Apologetics Made Simple

Equipping the Next Generation of Believers

Accounting for Logic-A Response to Alex Malpass

by Leave a Comment

 

Introduction

A while back, I debated Dr. Alex Malpass on the latter half of Bible Thumping Wingnut Show. In the debate, it was clear that Malpass had no understanding of Clark’s philosophy and he had admitted he never read Gordon Clark’s writings. Even after admitting that he never read Clark, Malpass wrote a commentary on the debate. 1 Even though he had not read Clark, he tried to talk about his philosophical system anyway. I responded to his commentary.  Academics are supposed to study a philosopher carefully before criticizing him, but I am guessing that Malpass doesn’t mind trying to take short cuts for the sake of coming off as an expert.

After some time had passed, Malpass wrote a piece that criticized Tim Shaughnessy’s article on accounting for logic (where Shaughnessy aligns his view with Dr. Gordon H. Clark). Even though Malpass’s piece does not address me directly, it does address my view of logic. Therefore, this blog post will be a response to Malpass’s blog post (or whatever he wants to call it).

Contrasting Clark and Van Til

Malpass:

For instance, here [His blog post, ‘The Problem with TAG’] I argue that there is no binary choice between Christianity and non-Christianity; there are different versions of Christianity, different monotheistic religions, different versions of theism, and different versions of atheism. 2

A quote from his cited blog post:

“This is the method [He is referring to Cornelius Van Til] of ‘internal critique’, where one assumes the interlocutor’s position to show that it leads to internal inconsistencies, as opposed to keeping one’s own assumptions fixed when analyzing the interlocutor’s position.

So two things need to be established:

  1. The Christian worldview can provide a non-self-contradictory account of human experience.
  2. The non-Christian worldview cannot provide a non-self-contradictory account of human experiences.

Talk of ‘the Christian worldview’ and ‘the non-Christian worldview’ is to be taken with a pinch of salt (although this will prove controversial later). Obviously, there are lots of different denominations of Christianity, including reformed Presbyterian, Lutheran, Catholic, Greek Orthodox, etc. Equally, there are many distinct non-Christian positions, including every denomination of every other religious worldview, plus every variation of atheist worldview, etc. If we take this plurality of worldviews into account, then the claim is that at least one Christian worldview can account for the intelligibility of human experience, and that none of the non-Christian worldviews can. This claim has not been demonstrate by presuppositionalists, and I will argue that we have reason to doubt that they can demonstrate this claim.”

Response:

Oy Vey! Where to begin? I’ll start by saying that Malpass has no idea what he is talking about. Van Til and Clark approach critiquing philosophical systems differently. Van Til argued from, as Dr. Greg Bahnsen would put it, ‘the impossibility of the contrary’ (although Van Til never formally articulated TAG in any of his writings or lectures because, as far has he was concerned, the Christian worldview must be true for syllogisms to work). In contrast, Clark tested other worldviews for logical consistency. Van Til didn’t believe it was possible for another worldview to be logically consistent, whereas Clark thought it might be possible, but also stated that he opined that worldviews that were based on false propositions would probably run into a problem at some point.

Clark never held that logical consistency demonstrates a claim. Therefore, the two points that Malpass says need to be established are not relevant to the Clarkian apologetic. Heck, Clark would argue that experience doesn’t demonstrate the truth of any proposition (If Malpass would actually take the time to read Clark, he’d be aware of that). It is obvious that Malpass isn’t familiar enough with Clark to be able to distinguish between those who use TAG and Clarkians.  If he doesn’t know the difference, he needs to read Clark before he criticizes him so that he can stop spreading misinformation. It looks like he still has not heeded my advice. If I were a student of his and were aware of him being so careless in criticizing other philosophies, I would be concerned about the quality of education that I would be receiving.

As for the definition of Christianity, Shaughnessy has told me that he defines it as the 1689 London Baptist Confession of Faith (Clark and I would define it as the Westminster Confession of Faith). ‘Christianity,’ like other words, can have multiple definitions. In the English language, it is not uncommon for a word to have at least four distinct definitions. Just because people define the word  ‘Christianity’ in different ways does not mean that Christians have a problem with the word when they defend the faith. The Christian can simply give the definition of Christianity that they are using. As long as the term is defined, there is no philosophical problem to be found with the term. Why would an atheist want to talk about what Lutherans believe if they are arguing with a Baptist? It is not relevant to the conversation at hand. If Shaughnessy and I have a discussion about our disagreement on how we should define Christianity, per both of our confessions of faith, we would have to go to the Bible to argue our cases. The same goes with any Christians that have disagreements (2 Timothy 3:16), but we are also taught to not focus on trivial matters that distract us from the Gospel (Titus 3:1-10). Fortunately, salvation does not require a perfect theology so those who hold to erroneous theology can still be saved as long as they believe Jesus Christ died for their sins and rose from the dead (which would result in turning away from their sin).

Now, what of Malpass’s assertion that the choice between the Christian and non christian worldview being non binary? In my case, I define Christianity as the Westminster Confession of Faith. Either you accept the confession or you don’t. In this case, the choice is clearly binary.

Alex Malpass:

“More specifically with regards to the broadly Clarkian idea of deriving logical principles from the Scriptures, I have argued here [he cites a blog post that addresses me] that this is incoherent. Derivation requires a logical framework, which is constituted in part by logical principles (or axioms); derivation is a logical notion, and thus presupposes logical principles.”

Response:

Malpass is correct to point out that deriving logical principles from scripture would involve the assumption of logical principles, but it is not problematic for Clark’s philosophy. It is one thing to assume a proposition, it is another to demonstrate it. Just as it is with mathematics, one must often possess a true proposition before they can demonstrate it. All truths must be possessed prior to being able to demonstrate them. Nevertheless, I have already responded to his accusation in an earlier blog post that Malpass has not yet bothered to address. He is only reasserting a line of argument that has already been debunked.

What is Logic?

Malpass:

“Shaughnessy’s view of logic seems to be entirely gained from the study of Clark, in that he is the only author cited (rather than, say, Aristotle or Frege) on the topic of what logic is. This is unfortunate, because it seems that  Shaughnessy is unaware of the controversy surrounding the topic.”

Response:

While it is important to be aware of “controversy,” controversy says nothing of whether or not Shaughnessy’s position on logic is true. Malpass might as well argue, “Shaughnessy’s view of the truth doesn’t take into account the controversy about truth.” The presence of a controversy doesn’t mean that it’s a problem for the position in question. If it were, no one could know anything (and it’s easy to see that notion is a self-defeating proposition).

