Part 1 Logical Reasoning
Logical Reasoning addresses the transition from one belief to another and the study of this portion of philosophy seems somewhat dry; however logical reasoning actually matters and therefore requires that we have clarification on the topic. There are a number of important concepts associated with logical reasoning.
Part 2 Validity
It is important to know that validity is different from the consideration of truth. Validity concerns the issue of one's argument. An argument is either valid or invalid whereas truth is either true or false. We speak of the validity of moves or transitions from one premise to another. Good reasoning must be valid. Good beliefs ought to be true. This is an important distinction.
Part 3 Premises and Conclusion
The most basic distinction made in logic centers upon the Premises of the argument and the Conclusion of the argument that is based upon the Premises. The beginning of the argument consists of the premise and the conclusion of the argument or the end point of the argument is the conclusion. The conclusion of the argument will be inferred from the premises of the argument. Validity has to do with whether the conclusion legitimately derives or validly derives from the premises.
Part 4 Example
Consider for example the most common of arguments proposed by Aristotle that says, "All men are mortal. Socrates is a man. Therefore Socrates is a mortal." In this argument we have premise one, premise two and the conclusion that is based upon the two previous premises or perhaps we should say is inferred from those premises. We could summarize the argument as follows: If it is the case that all men are mortal and if it is the case that Socrates is a man, then it is to be inferred that Socrates as a man is mortal. Socrates must be and cannot fail to be mortal. This is said to be a valid argument. Since the premises are true, then the conclusion must also be true.
Consider another example. If we said, "All men are mortal. Socrates is a man. Therefore Socrates is a philosopher" this would constitute an invalid argument. Or if we said, "Some men are mortal. Socrates is a man. Therefore Socrates is a mortal" this conclusion would also be invalid. Consider also another symbolic approach to the same Aristotelian syllogism. Consider that "All f's are g. x is an f. Therefore x is a g." In this example we have simply used the letters f and g to stand for being a man and being mortal. Consider another example. "All cats purr. Tabby is a cat. Therefore Tabby purrs." This example is true. This example helps us to establish the general form of argumentation and helps us to consider whether an argument is either valid or invalid.
Part 5 Universal Instantiation
Logical reasoning also employs the concept of universal instantiation. But what is meant by the designation. The designation indicates that if everything is f then any particular thing must also be an f. It is really very simple. For example, "If everything is a particular physical object, then any particular thing must be a particular physical object." This is called universal instantiation. These types of universal propositions move from a general to a specific instance. What we are interested in is not whether the premises are true, but if the premise is true and if the conclusion the fore is derived from or inferred from the premise. Obviously everything is not physical but this is beside the point with the statement. This is not what we are debating or considering at this point. We are simply looking for a valid argument in which the conclusion is legitimately derived from the premise or premises.
Part 6 Existential Generalization
Another concept employed in logical reasoning is existential generalization. But again what is meant by this designation? The terms refer to the taking of a general statement and then inferring a conclusion from that statement. For example, if a Socrates is a man then something is a man. This means that we take a particular statement and infer an existent statement that is generally true.
Both of these categories should seem to be self-evident rules of inference. We should listen to these statement and simply respond, "Yes and your point is . . . . " These inferences are not even remotely disputable. They are obvious or self-evident. If we follow the rules of logic then we cannot go wrong. If the premises are correct then the conclusion will also be correct.
For example, I can say, "Show is white and grass is green." I can infer from that that all snow is white and all grass is green. It is straightforward.
It is important to understand the inescapability of logical laws. However, consider Descartes. He was interested in what could be doubted. He doubted an enormous amount of possibilities. He argued that we couldn't doubt the self and he also argued that we couldn't doubt the laws of logic. In fact, the laws of logic are immune to doubt for Descartes as is the self or the cogito, I think therefore I am.
To some this sounds very dogmatic but it is nonetheless the case. One thing to notice about the indisputability of logic is that to true to doubt this is to use logical principles to move in the direction of doubt and this is inherently a contradiction. The rules of logic are the inescapable rules of logic that govern reasoning.
