Introduction (Part 4) – What Constitutes A “Sound And Valid Argument”?

AN ARGUMENT

An argument can be in the following forms:
• a deduction – based on logic (i.e., the conclusion logically follows from the premises), or
• an induction – drawing a conclusion based on observation: “The sun rises every day and is therefore likely to rise tomorrow.” However, it is not guaranteed to rise tomorrow; it is simply more likely than not.

A “SOUND” ARGUMENT: HOW DO WE KNOW A PREMISE IS TRUE?

A “sound” argument is one in which each premise is true.

We can figure out if a “premise” is true based on:
direct experience with the facts (observation, empirical evidence),
a self-evident truth (either “a priori logic ” like 2+2=4, or something that is “true by definition” like “all bachelors are unmarried”).

A “VALID” ARGUMENT: DOES THE CONCLUSION LOGICALLY FOLLOW?

A “valid” argument is one in which the conclusion logically follows from the premises.

“SOUND” AND “VALID”

For any argument we hear, we must ask these two questions:
1. SOUND: Do we agree that each premise is more likely true than not? (if not, the argument is unsound)
2. VALID: Does the conclusion logically follow from the premises? (If not, the argument is invalid).

A DEDUCTIVE ARGUMENT

Here is an example of a deductive argument:
Premise 1: All men are mortal.
Premise 2: John is a man.
Conclusion: Therefore, John is mortal.

Let’s apply the criteria for “soundness” and “validity” to this deduction:
1. SOUND: Do we agree that each premise is more likely true than not? (if not, the argument is unsound)
2. VALID: Does the conclusion logically follow from the premises? (If not, the argument is invalid).

Soundness:

Is the above premise 1 true in saying that “all men are mortal”? I can’t observe every man who has ever existed to see if they eventually all die, so my knowledge about that is incomplete. However, based on my observation, I can be 99% sure that premise 1 is true.

I can observe that premise 2 saying “John is a man” is also true.

Validity:

Does the conclusion that “therefore, John is mortal” logically follow from the two premises? It seems that the conclusion would be true beyond a reasonable doubt (highly likely).

PROBABILITY

A “deduction” can have premises that we are 100% sure are true. If the conclusion logically follows from the premises, that deduction provides “a guarantee of truth.”

However, when we are talking about the existence of God, never let anyone demand that there be a 100% guarantee of truth before they will believe something. On this subject, that would be an impossible standard to require of atheists or Christians. The question we should all be asking is, “Which view seems more likely to be the best explanation?”

A “deduction” can also contain premises that are NOT 100% sure, but are “more likely” to be true (having a probability of greater than 50%). So if the conclusion logically follows, it could be “more likely than not” or “more likely than an alternative explanation.”

An inductive argument:
• is based on observation of a sample or part of a group (“I’ve watched the sun rise every day of my life”),
• draws a conclusion or generalizes about the entire group (“therefore, the sun is highly likely to rise every day in the future”).

An inductive argument never really provides a guarantee of truth. Rather, it provides a likelihood or probability “greater than 50%” and “less than 100%.”

In assigning a probability to the conclusion of an argument, that is entirely dependent on how likely the premises are. As we said in a previous blog, a probability is only relevant if there is adequate background information to substantiate that probability (observations, a priori logic or something true by definition).

SIMPLICITY

In any discussion about inductive arguments and probabilities, “simplicity” is enormously important. A theory that is the simplest is considered by scientists and philosophers to be the most probable and thus to have the most “explanatory power.” Other things being equal, “the simpler is the sign of the true.”

Oxford philosopher Richard Swinburne describes in detail what this concept of “simplicity” refers to: 
“The simpler a theory, the more probable it is. The simplicity of a theory, in my view, is a matter of it postulating few (logically independent) entities, few properties of entities, few kinds of entities, few kinds of properties, properties more readily observable, few separate laws with few terms relating few variables, the simplest formulation of each law being mathematically simple . . . A theory is simpler and so has greater prior probability to the extent to which these criteria are satisfied.”
Richard Swinburne, The Existence of God (Oxford: Oxford University Press, 2014), 53.

Examples Of Simple Arguments

To say that God is “all-powerful” is a much simpler hypothesis than having to describe in detail exactly what limited powers he might have. To say that God is “all-knowing” is simpler than having to describe exactly what he knows and does not know. It is a simpler explanation to say that God is “eternal” rather than suggesting that he did not come into existence until a certain date and time. To suggest that God “created all things” is a much simpler explanation than identifying all the factors that combined to create each element of this existence.

Science philosopher David Berlinski puts it like this:
“The more sophisticated the theories, the more inadequate they are.”
David Berlinski, The Devil’s Delusion: Atheism and It’s Scientific Pretensions (New York: Basic Books, 2009), xv.

SCOPE

In evaluating inductive arguments, a second criterion is the “scope” of the argument.

“Scope” has to do with an argument or explanation’s ability to explain more phenomena.

Let’s say that we’ve been working on a problem that has a number of unexplained characteristics and there are three different inductive arguments that attempt to explain these phenomena. In evaluating the three arguments, we find that one provides answers for more of the unexplained phenomena that we’ve been observing. That argument could be said to have greater “explanatory power” because it explains a wider range of phenomena. Scope is a less important criterion than simplicity, but still relevant.

If the inductive argument or theory really does explain a number of phenomena, that’s a good thing. However, some people try to stretch an argument or theory to apply to more phenomena than is logically justifiable.

Examples of Applying an Argument/Theory Too Broadly

In thinking about the scope of an argument, consider Origin of Species by Charles Darwin. Can you tell us the full original title of that book in 1859? It was “On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life.”

Even though the full title of Darwin’s 1859 book incorrectly addressed “favored races,” people have tried to apply his theory of evolution in ways that were probably never intended:
• Hitler used it to justify competition between races in a way that led to genocide.
• Margret Sanger used the theory to justify aborting babies of what she thought were “inferior races.”
• Militant atheists will sometimes exaggerate the scope of the theory to say it explains the origin of the very first life form on earth.
• Sociobiologists mangle and stretch evolutionary theory to say that it explains how we obtained morality and conscious awareness.

Regarding “scope,” an inductive argument has greater “explanatory power” if it explains more phenomena. As we said, “scope” is a less important criterion than “simplicity,” but still relevant. Also, we should be careful not to try and apply an inductive argument too broadly (i.e., apply it to more things than are logically justifiable).

CONCLUSION

Because logic can be a dry subject we will stop at this point.

If you recall nothing else, always remember to ask these three questions:
1. Do I agree that each of the premises is true?
2. Do I agree that the conclusion logically follows from the premises?
3. What is the simplest explanation?

If you can answer “yes” to question 1, you have a “sound argument.” If not, the argument fails. If you can answer “yes” to question 2, you have a “valid argument.” If not, the argument fails.

And always keep in mind that the simplest explanation normally has the greatest “explanatory power.”

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