Malpass:

So, we see him state that logic is “the correct process of reasoning which is based on universally fixed rules of thought”. This idea, that logic is about laws of thought, is a historically significant idea, coming to prominence in the 18th and 19th centuries, but it has never been a universal consensus among logicians and philosophers. These days it is not widely represented among practising logicians and philosophers at all (see this for a quick overview). The reason for this is that in the contemporary setting logic has a much broader extension, and can cover systems which deviate wildly from how we might realistically model thought (which is the preserve of logicians and computer scientists working in artificial intelligence).

Response:

If the presence of controversy surrounding logic were a problem for Shaughnessy’s position, why is Malpass referring to the Stanford Encyclopedia of Philosophy without question?  If the presence of controversy is a problem for Shaughnessy’s position, it is also a problem for everyone else’s position. It is very clear that Malpass is not being fair to Shaughnessy’s position.

Malpass:

Logic, thought of broadly as concerning valid inference for various types of argument forms, is not considered to be tied in any special manner to how we think. There may be a logic to how we think, but logic is not just how we think. Never-the-less, Shaughnessy makes no mention of this, and simply asserts that logic has this 18th century relation to cognition.

Response:

Malpass is confusing the definition of logic with the ontology of logic (in this case, the discussion of how logic relates to a person’s mind). The definition of logic that Shaughnessy provided says absolutely nothing about the human mind. His definition only references necessary inference. The definition given by Shaughnessy does not require that people always think according to the laws of logic. The truth of a proposition is not demonstrated by people’s adherence to it.

Now, if we take a look at the ontology of logic, the reason why these rules of thought are fixed is because these rules are the structure of God’s mind. Because God is omniscient, he knows all true propositions. Because God has revealed in the scriptures that the laws of logic are true, God has always known them to be true. Because God has always known them to be true, logic has always been true. Because logic has always been true, the rules of thought that are expressed in logic are universal and fixed. 

If one looks at Shaughnessy’s definition, necessary inference is a part of his definition. Shaughnessy is not claiming that people always think logically, nor does Gordon Clark. We have all heard the adage, “rules are meant to be broken.” Perhaps Malpass is working towards being Exhibit A.

Malpass:

His out-of-date description of logic becomes confounded with outright misunderstandings when he spells out what he considers to be the three laws of thought.

Response:

And here Malpass proceeds to ‘step in it’ on the basis of his careless representation of Shaughnessy.

Malpass:

It is utterly standard, when going down this non-modern view, to list the three laws of thought as: ‘the law of identity’, ‘the law of non-contradiction’ and ‘the law of excluded middle’. What is odd is the way these are cashed out by Shaughnessy. For instance, the law of non-contradiction is cashed out as “A is not non-A”, and the law of excluded middle is cashed out as “A is either B or non-B”. It seems to me that there is a failure of Shaughnessy to distinguish clearly between different aspects of vocabulary. There is a fundamental difference between logical vocabulary that refers to things directly (like ‘Alex’, ‘London’, ‘your favourite type of ice cream’, etc) and those which express facts (‘Alex is in London’, ‘vanilla is your favourite type of ice cream’, etc). The first are called ‘terms’, and the latter are called ‘propositions’. Propositions can be thought of as made up of terms standing in certain relations to one another. Crucially, propositions are given truth-values, true or false; terms are not.

Response:

After saying that Shaughnessy’s definition of logic (a term, if you will) is outdated and false, Malpass goes on to say that terms (and by necessary extension, their definitions) cannot be true or false. If this is the case (and it is), why whine about Shaughnessy’s use of the word ‘logic?’

Furthermore, Shaughnessy does distinguish the the terms, ‘the law of identity’, ‘the law of non-contradiction,’ and ‘the law of excluded middle’ from propositions when he gives references a proposition for each term. One has to wonder if Malpass is even taking adequate time to assess Shaughnessy’s article.

Malpass:

In Shaughnessy’s expression of the law of non-contradiction, we have a letter ‘A’, which seems to be a term, as it is something we are predicating something to, but then the predicate we are ascribing to it is that it is “not non-A”. The problem is that we have a negation fixing to a term, ‘non-A’. As I have pointed out before, negation is a propositional operator, and its function is to switch the truth-value of the proposition is prefixes from true to false (or vice versa). If we prefix it to a referring term, like ‘A’, then (because terms don’t have truth values), the resultant operation is undefined.

Response:

I can definitively confirm that symbols such as ‘A’ in Shaughnessy’s description of logic represent propositions and not terms. Shaughnessy’s use of negation should have made that obvious to any person who is familiar with logic.

Malpass:

It is bizarre to say that either ‘A is B or non-B’. There is no predicate ‘non-B’; rather, either B applies or it doesn’t.

Me:

‘A is B or non-B’ refers to the law of excluded middle. Proposition B is a potential propositional statement about A. ‘Non-B’ represents the negation of proposition B. These are two definitive propositions in which there is no middle ground. Although the phraseology is not conventional (and who says it has to be as long as Shaughnessy defined his terms?), the propositional content is accurate. There is no problem with Shaughnessy’s description of the laws of logic.

Malpass:

So we have an out-of-date view of logic, coupled with a technically incorrect presentation of the principles under discussion. It’s not a great start to an article about the nature of logic.

Me:

So we have a logic professor that struggles to understand logical expressions, misrepresents his opponents, and can’t distinguish confuses a definition of a word and ontological issues that are relative to the word.  This is probably why no Clarkian has bothered to respond to Malpass up until now. He has made so many errors that the process of correction is tedious to the point of it being burdensome (I was hoping someone else would do it so I wouldn’t have to).

Logic in the Bible

Malpass:

Perhaps Shaughnessy’s misrepresentation of the basic laws of thought is more understandable when we see where he is going with all of this. The ultimate point he will be driving at is that these laws are found in the Bible. Various snippets of the Bible are then presented as evidence of this, but because they don’t really fit that well with the laws when expressed properly, he has written them in such a way that the claim that they are found in the Bible becomes (slightly) easier to swallow.

Response:

Logic is a propositional enterprise. As long as the propositions are correct, and the symbols within the proposition are defined, there is no issue with phraseology.

Malpass:

In the book of Timothy, it is said that God cannot contradict himself. I say that this is completely irrelevant to the principle of non-contradiction. There is a difference between saying things, and things being true (or false). The law of non-contradiction is about the latter, not the former. It isn’t a rule which says ‘thou shalt not contradict thy self’. It says that there is no proposition for which both it and its negation are true. It doesn’t proscribe what you can or cannot say at all.