To some ears this sounds very dogmatic but it is nonetheless the case. One thing to
But it is also not only true that logic applies to reason, but logic applies in relation to the world itself. We talk of the laws of logic as applied to the world. This world must obey the laws of logic. Perhaps we are inclined to ask how this can be the case. Surely things can vary between worlds. What is logical in this world is not necessarily logical in another world. But this is a contradiction. There are three traditional worlds of logic.
Part 7 The Law of Identity:
The law of identity argues that everything is identical to itself. Read that statement very closely. In fact, the statement should strike us as common or banal. Whatever is a certain thing is always that particular or certain thing. While this seems to be trivial it is a law that cannot be rejected. It sets a limit to thought. You cannot conceive of an object that fails to be identical to it. To do so would be a perplexing reality. The law sets a limit to thought and tells us what is within the realm of intelligibility.
Part 8 The Law of Excluded Identity:
This law is also called Leibniz law. Leibniz was the great 17th century philosopher who developed the law. He proposed that if things are identical they have all of their properties in common. There are in reality two versions of the law. The other version of the law says that if two objects have all qualities in common they are identical. This is not our concern at this point. Here we are considering the idea that if things are identical they must be exactly alike in properties. If a is b then a must have the properties of b. Whatever a has then b must also have. If you can show otherwise you show that a is not b. This again is a self-evident truth.
Part 9 Marilyn Monroe and Norma Jean Baker
Consider for example Marilyn Monroe and Norman Jean Baker. Marilyn Monroe was her screen name. Norma Jean Baker was her birth name. Leibniz says whatever is true of one is also true of the other since these two designations refer to the same person. Marilyn Monroe is identical to Norma Jean Baker. Whatever is true of one is also true of the other. If Marilyn is in "Some Like It Hot" then also Norma was in "Some Like It Hot." She may not have been called Norma but she was nonetheless the same person. If Marilyn Monroe went to High School at a particular location, then Norma Jean Baker also went to High School at that same location. Again, this is a self-evident truth.
Part 10 The Law of the Excluded Middle
The law of excluded middle contends that everything has a given property or it lacks that property. Either an object is red or the object is not red. A blue object is not red. Every object either is or is not red. Every proposition is either true or it is false. It cannot be both true and false. Everything is either a man or not a man. Everything is either a physical object or not a physical object. Again, this also is a very trivial but nonetheless significant principle.
Part 11 Vagueness
What about borderline circumstances? Isn't there a middle ground? We might say, "Everything is either a child or not a child." But what about an adolescent? This is a legitimate point but it still does not compromise the law of excluded middle. We can simply reframe the statement to say everything is not definitely red or is definitely red. This does not compromise the heart of the principle.
Part 12 The Law of Non Contradiction
The law of non-contradiction says that nothing can have a property and not have a property at the same time. Nothing can be red and not be red at the same time. Nothing can be a man and not be a man at the same time. These properties contradict one another. No proposition can be both true and false at the same time.
Remember that the law of the excluded middle says that every proposition is either true or false. This law however says that nothing can be true and false at the same time. Reality depends upon the law of non-contradiction. For example, if show is white ben be both true and false then what use is the premise and reasoning would completely break down. It is actually inconceivable that something could be red and not be red at the same time for an additional example.
These are the self-evident laws of logic. But why are these laws important? These laws are important because of the spirit of our times that says that everything is up for grabs. We live in an age when we believe that everything is revisable or that everything is fallible. In other words, what we believe now can change in the future. But the fact is that not everything is up for change and the laws of logic are a prime example. They do not depend upon our minds and they are the bedrock of all thought and possibly all reality. The laws of logic are immune from the doubt of the skeptic and they have to do with the fundamental nature of rationality itself.
Part 13 Modus Potens
One additional topic merits our attention. It is known as the rule of inference or the Modus Potens. It essentially says that if we know p and know that p is then q then we know q. For example, if you know that it is raining and if it is raining that the ground is wet you can therefore infer that the ground is wet outside. In short, q follows from p. We use this approach frequently. We say, "I will persuade you to accept p and then that p is q and then q. We are simply attempting to get the other person to accept something which follows from an already held to belief.
