The Basics of Argument
I. Truth
II. Belief
III. Some Additional Logical Basics
IV. Consistency
V. What is an Argument?
I. Truth- A sentence is true if what it expresses matches or corresponds to what is the case in the world. So, "The earth is flat." is false, but "The earth is spherical." is true. And "The earth orbits the Sun," is true, and "The earth is at the center of the universe with the Sun and planets orbiting around it," is false. The truth is objective—it does not depend upon what people think or believe. Truth is mind-independent. It remains what it is whether we form beliefs about it or not. Even if there was no one with a mind to think about it, or believe it, it would still be true that the earth is round, and that 2 + 2 = 4.
In the above examples, there have been times and places when many people believed that "The earth is flat," or "The Sun orbits around the earth." That is, they believed that these sentences were true. We might be tempted to say that these sentences were "true for them." To use "truth" in this way would conflict with the definition of truth above, and it is not intelligible. What these examples make clear is that belief and truth are distinct. When a person S believes some sentence, then S takes it to be true. S assents to that sentence; S believes that it is true. But whether or not the sentence is actually true is an independent matter from whether or not S believes it. There are countless cases where we have believed a sentences (taken it to be true), but we were wrong because it was in fact false--like the flat earth case above. And there have been countless cases where no one believes something, but it is true. There is a cure for cancer out there, we presume, but no one has discovered it yet.
And notice that if one person S believes that the earth is flat, and another person R believes that the earth is round, they both take different things to be true. But only one of them is right, and the other one is mistaken. What they both believe cannot be true because what each one believes rules out, or is incompatible with what the other believes.
CP: Correspondence Principle. A declarative sentence is true just in case it corresponds to the facts as they actually are. A declarative sentence is false just in case it fails to correspond to the facts as they actually are.
OTV: One Truth Value. Every proposition has exactly one truth value. It is either true or false, but not both.
II. Belief- To believe a claim is to assent to it or to have an attitude towards it such that you think it is true. It may or may not be true, but to believe it is to think that it is. So many people believed that the earth is flat. Some may still believe it. Belief is subjective because it is dependent upon an individual to possess it. Belief is mind-dependent. There are no beliefs without minds.
We are employing belief in a broader sense than it is often used. We will include all claims that a person would agree to, whether they are trivial or momentous, among their set of beliefs. So you believe that February follows January. And you believe that the chair you are sitting on is not made of cheese. And you believe that when the sun is shining, it is day time.
BP: Belief Principle. Whenever a person considers any proposition, that person must believe the proposition, or disbelieve the proposition, or suspend judgment about the proposition. A person cannot at any time have more than one of these attitudes toward one proposition.
RB: Rational Belief.
Believe: If a person’s evidence concerning a proposition supports that proposition, then it is rational for the person to believe the proposition.
Disbelieve: If the person’s evidence goes against the proposition, then it is rational for the person to disbelieve the proposition.
Suspend Judgment: And if the person’s evidence is neutral, then it is rational for the person to suspend judgment concerning the proposition.
Fallibilism is the view that it is possible for it to be rational or reasonable for a person to believe a proposition even though it is false.
PB: Proportional Strength of Belief. It is rational to proportion the strength of one’s belief to the strength of one’s evidence. The stronger one’s evidence for a proposition is, the stronger one’s belief in it should be.
III. Some Additional Logical Basics
Principle of Sufficient Reason For every truth or thing that exists, there is a sufficient reason or explanation for its being true or existing, rather than otherwise. Truths have an explanation, existing things have a reason for their being. Events do not occur, things do not come to exist, and truths do not come to be ex nihilo or from nothing; there is always an explanation behind them.
Logical Possibility Any proposition whose opposite does not imply a contradiction is logically possible. That is, if the sentence does not include a contradiction like, "Mike is a married bachelor." then the state of affairs that the sentence describes is logically possible. So it is log. poss. that Mike is a bachelor. And it is logically possible that he is married. And it is logically possible that Mike (an unaided human) could fly. But it is not logically possible that 2 + 2 = 5, or that circles have sides, or that the Pythagorean Theorem is wrong, etc.