Shaughnessy:

“The law of non-contradiction (A is not non–A) is an expression of the eternal character and nature of God, “for he cannot deny [contradict] himself” (2 Tim. 2:13). The law of identity (A is A) is expressed in God’s name, “I AM WHO I AM” (Exodus 3:14), and the law of the excluded middle (A is either B or non-B) is expressed in Christ’s own words, “He who is not with Me is against Me” (Luke 11:23).“

Malpass:

Let’s take these one at a time. It is hard to take them seriously, but I will try.

In the book of Timothy, it is said that God cannot contradict himself. I say that this is completely irrelevant to the principle of non-contradiction. There is a difference between saying things, and things being true (or false). The law of non-contradiction is about the latter, not the former. It isn’t a rule which says ‘thou shalt not contradict thy self’. It says that there is no proposition for which both it and its negation are true. It doesn’t proscribe what you can or cannot say at all.

Response:

Malpass claims that God not being able to contradict himself (as Shaughnessy pointed out using 2 Timothy 2:13) is not relevant to the principle of the law of contradiction. Pish posh. The law of contradiction cannot be true unless there are true and false propositions. Is the statement, “God cannot deny himself” not a statement that can be true or false? It’s a proposition so it necessarily must have a truth value.

What about Titus 1:2? “….In hope of eternal life, which God, who never lies, promised before the ages began.” This does not mean that God lies, it does not mean that God always lies, it means that God doesn’t lie. Therefore, anything that God reveals, when scripture concerning God’s nature is taken into consideration, is necessarily true. Malpass claims that 2 Timothy 2:13 isn’t a claim about a proposition being true, but when the entirety of what scripture says concerning God’s nature is taken into consideration, it is clear that 2 Timothy 2:13 is a declaration of truth.

Malpass:

For example, I can contradict myself, and sometimes do. Does this mean I broke the law of non-contradiction when I did so? No, of course not. Imagine I say ‘It is sunny now, at 14:07’, and then a few minutes later, ‘It was not sunny then, at 14:07’. The two sentences I uttered were expressing (from different times) that it was and was not sunny at 14:07. Obviously, it would be a contradiction if both of these were true, as p and not-p would both be true (exactly what the law of non-contradiction forbids). But were they both true? That would mean that it was both sunny and not sunny at the same time. Conventionally thinking, this is impossible. Therefore, while I contradicted myself, I didn’t break the law of non-contradiction. I expressed a true proposition, and then when I uttered the negation of that proposition what I said was false (or vice versa). Contradicting yourself isn’t a case of breaking the law of non-contradiction.

Response:

If Malpass had claimed that it was both sunny and not sunny at the same time, that would be a contradiction. It is possible for it to be both sunny and cloudy at 14:07 because time  passes between 14:07 and 14:08.  Even the two propositions in question make it clear that it was initially sunny and then at a later  time it was not sunny. Furthermore, logic isn’t temporal, but the content of propositions in a syllogism or an expression can express temporarality. In the case of Malpass’s example, the propositions he chose in his example clearly express temporality.

A contradiction, as Shaughnessy is currently using the term, is the expression of the truth of two propositions that are mutually exclusive. When Malpass criticizes Shaughnessy, he is taking a lot of liberty with the definition of ‘contradiction.’ This makes Malpass’s criticism of Shaughnessy beside the point. I would like to know what definition of ‘contradiction’ Malpass is using because the definition he is using is certainly foreign to any logic textbook that I’ve read.

Malpass:

Back to the Biblical example, God cannot contradict himself. So what? The law of non-contradiction is true even though people can contradict themselves. An example of a being, even an infinite one, who cannot contradict themselves, is not an example of the law of non-contradiction. To think that it is, is to mix up the idea of saying two contradictory things with two contradictory propositions both being true.

Response:

In the case of 2 Timothy 2:13, ‘ἀρνέομαι’ is the word that is used for ‘deny.’ This word means to contradict. This is where Shaughnessy got the law of contradiction from. Scripture’s statement concerning God never contradicting himself is a clear affirmation of the law of contradiction. Again, Malpass doesn’t give us his definition of ‘contradiction,’ but it is clearly not the one that Shaughnessy is using. This is not surprising considering I had to correct Malpass on the poor definition he gave for the word ‘logic’ in my debate with him. Any contradiction is a violation of the law of contradiction, and any statement that is not contradictory is in adherence with the law of contradiction. In this case, since God, who reveals himself to be consistent in multiple passages such as 2 Timothy 2:13, is the determiner of truth, the truth will never be contradictory. This means that the law of contradiction is universal according to scripture. While it is true that people contradict themselves (Malpass is a great example of this phenomenon), God does not contradict himself, and that is why the law of contradiction is universal despite people contradicting themselves. After all, the truth of a prescriptive proposition is not predicated on a person’s adherence to it.

Malpass:

Shaughnessy does manage to state the law of identity correctly, which is that (for all referring terms) A = A. Everything is identical to itself. According to the example given, the law of identity is expressed in “I am who I am”, which is the answer God gives to Moses in the book of Exodus. It has always baffled me as to why this has been seen as a profound thing for God to say here. God tells Moses to go to the Pharaoh and bring the Israelites out of Egypt. Moses basically says, ‘who am I to do that?’ God says that he will be with Moses, but Moses wants a bit more reassurance for some reason:

“Moses said to God, “Suppose I go to the Israelites and say to them, ‘The God of your fathers has sent me to you,’ and they ask me, ‘What is his name?’ Then what shall I tell them?”

God said to Moses, “I am who I am. This is what you are to say to the Israelites: ‘I am has sent me to you.’” (Exodus, 3: 13-14)”

One of my favourite comedy series ‘Knowing Me, Knowing You’, staring Steve Coogan, features a pathetic TV chat show host, called Alan Partridge. In episode 2, he is interviewing an agony aunt called Dannielle, played by Minnie Driver, who is listing the things she likes in men:

Dannielle: Power is attractive. Sensitivity. Sense of humour. I like a man who knows who he is.

Alan: I’m Alan Partridge.

If you think that the law of identity is expressed by Exodus 3:14, then you should also hold that it is expressed in this little bit of Alan Partridge script.

I’m just going to leave that there.

