This final area of philosophical inquiry is somewhat other than the rest. Logic is not so much a part of human life to investigate, as a tool we seem capable of accessing in order to do the investigation well. Logic is similar to language in that, while we can think reflexively about both, we need both in order to think reflexively, and think well. Yet, that there is also a second-order, philosophical question about why logic works, or what are logical connections, is itself certainly true. Still logic is essentially just good reasoning, and reasoning is something we do naturally. To study logic is to study the nature of reasoning, and develop methods and strategies by which our reasoning can improve, and truth attained.
Some forms of logic, like symbolic logic, are also similar to languages, albeit non-natural ones. They are highly abstract. In the late 19th and early 20th centuries, philosophers like Gottlob Frege, Georg Cantor, Bertrand Russell, and Alfred North Whitehead, developed symbolic logical systems designed to eliminate the ambiguity associated with classical forms of logic that deal with natural language. These systems, based on mathematical reasoning, attempt to illustrate purely structural relationships between entities, regardless of whether such entities are real or not, and they sometimes go under the umbrella term Logicism. These highly abstracted, a priori systems are very technical, and tend to be utilized by professional philosophers in specialized areas of research (like Logic itself).
Alternatively, Classical, or Aristotelian, logic is primarily a prescriptive set of rules regulating our mental operations when seeking the truth about claims about reality. Classical logic deals with natural language claims, and the relationship between words and sentences of natural languages (e.g. English, German, Mandarin, etc.), that is it deals with grammars. It is this kind of logic I will discuss here, since it is most commonly used in developing arguments related to the defense of the Christian faith, and many other areas of everyday philosophical investigation like philosophy of science, religion, aesthetics, and politics.
Formal & Informal Logic
Formal Logic is fundamentally about one thing: structural validity of arguments. This differs from informal logic, which primarily has to do with logical fallacies in premises.
Most people are familiar with some aspects of informal logic, for example fallacies like: the genetic fallacy, ad hominem fallacies, or the fallacy of composition. Most informal fallacies fall into larger categories like: Fallacies of Ambiguity, Relevance, or Sufficiency. Informal fallacies are not less damaging than formal ones, they are just not related to the “form” of an argument. They have to do with language and the meaning of words and sentences.
Informal fallacies usually apply to the sentences themselves, not to the relational structures, or grammar, of arguments. Here is an example of an informal fallacy:
Socrates is a Greek. Greek is a language. Therefore, Socrates is a language.
This is an example of a fallacy of Ambiguity, since the term “Greek” has multiple meanings in common parlance. Thus, it would have to be clarified what the term means in the context it is given. Here is another informal fallacy:
John is an evangelical Christian, so what would he know about science? Even if he has a PhD in micro-biology, he can’t do real science.
This is an example of a fallacy of Relevance, in this case a kind of ad hominem attack, or attack against the person. More specifically this particular instance is a “poisoning the well” fallacy, making an initial claim about a person (or group) that tries to undermine any future claims they may make about a given topic, here the biological sciences. The fact that John is a Christian is simply irrelevant to his being able to practice science well or make accurate pronouncements on scientific issues.
Another kind of fallacy of Relevance is the Genetic Fallacy, which attacks the source of the claim, as opposed to the claim itself:
Evolution endowed human beings with certain cognitive capacities that led to the rise of beliefs in God and gods among early, prehistoric communities. Therefore, belief in God is irrational.
Here, it is argued that because it may be the case that human beings, over a long prehistory, developed certain cognitive capacities that facilitated the belief in supernatural beings, or a supernatural Being, that therefore the belief in those beings, or Being, is irrational. However, the source of the formation of the belief is not ultimately what determines if the belief is true. That must be determined on other grounds, otherwise the Genetic fallacy has been committed.
One final kind of informal fallacy is the fallacy of Insufficiency. This usually has to do with premises that do not rely on a sufficient amount of data or factual evidence to be considered strong premises. For example:
My friend Joe has been smoking all his life, and he has never had any problems with his lungs; therefore, smoking is just fine!
Here we have the fallacy of Hasty Generalization, which bases a radical conclusion, to assume smoking is fine for your health, on a very small amount of evidence: knowledge of just one friend’s capacity to smoke and not get ill. That is called an appeal to “anecdotal” evidence and would be insufficient to warrant starting to, or continuing to, smoke.