Natural Possibility The laws of nature such as the universal law of gravitation, F = MA, and e=mc2 determine the range of what states of affairs are naturally possible. So it is not naturally possible for an unaided human body to fly—the musculature, bone structure, and other physiological traits prevent it. But it is naturally possible (we think) to cure cancer. The laws of nature, which are different from the laws of logic, could have been different without logical contradiction. The periodic table could have been different, gravity could attract at a different rate, or force could be equal to something different than mass times acceleration. If one of those different sets of natural laws were in place, then the range of what events that is naturally possible would be different.
A necessary truth is one whose opposite implies a contradiction. It is a proposition that must be true without exception. A = A is a necessary truth, as is "Bachelors are unmarried," and "Triangles have three sides." A necessary being is one whose non-existence is impossible. That is, a necessary being must exist; it cannot fail to exist. God is the only being typically characterized as a necessary being.
A contingent truth is one that can be true or it can be false without logical contradiction. "George W. Bush is the president" could have been false without violating the law of non-contradiction. He might have only been a gas station attendant. A contingent being is one that could have existed or could have not existed without logical contradiction. We humans are all contingent.
The Law of Non-Contradiction It is not possible for a thing to both possess and not possess a property at the same time in the same way. To make an assertion of the form X is P, like the ball is blue, is to claim that the ball has the property of blue and that it is false that the ball is non-blue. If we abandon the law of non-contradiction, then there is no meaningful difference between an assertion and its opposite. That is, our assertions cease to have meaning altogether. My claim that, "Today is Tuesday," doesn't say anything unless it denies some other state of affairs like, "Today is Wednesday." The law of non-contradiction is axiomatic to reason; that is, it is one of the most fundamental principles upon which reasoning and rationality are based. It cannot be argued for (it is the principle that makes arguments possible) nor can in be plausibly denied (to deny it is to already assume it.)
A priori truths are truths that can be known without an appeal to experience. They are true by definition or in virtue of the meanings of the words involved. "A square is a four sided figure," is an a priori truth. We do not need to count the sides of objects that are squares in the world to know that it is correct. "Mammals have warm blood," is another a priori truth.
A posteriori truths are truths that we discover and know on the basis of experience. "McCormick is 6' 1" tall," is a fact that can only be discovered by experience. It cannot be known by conceptual analysis the way "bachelors are unmarried" can. "Interest rates were at a 40 year low in July" is another example of an a posteriori truth.
IV. Consistency- A set of sentences is consistent if and only if it is possible for all of them to be true (at the same time.)
The set of sentences is inconsistent if it is not possible for all of them to be true at the same time.
So these sets of sentences are consistent:
1) Arnold is the governor of California.
2) Arnold is a former movie star.
1) The earth orbits around the Sun.
2) Pluto orbits around the Sun.
1) If the door is locked, then the store is closed.
2) The door is locked.
3) The store is closed.
But these sets of sentences are inconsistent:
1) Arnold is the governor of California.
2) Arnold is not the governor of California.
1) The earth is flat.
2) The earth is round.
1) God exists.
2) God does not exist.
1) If the door is locked, then the store is closed.
2) The door is locked.
3) The store is not closed.
V. What is an Argument?
A successful argument for a proposition p will be a set of premises or reasons (different than p) that are true and that when taken jointly would imply or indicate the truth of the conclusion p to a reasonable person who does not already believe p.
Rational commitment: So if a reasonable person does not believe p:
a. understands and believes that all of the premises in the argument are true, and
b. understands and believes that the premises when taken jointly imply or indicate the truth of p,
then, that person is rationally committed to believing p. To fail to accept p as true in these circumstances would be patently irrational.
So if I believe:
1) If a person is in California, then they are in the United States, and
2) Arnold is in California right now.
then I am rationally committed to believe that:
3) Arnold is in the United States right now.