Response:

In epistemology, the way to escape skepticism (in this case, I define skepticism as the view that no proposition can be known to be true), is being able to discern truth from falsehood. In Clark’s philosophy and in reformed tradition, scripture is our guide in discerning true propositions from false ones. This is why the affirmation of the law of identity that is expressed in Exodus 3:14 is significant.

In the case of the comedy, Clarkians don’t view ‘Knowing Me and Knowing You’ as a show that could escape skepticism if it were somehow expressed in a systematic fashion. Therefore, Clarkians do not have to hold that a comedy demonstrates the law of contradiction. I can’t believe I just had to explain this.

Malpass:

In the last example, Jesus saying “He who is not with Me is against Me” is an example of someone expressing something stronger than the law of excluded middle. The logical law of excluded middle says that for every proposition, p, either it or its negation is true. There are two propositions being considered in the saying above, put together in the form of a disjunction. The two propositions are:

‘x is with Jesus’

‘x is against Jesus’

The combined disjunction is universal, in that it applies to everyone:

For all x: either x is with Jesus or x is against Jesus.

However, this isn’t a logical truth. There is no logical reason to stop someone being neither with nor against Jesus.

If Jesus had said ‘Either you are with me or not with me’, then he would have said something which would have been logically true (because of the law of excluded middle).

Therefore, when Jesus says that everyone is either with him or against him, something which goes beyond the law of excluded middle, and it is not a logical truth. Why this has been picked to be an instance of this law can only be put down to either the author not understanding what the law actually states, or being so determined to find something that fits the pattern that they wilfully ignore the fact that it doesn’t.

Response:

The former independent clause in Matthew 12:30 reads, “Whoever is not with me is against me,” is an affirmation of the law of the excluded middle because “if X is not with me, X is against me affirms,” that there is no middle ground in being with or against Jesus Christ. In order for the proposition in this verse to be true, the law of excluded middle must also be true. Since the truth of the proposition in question is predicated on this law, and because the propositions in scripture are the thoughts of God, it is only reasonable to conclude that scripture affirms this law, for if it is not true, Jesus would be a liar, and as we know, God cannot lie (Titus 1:2, Numbers 23:19).

Truthfully, I have never been a fan of the law of the excluded middle nor the law of identity. As far as I am concerned, they both can be reduced to the law of contradiction. Given that the law of contradiction is already a law of logic, the other two laws seem unnecessary to me. Nevertheless, the universality of this law of identity and the law of the excluded are affirmed because the universality of the law of contradiction is affirmed in verses such as 2 Timothy 2:13. The only way that the law of the excluded middle and the law of identity could not be universal is if the law of contradiction is not universal. The logical forms do not have to be explicitly stated in the Bible, we must only see an affirmation of logical forms in the Bible in order to confirm that they are valid. This is because we already have terms and definitions that we use to reference the laws of logic. As long as we are aware of what we are, we can recognize an inference or law of logic when a proposition in scripture is predicated on the truth of the inference or law in question.

Malpass:

Shaughnessy then presents the standard presuppositional line, the one we all knew was coming, where they brag about how great their ‘account’ of logic is, and how rubbish ‘the other account’ is.

“The unbeliever cannot account for logic in his own worldview and therefore cannot account for his ability to think rationally. The challenge has been made many times to unbelievers to account for logic in their own worldview and it has always fallen short or gone unanswered. Never has an adequate response been given. In formal debates, the challenge is often ignored by the unbeliever, yet the challenge demands an answer because debates presuppose logic. The unbeliever is required to use logic in order to make his argument against Christianity consistent and intelligible, but only the Christian worldview can account for logic. He is therefore required to rob the Christian worldview in order to make his argument against Christianity intelligible.”

Ok, well we’ve all seen this over and over again. So I am going to meet the challenge head on, and provide a few different ‘accounts’ of logic, which could be ‘epistemological foundations’ for it.

First of all, what do we mean by and ‘epistemological foundation’ for something? Well, I take it to mean something in virtue of which we can come to know something. So, an epistemological foundation for x could be thought of an an answer to the question, ‘how is it that we are able to know about x?’

Given that, our question is: ‘How is it that we are able to know about logic (and in particular those logical laws)?’. In order to play the game right, I shall not appeal to God in any way, I will just go along with the idea that logical laws are things that have some kind of ontology capable of allowing reference to them, and I will just pretend that the three principles cited by Shaughnessy (identity, non-contradiction and excluded middle) really are ‘logical laws’, even though it is a clumsy and out-dated way to talk about logic. I will play the game anyway, just to be a good sport.

Response:

Before Malpass even gets started, I am already seeing problems. What does it mean to Malpass to “know” something? He has given no definition of knowledge, and I don’t know what the ‘something’ that allows us to know ‘something’ is. I guess we will soon find out.

Malpass:

Here is the first way of answering that question: we are able to know about logical laws because they are self-evident truths. This just means that to think about them is to know that they are true. They don’t need anything else to support my knowledge of them, because they are self-evident. This is a really simple answer, and there isn’t much more to be said about it.

Response:

This is not a good account for the laws of logic. As Malpass pointed out earlier in his blog post, these laws are frequently violated, and since a person thinking about a proposition does not make the proposition that is being thought about true, just thinking about a law of logic doesn’t make it true. The way to avoid skepticism is to distinguish true propositions from false ones.

If two people have a disagreement on a subject matter, this means that there are propositions that both of them believe that are in contradiction with one another. Does this make both of the propositions true despite the truth of the law of contradiction? If both propositions are true, the law of contradiction is false. If the law of contradiction is true, his account for the laws of logic fails.

Malpass:

Here is my second proposal: we are able to know about logical laws because they are synthetic a priori truths. In the Critique of Pure Reason, Immanuel Kant summarises his views on this type of knowledge as follows:

“…if we remove our own subject or even only the subjective constitution of the senses in general, then all constitution, all relations of objects in space and time, indeed space and time themselves would disappear, and as appearances they cannot exist in themselves, but only in us. What may be the case with objects in themselves and abstracted from all this receptivity of our sensibility remains entirely unknown to us. We are acquainted with nothing except our way of perceiving them, which is peculiar to us, and which therefore does not necessarily pertain to every being, though to be sure it pertains to every human being.”

Synthetic a priori knowledge has the property that it is integral to how we see the world. It is subjective, in the sense that Kant explains above (that is, if we were to remove the subject, then it would also disappear), but it is also universal, in the sense that it applies to “every human being”.