Most informal fallacies are found in inductive arguments, not deductive ones, and there are many more informal fallacies that we could give examples for. For a good introduction to Informal Fallacies, see here.
Formal logic, in contrast to informal logic, is concerned with demonstrating how syntax (the order of a sentence) is related to relational validity when two or more sentences are fit together in a grammatical structure. Formal logic is a means to demonstrate how, when declarative statements are strung together through certain operative words like “if…then” “and” and “or,” or “some” and “all,” and put into a sequential order, the conjunction of those sentences compel us to accept or reject a conclusion by the sheer light of reason. Errors in the structure of an argument, however, do not say anything about the argument’s conclusion being true or false, just that the arrangement, or form, of the argument does not show the conclusion to be true or false, because it contains a structural deficiency.
For example, the following argument is logically valid, but the conclusion is false:
Premise 1: All cats are blue
Premise 2: Tabby is a cat
Conclusion: Therefore, Tabby is blue
Here, the structure of the argument is valid, for if all cats really are blue, and if Tabby is a cat, then Tabby must be blue. Of course the problem is that premise 1 is simply false.
And, conversely, here is an example of a conclusion that is true, but where the argument is invalid, and therefore does not demonstrate the conclusion’s truth:
Premise 1: Some men are bald
Premise 2: Tony is a man
Conclusion: Therefore, Tony is bald
Now, it does so happen that the “Tony” I am thinking about, namely myself, is bald, and thus the conclusion is true. But, because the argument is not valid, it bears no weight on that conclusion. It is an invalid argument because premise 1 only says that “some” particular men are bald, and while premise 2 does pick out a particular man named “Tony,” there is no logical connection between the “some” of premise 1, and the “Tony” of premise 2 that forces us to conclude Tony is bald (even if this particular Tony does happen to be bald, that is purely accidental).
If however, like in the previous example, the universal affirmative “all” was used in premise 1, then the argument would be valid, although the conclusion would now be rendered false. Thus, the following is again valid, but false:
Premise 1: All men are bald
Premise 2: Brad Pitt is a man
Conclusion: Therefore, Brad Pitt is bald
Propositional or Semantic Content
Sentences however are not really what we are interested in, rather we are interested in something far more “mysterious,” namely propositions. Sentences are just the linguistic expression of propositions, or semantic content. Therefore, propositions themselves are often, and correctly, seen as non-linguistic, immaterial, yet real objects. This can be demonstrated as follows:
- The snow is white
- Der Schnee ist weiss
Both of these sentences mean exactly the same thing. However, they are clearly not the same sentence. What is identical is the proposition behind each set of words, i.e. that “snow is white.” But the words themselves are obviously not identical. Moreover, if we were to write a third sentence in Mandarin Chinese, we could have entirely different symbols, yet the same meaning or propositional content. Thus, we can show that propositions and their sentences are not identical.
Logic is therefore the main tool we use to “see” whether two or more sentences, linguistic devices that represent propositions, if tied together in some kind of grammatical structure, force us to think something may, or must, be the case. There is yet another kind of logic, modal logic, which deals expressly with the idea of whether or not certain propositions are “necessarily” true, or only “possibly” true, etc. Simple propositional logic however helps us to determine the truth value of a sentence, which itself is the linguistic expression of propositional content. In classical propositional logic then, there are only two possible values for any declarative sentence, “true” or “false.”
The grammatical structuring of sentences for the sake of determining truth is what we often call an “argument.” Arguments in philosophy come in two main categories: deductive and inductive arguments.
Deductive arguments are comprised of premises and a conclusion. The main thing to know about deductive arguments is this: if the premises are true, and the structure of the argument valid, then the conclusion MUST be true. The classic example of a deductive argument is this:
Premise 1: All men are mortal
Premise 2: Socrates is a man
Conclusion: Therefore Socrates is mortal
If P1 and P2 are both true, then it has to be the case that the conclusion follows. So it goes with deductive formulations of arguments. An example of a deductive argument often used in the Apologetics is the Kalam Cosmological argument, which usually is presented as such:
Premise 1: Whatever begins to exist has a cause
Premise 2: The universe began to exist
Conclusion: Therefore the universe had a cause
If P1 and P2 are true, then the conclusion must follow. Another way of thinking about Deductive Arguments is that they tend to start with a general theory or statement and reason toward a specific conclusion. This can been clearly seen in the two aforementioned arguments that start with broad statements about “all men” and “mortality” and “whatever begins” and “causes” to “Socrates” and “this universe.”
