My philosophy meetings are done for the semester, but in honor of Thursday night, here is another post on my philosophical journey.
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1. There is a structure to the way we reason, a structure whose basic contours have been discussed at least since Aristotle in the 300s BC.
From one point of view, there are three basic components of reasoning.
- There are assumptions.
- There are relationships between assumptions.
- And there are conclusions.
2. The relationships between assumptions are logic. There are no exceptions in this universe to the way logic works. Yes, it can take different forms. For example, logic can be expressed in stories. But the analysis that Aristotle and others abstracted always works as an analysis of good reasoning.
I want to emphasize this point because the late twentieth century had its share of detractors from logic as it historically has been used. I do not wish to argue that logic must be expressed in an Aristotelian way. However, I know of no approach that is as precise and reliable in its analysis of human reasoning. Other forms are far more prone to misdirection. They are, as it were, less mathematical.
Meanwhile, propositional logic -- as we might call it -- is always correct when it is formulated according to the rules. This makes it one of the most certain aspects of creation, closely related to math.
3. Aristotle laid out the fundamental pattern of logic in terms of what is called the syllogism. A syllogism has the form of 1) premise, 2) premise, 3) conclusion. The logic of a syllogism is valid if it works -- if the relationships between premises and conclusions work.
For example, take the following syllogism:
- All unmarried individuals are single.
- Jill is unmarried.
- Therefore, Jill is single.
This is an example of deductive reasoning. The conclusion, as it were, is contained in the premises. You might think of deductive reasoning as an upside down V. It starts with an assumption and expands to the conclusions that follow from it.
The other kind of reasoning is inductive reasoning. It's like a regular V. With it, you start with evidence and then draw a conclusion from there. We will look at inductive reasoning in a later section.
4. It's important to note that, just because the logic of a syllogism is valid doesn't mean it's true. It is true only if both of the premises are true.
For example, it is true by definition that "All unmarried individuals are single." But what if Jill is actually married? Then the conclusion is false even though the logic of the argument works.
5. As mentioned, the assumptions in logic are called premises. If the premises of an argument are true and the logic of an argument is "valid," then the conclusion of the argument is certainly true, without exception, and without any valid counter-argument.
Why then do we diagree? The primary weak point of our arguments comes from faulty or debatable premises. That is, debatable assumptions.
So there are two places where an argument may fail. It may fail because its logic isn't valid. And it may fail because one or more of its premises are false.
6. Where do our assumptions come from? First, sometimes they are wrong. Sometimes they come because we haven't interpreted the evidence correctly, as we will see. Perhaps we don't have all the evidence -- we rarely do. Perhaps we make a "hasty generalization" because we don't have all the evidence or we "connect the dots" in the wrong way.
Some of our assumptions are "unexamined," as we have seen. You may have heard the colorful saying that, "When we ASSUME, we make an A** out of U and ME." Jumping to conclusions when we don't have the facts or seeing what we want to see are major causes of bad thinking and faulty conclusions.
And here let me agree with some of the voices that have pushed back on logic in recent years. Mastery of logical reasoning does not guarantee moral clarity or correct conclusions. You can be an outstanding logician and hold troubling moral views or ridiculous perspectives.
For example, Gottlob Frege (1848–1925), as we will see, was a brilliant logician. He is one of the most important figures in the history of logic. Yet in his later writings he expressed horrible views about Jews. Logical rigor doesn't mean your conclusions are correct -- especially if your premises are off.
7. You no doubt have experienced or heard of the child that continues to ask "But why" until the parent finally responds in frustration, "Because I said so." This is a parable of all logic.
Let's say we have a premise in an argument. We might support that premise with other premises. We might have an assumption that is a conclusion from another argument. And so on, and so on.
Eventually, however, all thinking comes down to what we might call axioms or assumptions that are not provable or disprovable. They are necessary for us to make any arguments. In geometry, you might remember that "two points make a line." This isn't something to prove. It's an assumption.
In what is called Euclidean geometry, an assumption is that two parallel lines never meet. There are other geometries that don't make this assumption, but in everyday geometry, this is an assumption that is never proved. It's just assumed.
Later on our journey, we'll talk about some of our core assumptions. They might include premises like "The world outside me is real and distinct from me." How about "When an event would not have happened without the event before it, we say that the one event caused the other event"? What about "Time is the succession of one moment after another" and "Space is the potential for my movement beyond the extension of my body"?
The philosopher Alvin Plantinga (b.1932) has spoken of warranted and properly basic belief. He would argue that belief in God is "properly basic," meaning that it is foundational enough to our reality that God's existence doesn't necessarily have to be argued for. It is a reasonable assumption. Interestingly, he has also offered many arguments for the existence of God. [1]
8. Another word for an assumption in logic is a presupposition. In particular, a presupposition tends to be an assumption that more foundational or significant. Some schools of thought relate presuppositions to what they might call a worldview. Sometimes, worldviews are seen as large systems of assumptions.
I would argue that there are more and less helpful ways of thinking about worldviews, as we will see eventually. If a worldview is seen as a collection of related perspectives, it can be a useful construct. However, some treat worldviews as inevitable systems. Or, worse, they might see an element of a worldview and conclude a person then has a host of other positions they may not actually have.
We will explore this "bad logic" later on.
9. I've mentioned that logic has had its detractors in recent decades. I had a student once -- now a professor himself -- who went to Princeton Seminary, which has a fair amount of what might be called "post-liberal" thinking. Post-liberal thinking tends to be anti-evidentiary thinking.
We had an interesting conversation after his first year. Clearly, the significance of Reason was being called into question. In Christian circles, we often find faith and reason pitted against each other.
I remember making a distinction between what we might call "macro-reason" -- that is, large systems of assumptions and conclusions -- and what I called "micro-reason." In that conversation, micro-reason referred to the simple logic that we have been exploring in this post.
You cannot avoid this logic if you have any thoughts at all. You cannot argue against Reason without using logic. You cannot interpret the Bible without logic. Let that sink in.
The concept of the Wesleyan Quadrilateral has reason as one of the four sides. But in reality, it is unavoidable at the center. We use reason to interpret Scripture, experience, and tradition.
We cannot escape it. As soon as we form a sentence, we have used reason. Reason thus is the unescapable foundation of all truth, at least in this universe.
[1] Captured in the book by Jerry Walls and Trent Dougherty, Two Dozen (or so) Arguments for God (Oxford University, 2018).
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Introduction1.1 What is philosophy?
1.2 Is philosophy Christian?
1.3 Unexamined assumptions
1.4 Socrates and the Unexamined Life
Logic
2.1 The Structure of Thinking (this post)
2.2 When Thinking Goes Wrong
2.3 Three Tests for Truth
2.4 Knowing the Bible
2.5 Plato and Aristotle
2.6 The Story of Logic
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