Response:

I concur that the laws of logic are possessed by man a priori (man is made in the image of God and God’s mind isn’t blank); however, despite this correct statement, Malpass’s account for logic falls short. The definition of synthetic and the identification of synthetic truths require that the person believe propositions about the world. Given the laws of logic and the rules of inference, how can a person get from a priori propositions such as the laws of logic and validly draw an inference via a non-propositional source such as sensation so that he may draw a conclusion (which would be a proposition)? There is no such rule of inference that allows such an inference to be valid. Neither Malpass nor Kant can ignore logic while trying to account for it. He attempts to show, as Kant attempted to do, that a world without the laws of logic would be absurd, and therefore, they must be true, but the argument assumes, without basis, that non-propositional sources such as experience and sensation can give knowledge. Furthermore, it assumes that a propositional conclusion may be validly drawn from a non-proposition which stands at odds with logic. Last but not least, at best, Kant’s philosophy, even if it could get that far, only gives us a perception of the world. For all Malpass and Kant knows, the world could be very different from how they perceive it. If Malpass thinks none of this is problematic, it would be interesting to learn his definitions for ‘knowledge’ and ‘truth.’

He then goes on to attack Van Tillian presuppositionalism’s hypocrisy (which has nothing to do with Clarkian presuppositionalism). Since I am a Clarkian, I will let Van Tillians deal with him on that matter. Since he thinks the critique is relevant, it is obvious that he doesn’t understand the difference between Clarkian and Van Tilian apologetics. It’s hard to understand why Malpass would keep interacting with Clark’s ideas without knowing anything about them.

Malpass then gives a 3rd attempt to account for logic, but he qualifies it with saying that he doesn’t agree with that particular account (then why bring it up?).  Therefore, I will not thoroughly address it. I will say that he laid out the following argument:

“1. We are justified to believe in all the entities that are indispensable to our best scientific theories.
2.  Laws of logic are indispensable to our best scientific theories.
3. Therefore, we are justified to believe in the laws of logic.”

He claims that this argument can be used because Shaughnessy would agree with premise 2. No Clarkian would agree that premise 2 gives any justification to the laws of logic because scientific theories do not demonstrate the truth of any proposition. No Clarkian believes that science is a truth-finding method. This goes to show, yet again, that Malpass hasn’t read Clark, and by consequence, he doesn’t understand Clarkian presuppositionalism.

As I told Malpass in my debate with him, he needs to read Clark before attempting to criticize Clarkian presuppositionalism. This is about the 3rd time I have said it. I am guessing that he is too lazy to do his due diligence prior to criticizing another philosophy.

Conclusion

Malpass:

So, above are three distinct views about the epistemological foundations of logic. None of them required God, or Jesus, or Reformed theology at all. No doubt, they will continue, over at BibleThumpingWingnut.com, to claim that “The challenge has been made many times to unbelievers to account for logic in their own worldview and it has always fallen short or gone unanswered. Never has an adequate response been given“. In reality though, for those of us who have spent a long time doing philosophy seriously, these claims are easily countered. I’m not saying I have all the answers; I’m saying that they don’t. I don’t know what the ‘right answer’ is about the nature of logic, or how epistemology and logic fit together. It is an incredibly complicated area. As with philosophy, it may be something we will ultimately never answer. It may be that for some reason the question itself doesn’t make sense, but that this realisation doesn’t come for many generations yet. Maybe the answer was given in some obscure scroll, now long forgotten by history.

Response:

Malpass is saying that although he gave three accounts for logic, he doesn’t know that any one of them are successful. When Shaugnessy stated, “The challenge has been made many times to unbelievers to account for logic in their own worldview and it has always fallen short or gone unanswered. Never has an adequate response been given,“ he was referring to atheists not being able to account for logic. Malpass, by admitting ignorance concerning the issue, has just conceded that the very quote he is disputing is correct. I would be surprised, but we are talking about someone who attempted to account for logic by contradicting its rules. 

Footnotes:

1. To see his article, ‘Thoughts on Jason Petersen’s ‘Argument,’ see: https://useofreason.wordpress.com/2016/01/14/thoughts-on-jason-petersens-argument/

2. To see his article, The Problem with TAG, see: https://useofreason.wordpress.com/2015/11/07/the-problem-with-tag/

 

Notes:

    A Response to Dr. Alex Malpass on the Axiom of Revelation and 1 John 2

    by Leave a Comment

    Introduction

    Recently, I debated Dr. Alex Malpass on the Bible Thumping Wingnut show. Overall, I feel that the debate went very well for me, but I do not think that it went well for Dr. Malpass. To be fair, Dr. Malpass did have quite a few drinks prior to debating me, and the debate itself was not planned. Tim Hurd (the host of the show) asked me to argue for a contention that is very specific. The contention was, if Christianity is true, logic (the science of necessary inference) can be accounted for. The reason why I am writing this blog post is because a friend brought a blog post, Thoughts on Jason Petersen’s ‘Argument’,  to my attention. 1 This blog post will be commenting on what was said in his blog post.

    Dr. Malpass:

    At the end of my time on the BibleThumpingWingnut, after a few hours (and about 4 whiskeys, at about 3AM), Tim introduced a new person into the discussion to ‘engage’ with me for a bit. This was Jason Petersen, who advocates a version of Clarkian presuppositionalism.

    My response:

    In the debate, I had strong words for Dr. Malpass when he attempted to articulate the Clarkian apologetic. His articulation was not at all correct, and when I asked him if he had read Dr. Gordon Clark’s works, he said that he hadn’t. I rebuked him for being so careless in his criticisms. How can one criticize someone whom he has not read? It seems that either Dr. Malpass is a fast reader, or he has still not learned his lesson. What does he mean by a ‘version’ of Clarkian presuppositionalism? What other version is there? There is only one version.

    Dr. Malpass:

    Jason began by laying out an axiomatic demonstration of how you can go from the principle that the bible is the word of god to the conclusion that you can account for the laws of logic.

    My response:

    For the sake of context, I will give an account of what happened. I was asked by Tim to argue that if Christianity is true, one can give an account for logic. In my argument, logic is defined as the science of necessary inference. 2 I started with the axiom, “The Bible Alone is the Word of God written,” and argued that from this axiom, the Christian can give an account for logic. I began by pointing to 1 John 2:21, “I write to you, not because you do not know the truth, but because you know it, and because no lie is of the truth.” The proposition, “no lie is of the truth” is an affirmation of the law of contradiction. At that point, Dr. Malpass kept the conversation from going any further by invoking a definition of ‘lie’ that is different from the definition used in 1 John 2:21. Because we did not agree on the definition of ‘lie’ that was being utilized in 1 John 2:21, the discussion did not move forward.