Because Deductive arguments are meant to force one to either accept a conclusion, or reject the truthfulness of one of the argument’s premises, the structure of deductive arguments has to follow certain rules of logic. One way to try and test for the validity of an argument is through Natural Deduction.
Natural Deduction utilizes some intuitive rules of logic, or rules of inference, to create deductively valid arguments. The nine most useful rules of inference are: modus ponens, modus tollens, addition, disjunctive syllogism, simplification, conjunction, hypothetical syllogism, constructive dilemma, and absorption. The aforementioned examples both use the rule “modus ponens” as a means of demonstration. Valid, or sound, deductive arguments are the strongest kinds of arguments, since they force a conclusion upon the hearer.
However, there are very few deductive arguments for anything that cannot to some degree be questioned in the soundness of their individual premises, even if their structures are valid. Finally, the main fallacy associated with Deductive Arguments, is “begging the question” which goes something like this:
Premise 1: The Bible says that God exists
Premise 2: The Bible is true because it is God’s word
Conclusion: Therefore, God exists
Here, the conclusion may be true (I certainly think it is), but the argument is helpless to show it true, because it requires God’s existence to show that the Bible is true (premise 2), yet God’s existence is what the argument is supposed to prove. Thus, from this argument alone, we cannot know the Bible is true, and if we cannot know the Bible is true, then we cannot know that God exists. It “begs the question” or, in other terms, it is “circular reasoning.” Atheists can run into similar problems:
Premise 1: Reason tells us that God does not exist
Premise 2: Reason is the source of all truth
Conclusion: Therefore, God does not exist
Same problem here, since to claim that “Reason” is the source of all truth, requires the use of reason itself. But, how do we know that the very tool we are using to attain truth is itself reliable? Thus, it “begs the question” about whether or not reason really is the source of all truth by simply asserting it to be the case.
Inductive arguments, in contrast with deductive ones, are meant to give strong reasons for the likelihood of a conclusion, but do not force a decision upon the hearer to either accept the conclusion, or reject one of the premises. The hearer could think the premises are strongly supported by the facts, and that the conclusion is strong based on the conjunction of those factually supported premises, yet still believe that there is room for the conclusion to be false. Induction is the primary form of scientific reasoning, and usually starts with particular or specific observations in order to work toward a general conclusion. Inductive arguments are therefore probabilistic in nature. Here is a common example:
Premise 1: Every time I have walked Susie’s dog, it has not bit me
Premise 2: Tomorrow I will walk Susie’s dog
Conclusion: Therefore, when I walk Susie’s dog tomorrow, he won’t bite me
Here, we can see that the conclusion is not certain, but it very well may be probable, especially if the dog walker has walked Susie’s dogs several times without incident. It may not be necessary for me to believe with certainty that Susie’s dog will not bite the walker, but I may wind up believing that due to the pattern that has been set. This is an example of what we might call an inductive generalization.
Premise 1: 85% of Americans own at least one TV set
Premise 2: Tom is an American
Conclusion: Therefore, probably Tom owns a TV set.
Inductive arguments can focus on one set of data, e.g. past dog-walks, ratio of TV’s to American citizens, and try to make a strong, albeit not absolute, inference to the truth. Some, like the second example, can be statistical in nature, and thus, if done right, can be fairly compelling.
Many arguments for or against the existence of God due to the problem of Evil are probabilistic, or inductive ones:
Premise 1: If an an all-loving, all-powerful God exists, then there likely would be no gratuitous evil in the world
Premise 2: There is gratuitous evil in the world
Conclusion: Therefore, it is unlikely that an all-loving, all-powerful God exists
Here, one can see that the conclusion is not certain, it is only a probability argument, and one not based on quantifiable data, but a common sense, qualitative notion of likelihood. There are many responses to this kind of argument against God from the PoE, and both premises can be challenged.
