This article will cover 6 logical insights which are applicable to scientific analysis and philosophy.

**1 – The Expanded Principle of Non-Contradiction**

Two nonequivalent statements cannot simultaneously be true and contradictory.

The principle of non-contradiction holds that if A is true, A’ (that is, the negation of A) cannot also be true. An example would be “blue is a color” and “blue is not a color” cannot be true at the same time.

The expanded principle holds that “blue is a color” and ANY STATEMENT which would imply that blue is not a color cannot be true. An example of the use of the principle in practice is as follows: 1 Apples are red 2 Jimmy’s statement implies that apples are not red, therefore 3 Jimmy’s statement is false.

This principle makes Christian apologetics easy. You do not have to study Buddhism, Mormonism, Islam and so on extensively to prove that they are false. The apologist must only prove that 1 Christianity is true and 2 The other ideology in question is contradictory of Christianity. On the other hand, if the other ideology in question is not contradictory of Christianity they could both be true! For example, as far as I am aware, laissez faire conservatism and Christianity are not contradictory.

**2 – Bias Analysis**

Scientists, the media and others like to maintain an appearance free from bias, but we know this is not the case for a variety of reasons. People are necessarily biased. Maybe I need to do an article specifically on that concept, but if you agree that people are necessarily biased then you will probably agree with my next statement: Given that people are biased it is better for them to disclose their bias than to conceal it.

In academic papers the first part of the paper is the summary, followed by an introduction describing the hypothesis, followed by a literature review and then there are several later sections as well. I propose that a bias analysis including a self-assessment and an analysis of the bias of those discussed in the literature review should become a regular ingredient for academic papers.

**3 – Distributed and Normative Analysis to Minimize Bias**

To further minimize bias it may be a good idea for similar studies to be carried out by various people along the ideological spectrum. For a full bias analysis the number may be required to exceed 30 or even 100 studies on the same topic if the topic is divisive in order to create a statistically reliable representation of ideologies. This will create an effect similar to what happens on Wikipedia. Everyone is biased, but the community interaction produces an equilibrium which reflects the consensus of the entire population. This consensus is still biased to a degree by the culture of the times and so on, but it is expected to be significantly less biased than any particular contributor.

**4 – Presumption of Innocence in Fact and Interpretation**

It should be the scholarly method to assume the status quo as is done already in statistical hypothesis testing. In keeping with that tradition, no fact revealed by preceding scholars should be presumed false. Furthermore, if some fact seems logically odd but could possibly be interpreted to be true, it should be presumed to have the true interpretation. For example if someone says that apples taste both good and bad it can be considered logically odd or even flat out impossible and contradictory. Yet we can and should grant a generous interpretation of the meaning, for example the meaning might be that apples taste good in a way and bad in some other way, so that overall it is neither perfectly good nor perfectly bad but is a mixture.

**5 – Presumption of Independence**

In statistics it is presumed that two variables are independent until evidence is found otherwise. If we are to be logically consistent then we should apply this to other fields of logic as well. This becomes vitally important in the following method of deduction, statistical deduction.

**6 – Statistical Deduction**

If something is more likely to be true than it is not to be true, ceteris paribus, it should be considered true. This can be used in deductive logic to provide some very unusual proofs. Traditionally in deductive logic if something is not absolutely true it cannot be used as a premise. Using statistical deduction we can use statements which are not always true as premises if we know their rate of truth. For example, the statement “people like chocolate” is not always true, but it is sometimes true.

When these premises are independent, and we presume they are independent unless we have statistically significant evidence to the contrary, we can simply multiply their rate of truth and come up with a rate of truth for the conclusion.

For example: 1 A particular person likes chocolate (20% true) 2 If a person likes chocolate they will buy a bar of chocolate today (5% true), therefore 3 A particular person will buy a bar of chocolate today (1% true).

This can be rate-interpreted or absolutely interpreted. The rate interpretation could be that the particular person is expected to purchase a bar of chocolate each 100 similar days or that 100 similar people would be expected to result in a sale of 1 chocolate bar today. The absolute interpretation would be that a particular person is not expected to buy a bar of chocolate today.

If dependence is demonstrated it does not mean that we cannot use this form of reasoning. Instead, it means that we must further account for the dependence within the mathematical equation.

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