    Dr. Malpass:

    After he explained his ‘axiom of revelation’, which is that the bible is true, he moved to a passage which contains the phrase ‘no lie is of the truth’. We got a bit stuck on this, as I objected that lies can be inadvertently true, as for example when someone intends to deceive, says something they believe is false, but which happens to be correct. I think that this would still count as a lie, but Jason disagreed, urging that we should use the biblical definition instead. I was tired and a bit drunk, so I may have missed what was going on at the time. I thought I should get a more sober reflection down here instead.

    My response:

    And here is the hang up. Dr. Malpass attempted to invoke a different definition of ‘lie’ than what was used in 1 John 2:21. He did this by inserting a fallibilist constraint on the lie that is referred to in 1 John 2 whereas in this particular reference to ‘lie,’ which is made by the apostle John, there is clearly no room for fallibility on the part of the person (antichrist) that is telling the lie. If the definition of ‘lie’ is changed and then used in 1 John 2:21, the proposition in 1 John 2:21 now has a different meaning. It is not proper to represent something, be it a person, proposition, or philosophical system by changing the definitions of the terms that the opposing position is using. Doing so would result in a misrepresentation, in this case, of 1 John 2:21.

    In order to show what was meant by ‘lie.’ I briefly, despite the protesting of Dr. Malpass, gave an exposition of 1 John 2. I will reiterate some of the points made one more time. Starting at verse 18 of 1 John 2, the apostle John is warning Christians about the antichrists. 3 These antichrists are liars. However, the Christians have knowledge. They know the Gospel, and they know what Jesus taught. And because they know these things, they know that none of the antichrist’s lies are true. The Greek word for ‘truth’ that is used in v 21 is ‘alétheia.’ This particular word refers to the divine. Simply put, the word is used for an infallible truth. The Greek word that is used for ‘lie’ is ‘pseudos.’ The literal translation of this word is ‘falsehood’, but it can also be translated as ‘lie.’ When this term is invoked, it refers to either a falsehood or a spoken falsehood (lie). Now that the terms are defined, we will finish the point that is being made. If the truth referred to in 1 John 2:21, is an infallible truth, then the lie that is told must be false.

    Now, we should contrast this with his objection. He objects that someone could think they are lying but inadvertently tell the truth. Clearly, this is not how the Bible describes the antichrists. These antichrists are deceivers. They are antagonistic to Christianity (Matthew 7:15). Therefore, the definition of ‘lie’ that Dr. Malpass invokes is not the same as definition that is invoked in 1 John 2:21. If Dr. Malpass wishes to offer a criticism of the Bible, he must use the definitions that are invoked in the passage in question. If I were teaching and I had a student that attempted to critique a position by changing the definition of words in a way that changes the meaning of what the opposition is articulating, I’d give him an ‘F’ without a second thought. Surely, if I were debating someone about evolution, and I invoked a different definition of evolution in order to more easily critique evolution, evolution supporters would jump all over it.

    I will also say in passing that Dr. Malpass misrepresented my objection. I did not argue that people cannot intend to lie whilst being unaware that they are telling the truth. What I argued is that the word ‘lie’ is not used in this sense in 1 John 2:21. I urged Dr. Malpass to use the Bible’s definition because Dr. Malpass asserted that the statement, ‘no lie of the truth’ that is found in 1 John 2:21 is false. If Dr. Malpass is asserting that a proposition in the Bible is false, he must represent that proposition accurately or else he is arguing against another proposition all together (via a strawman fallacy). Because Dr. Malpass is critiquing the Bible, he must use its definitions when referencing the propositions in question. This is the proper way to interact with opposing positions, and Dr. Malpass, as someone who has a Ph.D in philosophy, should be well aware of this. How else could he had obtained his Ph.D in philosophy without representing other philosophers according to the way they define their own terms? Unless, of course, the instructors were incompetent, but from what I understand, the University of Bristol is in good repute.  I hope that this mistake was simply a result of Dr. Malpass drinking too much whiskey.

    Dr. Malpass:

    As I understand what was going on, Jason was starting with his axiom, and then deriving things from that, part of which included the law of non-contradiction. His point was (I believe), that ‘no lies are of the truth’ is an instance of someone stating the law of non-contradiction, i.e. ~(p & ~p). I think this is an exegetical stretch, and even if interpreted as generously as possible it gives a different law, the semantic principle of bivalence. So I say that ‘no lies are of the truth’ means ‘all lies are false’, which I said was false, due to my understanding of what lying means.

    My response:

    Dr. Malpass, once again, inserts a fallibist constraint on the word ‘lie’ that is invoked in 1 John 2:21. The proper understanding of its usage has already been shown, but Dr. Malpass has made an additional error that warrants attention. Dr. Malpass erroneously, and without warrant, assumes that just because he understands what ‘lying’ means in a certain way, that the apostle John, who lived thousands of years before him, would have understood it the same way when he penned 1 John 2. As anyone who is familiar with the English language is aware, the same word can have multiple definitions and can also be used in a different sense. In fact, it is not uncommon for a word in the English language to have four definitions. Certainly, I would not deny that someone could tell what they think is a lie whilst being unaware that what they are saying is true, but for reasons already explained, there is no room given for such a circumstance in 1 John 2.  Dr. Malpass has interpreted the statement in 1 John 2:21 as ‘all lies are false’ because he is stuck in his own definition of the term ‘lie’ that is in question. But if one recognizes that the word ‘lie’ (and looks at the Greek meaning of the word that is used in 1 John 2) that is invoked in 1 John 2, it is in reference to a falsehood that stands in opposition to the infallible, universal, and eternal truth of the Gospel, the meaning of the passage is quite clear.  These lies that are told are falsehoods (as shown from the Greek), and none of these falsehoods are true. Therefore, we have, from 1 John 2:21, a distinction between what is false and what is true. From this passage, we also recognize that if there is a distinction between truth and falsehood, ‘truth’ and ‘falsehood’ cannot be two terms that are synonymous in meaning, for if they were, what point would there be in making a distinction between these two terms? If the meaning of the terms were synonymous, there could be no distinction. Therefore, with this distinction between ‘truth’ and ‘falsehood’, we have, from the scriptures, an affirmation of the law of contradiction.

