HU Logic

According to standard categorical logic, statements of the form All S are P must have some sort of noun-phrase in the predicate.  Thus ‘All dogs are mammals’ is fine, but ‘All dogs are four-legged’ is not.  Why is this a requirement? Standard categorical logic is based on Aristotelian logic and inherits some of Aristotle’s assumptions. So one reason for the noun-requirement is that given Aristotelian metaphysics predicates without nouns are incomplete. To understand why, we first need to keep in mind that  predicates (parts of language) correspond to  properties (parts of the extra-linguistic—that is, non-linguistic—world).  Predicates without nouns are incomplete because, according to Aristotle,  properties  must inhere in objects in order to exist.  There are no free-floating properties—properties without some subject that they attach to.  Thus, statements like ‘All dogs are four-legged’ while grammatic...

To obtain the contrapositive of a categorical proposition (1) switch the subject and predicate, and (2) replace the subject and predicate with their complements First, consider A-statements All S are P  Contrapose All non-P are non-S Let’s use an  example  to help us determine whether contraposing an A statement is valid. All dogs are mammals Contrapose All non-mammals are non-dogs The original states that all members of the dog class are members of the mammal class. The dog class is completely contained within the mammal class.  The contrapositive states that all members of the non-mammal class are members of the non-dog class. The non-mammal class is completely contained within the non-dog class.              In other words, if x is a non-mammal, then x is a non-dog Intuitively, it does seem like both the original A and contrapositive A are saying the same thing. If...

We have the following categorical proposition: A: All things are eternal E: No things are eternal I: Some things are eternal O: Some things are not eternal If Xianity is true, then A is false, E is false, I is true, and O is true.  Why? On Xianity, only God is eternal (some think that Xianity is compatible with the eternal existence of some abstract objects—sets, numbers, properties, propositions, etc; but let’s ignore this for now since granting it does not substantially change anything below) and God is not the only being that exists. Hence everything other than God is not eternal. Hence, some things are not eternal. Hence, on Xianity both I and O are true.  Ok, so one (perhaps small but not insignificant) step towards showing that God is exists is to show that the E proposition above is false.  Step 1: Show that ‘No thing is eternal’ is false. One way to do this (not the only way, and perhaps not even the best way) is consider the obverse of ‘No th...

Ok, here's a little extra credit exercise that helps show how the square of opposition can clarify things for us.  I will give a little bit of extra credit for those who attempt to answer the question below.  You must explain your reasoning to get the extra credit. You must email me your response prior to class on Monday.  Enjoy! Consider the following statements: A: All things are eternal E: No things are eternal I: Some things are eternal O: Some things are not eternal By 'things' I mean: event, process, object (concrete and abstract), organism, person, etc (any thing you can imagine) By 'eternal' I mean: having no beginning and no end (For example: if there really is only one kind of thing (perhaps materialism is true let's pretend and there is really only one kind of thing, namely, matter) and that thing is eternal then A is true--there are other ways A could be true) What does theism in general and especially Christian theism in particular imp...

In this post, we will briefly consider two famous arguments that are in need of lots of interesting work to make them valid and persuasive. Rather than do that work here, I just want you to see the original arguments and how you are now in a good position to see their defects as stated. I am not saying that they cannot be remedied. But the attempted remedies are trickier than meets the eye. Put differently: once we recognize that the original arguments are not valid, the force of the arguments begins to diminish a bit.  The Logical Problem of Evil Lots and lots of people think that the existence of evil is a real problem for the existence of God. But clearly stating the problem is not as easy as some have thought, and once the problem is clearly stated the ways out of it are more numerous than initially believed. Here's a first stab at the problem: 1st try:  Evil exists. Therefore, God does not exist.  Obviously, that won't do. Something else must be added....

For each of the statements below, provide an example that shows why the statement is either true or false. I will do it for the first one by way of illustration. You can post your responses here or email them to me for extra credit.  1.      If an argument is valid then it has true premises and a true conclusion To show that 1 is false, I need to show that it is possible for an argument to be valid and have either false premises or a false conclusion. For overkill I will give an example of both.  Valid argument with false premises: If grass is red, then it is cold. Grass is red Hence, it is cold The premises of the above argument are false, but the argument is valid. Valid argument with false conclusion The biggest Indiana city north of Indianapolis is the capital of Indiana Fort Wayne is the biggest Indiana city north of Indianapolis Hence, Fort Wayne is the capital of Indiana The conclusion of the above argument is...

Hypothetical Syllogism (sort of) 1.      If morality is not objective, then sin is not objective 2.      If sin is not objective, then sin is either determined by the individual, the culture, or does not does not exist 3.      If sin is determined by the individual, then any individual can determine that he/she is not a sinner 4.      If any individual can determine that he/she is not a sinner, then there is no need for Jesus 5.      Hence, if sin is determined by the individual, then there is no need for Jesus 6.      If sin is determined by the culture, then any culture can determine that there is no sin in that culture 7.      If any culture can determine that there is no sin in that culture, then there is no need for Jesus 8.      Hence, if sin is determined by the culture, then there is no need for Jesus 9. ...