Abductive or Inference to the Best Explanation
As Apologists we often use deductive and inductive arguments to either force a conclusion regarding a specific theistic belief (e.g. God exists), or to compel one to accept the likelihood of a specific belief (e.g. probably Jesus rose from the dead). However, when defending Christianity as an all-encompassing worldview, our apologetical project often synthesizes together many different deductive and inductive arguments to show that, on the whole, Christian theism is the best explanation for the world, and our experience of that world.
This kind of reasoning, where we take into account various scientific and historical facts, philosophical arguments, and other natural and human phenomena to provide an overarching theory, or explanation, is called abductive reasoning, or inference to the best explanation. This is perhaps the most commonly used form of reasoning today in Christian Apologetics, and is often called “cumulative case” reasoning by popular authors and speakers. This kind of reasoning tries to fulfill certain explanatory criteria, such as: explanatory power, explanatory scope, lack of ad hocness, simplicity, predictive capacity, etc., and show why Christianity is a better fit to explain certain facts about the world.
One can think of many facts, or givens, about our experience of reality that seem to be best explained by a broadly religious, or even specifically Christian, explanation of the world.
- the almost universal belief in human souls,
- compelling reports of near death experiences,
- the existence of anything at all,
- the intuition of cause and effect,
- the hard problem of consciousness,
- the argument from desire,
- the phenomenon of beauty in both the natural world and in human art,
- the sense of having free will,
- the nature of morality,
- the abundance of miracle reports,
- the complexity and variety of biological life,
- the historical witness to the life, death and resurrection of Jesus of Nazareth,
- the rise, global spread, and longevity of the Christian faith,
- and, of course, personal religious experiences and changed lives.
When all taken together, and weighed against various competing hypotheses, one can see how the Christian worldview is a powerful explanatory hypothesis when put up against other views like naturalism, pantheism, or polytheism. While cumulative case arguments are not arguments in the same sense as deductive ones, they get right to the heart of answering the most fundamental human question: why? Abductive reasoning of this sort is also the primary way scientific theories are developed. It is the most common, and natural, form of logical argumentation.
Conclusion to Philosophical Apologetics
This series on Apologetics has first taken into account the four main areas of Philosophical inquiry: Metaphysics, Epistemology, Ethics, and Logic. At this point the young Christian, or the Christian young in the faith, may feel overwhelmed. How, after all, can one learn “all this stuff!?” While it is clearly not necessary to be an expert in any of these fields to evangelize, since the power of the Gospel is itself sufficient to convert even the hardest heart, we should also not relinquish the battlefield of ideas to the skeptic, the materialist, or the co-religionist. The pursuit of knowledge is part and parcel of the Christian life of discipleship, and so I end this section with the words of one of the “greatest” of Christ’s disciples, John Wesley:
If we are “overseers over the Church of God, which he hath bought with his own blood,” what manner of men ought we to be, in gifts as well as in grace? …
To begin with gifts, and with those that are from nature: Ought not a Minister to have, First, a good understanding, a clear apprehension, a sound judgment, and a capacity of reasoning with some closeness? Is not this necessary in an high degree for the work of the ministry? Otherwise, how will he be able to understand the various states of those under his care; or to steer them through a thousand difficulties and dangers, to the haven where they would be? Is it not necessary, with respect to the numerous enemies whom he has to encounter? Can a fool cope with all the men that know not God, and with all the spirits of darkness? Nay, he will neither be aware of the devices of Satan, nor the craftiness of his children.
He goes on…
Some knowledge of the sciences also, is, to say the least, equally expedient. Nay, may we not say, that the knowledge of one (whether art or science), although now quite unfashionable, is even necessary next to, and in order to, the knowledge of the Scripture itself? I mean logic. For what is this, if rightly understood, but the art of good sense? of apprehending, things clearly, judging truly, and reasoning conclusively? What is it, viewed in another light, but the art of learning and teaching, whether by convincing or persuading? What is there, then, in the whole compass of science, to be desired in comparison of it?
Is not some acquaintance with what has been termed the second part of logic (metaphysics), if not so necessary as this, yet highly expedient, (1.) In order to clear our apprehension (without which it is impossible either to judge correctly, or to reason closely or conclusively) by ranging our ideas under general heads? And, (2.) In order to understand many useful writers, who can very hardly be understood without it?
John Wesley, An Address to the Clergy (1756)