    Dr. Malpass:

    But let’s assume that the intentional aspect of lying is not important, and as such lying just means saying a falsehood. This makes the sentence ‘no lies are of the truth’ analytically true (i.e. true by definition). Fair enough. It just means ‘no falsehood is true’. In other words, it means that if something is false, it is not also true. The principle of bivalence says that every proposition takes exactly one truth value: true or false; i.e. that if a sentence is true, it is not false, and vice versa. For some reason, Jason thinks that the sentence actually should be read as meaning ‘it is not the case that both p and not-p’; i.e. it is not the case that p and it is not-p. Notice that this doesn’t use the word truth at all. The difference may seem minor, but it allows that there can be logics where some proposition is neither true nor false (so no bivalence), but where it and its negation are still incompatible (so keeping non-contradiction), etc.

    My response:

    It is not a ‘sentence.’ ‘No lie is of the truth’ is a part the singular sentence that is found in verse 21. Dr. Malpass has either not looked at the sentence in verse 21 carefully enough or he is not careful enough about his wording, or perhaps I am being too picky.  My point was that the passage makes a distinction between a falsehood and the truth. Two mutually opposing propositions cannot be true in the same time and in the same sense. This is the law of contradiction. Just the same, the example given, “…that both P and not-P,” Dr. Malpass contends, does not even contain the word truth. Indeed it doesn’t, but Dr. Malpass confuses the form of the law of contradiction with its application concerning propositions external to itself. The definition of the law of contradiction is a proposition that is stated symbolically. It is simply, ‘P’and ‘not P’ cannot be true in the same time and/or sense. ‘P’ and ‘Not P’ are blanks to be filled when the law of contradiction is applied to propositions external to itself. Clearly, 1 John 2:21 says, “I write to you, not because you do not know the truth, but because you know it, and because no lie [not-p] is of the truth [p].” In other words, the lie (not p) is not the truth (p). Therefore, it is indeed an affirmation of the law of contradiction because the form of the law of contradiction is utilized in the proposition that is communicated.

    Dr. Malpass:

    Anyway, we can forgive the fact that a) the sentence is false (because I am right about what lying means), b) the sentence at best means something similar to the principle of bivalence, and c) it doesn’t mean the same as the principle of non-contradiction. We can forgive all of those and just assume that he was right. So let’s just say he starts from his revelational axiom, and then ‘derives’ the principle of non-contradiction. That seemed to be what he wanted to do. I say that this is horribly flawed anyway, despite the above.

    Response:

    In regards to the principle of bivalence, I have already demonstrated the law of contradiction from 1 John 2:21. 4 This means that the notion of the possibility of the law not being validated is of no concern. The law of contradiction can be found throughout scripture, even Genesis 1:1. If there is any necessary distinction between a true and false proposition (as would have to be the case for the propositions of scripture to be true), there is an account for the law of contradiction.  I chose 1 John 2:21 because it is among the most obvious of examples. In order for truth or knowledge of it to be possible, the law of contradiction must hold. The Westminster Confession of Faith states,  “The whole counsel of God concerning all things necessary for His own glory, man’s salvation, faith and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture: unto which nothing at any time is to be added, whether by new revelations of the Spirit, or traditions of men.” 5

    Dr. Malpass:

    So he has an axiom: everything in the bible is true (he actually says ‘the bible alone is the word of God written’). This basically just means that every proposition in the bible is true. So think of the bible as a set of propositions, B = {a, b, c, …} and that every member of the set is true. Then he says that he can go to one of those propositions, which is the law of non-contradiction (although he repeatedly dropped the ‘non’ for some reason).

    Therefore, the law of non-contradiction is true. In this way he derives it from his basic axiom.

    So, assuming a = the principle of non-contradiction, the argument so far is:

    Premise 1) a & b & c & … (i.e. all the elements of B)

    Therefore, a

    However, the inference from B to a (from all the things in the bible, to the one particular thing in the bible), relies on the inference rule called ‘conjunction elimination’; from p & q one can infer p:

    Premise 1) p & q

    Therefore, p

    Therefore, Jason’s ‘axiom’ needs to be supplemented with, at least, the inference rules of classical logic, if he is to move off his axiomatic starting point to derive anything (even if it is contained as a conjunct in his conjunction). He doesn’t mention inference rules, but he must be assuming them or else he would be stuck with his axiom. So let’s be nice and give them to him. But that means he is assuming classical logic. And that means he is assuming the law of non-contradiction. So he doesn’t need to ‘derive’ the law of non-contradiction, as he would in fact be assuming it at the outset.

    Response:

    The law of contradiction can be referred to as either the law of contradiction or the law of non-contradiction. 6 I do not say ‘non-contradiction’ because I find the prefix ‘non’ to be superfluous when in reference to the law of contradiction because it adds nothing to the term in regard to its meaning.

    That aside, how is it that Christians account for logical forms? Simply, if the logical forms are found in scripture, they are valid.  There are a few examples of this. Dr. Clark lists a few examples:

    “On this basis-that is, on the basis that Scripture is the mind of God-the relation to logic can easily be made clear. As might be expected, if God has spoken, he has spoken logically. The Scripture therefore should and does exhibit logical organization. For example, Romans 4:2 is an enthymematic hypothetical destructive syllogism. Romans 5:13 is a hypothetical constructive syllogism. 1 Corinthians 15:15-18 is a sorites. Obviously, examples of standard logical forms such as these could be listed at great length.” 7

    Frankly, the list of inferences that are made in scripture is quite comprehensive. In the same way, Christians can also account for mathematics. 8 If a logical form is found in the Bible, the Christian may consider it a valid inference, for it is God that is the source of logic (John 1:1). Because of this, we can account for the inferences made from the proposition, “The Bible Alone is the Word of God.” This is how the inference in question, conjunction elimination, is accounted for.

    In order to show how easy it is to account for conjunction elimination, I will use the very passage in which Dr. Malpass and I argued about. In 1 John 2, verses 13 and 14 are propositions that we can use to account for conjunction elimination. In verse 13, though several proposition are stated, one in particular warrants our attention, “I am writing to you, young men, because you have overcome the evil one.” In verse 14, we have a string of propositions that are connected by the conjunction, ‘and,’ “I write to you, young men, because you are strong,  and the word of God abides in you, and you have overcome the evil one.” In this example, we have the same proposition in two different verses. First, in verse 13, and second, in verse 14. Verse 14 is connected to other propositions via a conjunction, whereas verse 13, though preceded by a subordinating conjunction, is a proposition that stands alone because it is a stated as a singular reason for why the apostle John is writing to these young men. Therefore, we have an example of conjunction elimination in 1 John 2:13-14. Examples of this inference in scripture are bountiful. So much, in fact, that we found an example in the very passage that is in dispute.

