Every A is a B. s is an A. Therefore, s is a B.
Frege showed that every deductive argument is true in virtue of its form plus "definitions."
Frege gave a complete, mechanical analysis of all of deductive reasoning.
Deductive reasoning is contrasted with nondeductive confirming reasoning. A conclusion is
confirmed by some premises is the premises make it more reasonable to believe the conclusion, make it more likely that the conclusion is true, or in some way improve the situation with respect to the truth of the conclusion.
The most often discussed form of confirmation is
induction. It is often assumed that the only form of nondeductive confirmation is induction, that all the others can be explained in terms of induction.
Induction:
Every swan anyone has ever seen is white.
Therefore,
All swans are white.
Induction is arriving at a generalization on the basis of examples.
There is no generally agreed on definition of induction, but that is core kind of case, and that is what I will mean.
We also confirm via probabilistic reasoning:
More people who smoke die of lung cancer than people who do not smoke.
Therefore,
Smoking causes lung cancer.
Finally, we make extensive use of what the book calls explanatory inference, which is usually called inference to the best explanation.
Example: We can use the theory of electrons and semiconductors to build and repair TVs computers etc. The success of that use gives us reason to believe that there are electrons and semiconductors, and that they behave more or less as the theories tell us.
Observational vs theoretical
The details changed but the simplest version is that there are observation terms, words that name things we can see or otherwise sense and nonobservational, that is, theoretical terms, which don't.
In my example above, "electron" is a theoretical term.
In my example, perhaps, "TV" served as an observational term, but many of the people who used the distinction were phenomenalists (sensationalists).
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ShaughanLavine - 31 Aug 2005