    Dr. Malpas also objects by saying that the classical rules of inference must be assumed prior to the axiom of revelation, but let us not, as Dr. Malpass has done, confuse ‘assuming’ the rules of inference with ‘accounting for them.’ Certainly, not being able to account for an inference does not stop a person from utilizing a rule of inference. Though unbelievers do not accept the truth of the Bible, they can still use the rules of inference by simply assuming the rules of inference. This, however, does not amount to accounting for the rules of inference. Accounting for the rules of inference would involve validating the proper rules of inference. And the Bible is God breathed, and therefore, a product of God’s mind (2 Timothy 3:16). If the Bible is a product of God’s mind, then how can anyone deny that we have the wonderful opportunity to get a glimpse of how God thinks? If, when imparting the truth to His children, God utilizes a rule of inference, that inference may be considered valid because it it were not valid, the premises would not guarantee the truth of the conclusion that God reveals to us. And if the premises of the syllogism does not guarantee the conclusion, then the syllogism would be a lie, but God is not a liar (Titus 1:2). According to scripture, all things that God says is true must be true.

    But if the proper inferences from an axiom is so important. One might ask, how is it that Dr. Malpass can account for these inferences? It has already been shown that Christianity is able to do so. 9 If one cannot account for inferences, as Dr. Malpass argues, one cannot infer, but he gives us nothing in regards to his own epistemology. And if one attempts to start with a logical form, there is no content to fill the form. Christianity does not succumb to the critiques given by Dr. Malpass, but one cannot help but wonder if he is able to answer his own objection in a way that would allow him to avoid epistemological skepticism.

    In regards to whether Christians should start with the Bible or the law of contradiction, Dr. Clark also had something to say about this:

    “Even in the single words themselves, as is most clearly seen in the cases of nouns and verbs, logic is embedded. If Scripture says, David was King of Israel, it does not mean that David was President of Babylon; and surely it does not mean that Churchill was Prime Minister of China. That is to say, the words David, King, and Israel have definite meanings. The old libel that Scripture is a wax nose and that interpretation is infinitely elastic is clearly wrong. If there were no limits to interpretation, we might interpret the libel itself as an acceptance of verbal and plenary inspiration. But since the libel cannot be so interpreted, neither can the Virgin Birth be interpreted as a myth nor the Resurrection as a symbol of spring. No doubt there are some things hard to be understood which the unlearned wrest to their own destruction, but the difficulties are no greater than those found in Aristotle or Plotinus, and against these philosophers no such libel is ever directed. Furthermore, only some things are hard. For the rest, Protestants have insisted on the perspicuity of Scripture.

    Nor need we waste time repeating Aristotle’s explanation of ambiguous words. The fact that a word must mean one thing and not its contradictory is the evidence of the law of contradiction in all rational language. This exhibition of the logic embedded in Scripture explains why Scripture rather than the law of contradiction is selected as the axiom. Should we assume merely the law of contradiction, we would be no better off than Kant was. His notion that knowledge requires a priori categories deserves great respect. Once for all, in a positive way-the complement of Hume’s negative and unintentional way-Kant demonstrated the necessity of axioms, presuppositions, or a priori equipment. But this sine qua non is not sufficient to produce knowledge. Therefore the law of contradiction as such and by itself is not made the axiom of this argument. 10“

    Dr. Malpass:

    But maybe he has in mind a sort of non-classical logic, one that retains the ability to use conjunction elimination, but does not postulate as an axiom that there are no contradictions. But then the problem would be that there would be nothing to stop the paradoxical looking inference rule: ‘negation introduction’, which I have just made up, but would look like this:

    Premise 1) p

    Therefore ~p

    Presumably, Jason would want to object that this rule is not part of his implicit set of inference rules. But the question would then be, why not? It seems to me that the only thing Jason could appeal to would be the fact that there cannot be a contradiction, which just is the principle of non-contradiction. And if he said that he would be admitting that he does presuppose non-contradiction after all, and does not derive it from an axiom.

    The results for his logic if he did have negation introduction would be devastating. For a start, from his axiom B, one could derive ~B; from the axiom that the bible is true, one could derive that it is not the case that the bible is true. Even if he derived a from B (the principle of non-contradiction from the bible), one could also derive ~a from B (by deriving a from B, and ~a from a). So the bible would say there could be no contradictions, and it would say that it is not the case that there could be no contradictions.

    The point is that negation elimination is to be avoided at all costs. The best way to avoid it is to start with it as an axiom that there are no true contradictions.

    Response:

    That’s a negative. My philosophy does not involve non-classical logic. Therefore, anything said concerning non-classical logic is not relevant to my position. However, such a polemic would be self defeating. If the truth of P necessarily leads to the truth of ~P, the law of contradiction is false. If the law of contradiction is false, there is no distinction between P and ~P, if there is no distinction between both propositions of the non-classical variety, therefore, this critique by Dr. Malpass would be meaningless because the non-classical framework of the critique he gave would involve the rejection of the law of contradiction. One cannot use the law of contradiction to argue that a proposition is false if the one who invokes the law of contradiction accepts a framework that denies the law of contradiction.

    Conclusion

    Dr. Malpass’ objections have been answered. Let us hope that these answers will encourage him to do a bit more research before attacking a position that he is unfamiliar with. As someone who has a Ph.D in philosophy, he should know better. This is a mistake that he has already made twice. Let us hope he does not make that mistake a third time.

    Footnotes:

    1. https://useofreason.wordpress.com/2016/01/14/thoughts-on-jason-petersens-argument/

    2. Dr. Malpass incorrectly objected to this definition because he did not realize that in order to say that an inference is valid, it MUST be necessary.

    3.  An antichrist is a person that attempts fool others into think that he is a Christian, but is antagonistic to Christianity.

    4. The principle of bivalence holds that a that a proposition only has one truth value (it is either true or false).  This principle is not to be confused with the law of excluded middle.

    5. The Westminster Confession of Faith, Chapter I, Article VI; 2TI 3:15, GAL 1:8, 2TH 2:2.

    6. http://www.britannica.com/topic/laws-of-thought#ref180925

    7. http://www.trinityfoundation.org/journal.php?id=16

    8. http://www.trinityfoundation.org/journal.php?id=55

    9. All statements that have truth value in scripture are propositions.

    10. http://www.trinityfoundation.org/journal.php?id=16