----------INTRODUCTION----------

Based on the logical law of excluded middle there is a proposition and its negation. So a proposition is either (X) or (-X). For example:

(X) There is an apple on my desk.
--OR--
(-X) There is NO apple on my desk.

Logicians use symbols to exempt bias, so that is why I am and will be using symbols in these explanations.

When it comes to believing proposition (X) or (-X) as true or more likely true over its negation, there will always be a REASON why a person believes one proposition over its opposite (whether knowingly or not). All REASONS will be based on the content the proposition contains; that is, all except one REASON.

The one REASON a person can have for believing proposition (X) over (-X) --or vice versa-- (despite what its content is) is by blindly guessing/picking one at random and then deciding to try and make oneself believe it. This reason for believing a proposition over its negation/opposite is universally held as being an irrational reason; that means one would not be rationally justified to believe a certain proposition over its negation/opposite for that reason.

All other reasons one would come to believe (X) over (-X) --or vice versa-- have to based on the content of the proposition; we then look to see if the reason based on that content is rationally justified and also which proposition has more/better rationally justified reasons for belief.

I will give a list of a few possible propositions and their negations/opposites (so as to do add some possible content to these symbols):

(X) The stars in the universe are even in number.
(-X) The stars in the universe are uneven in number.

(X) The universe is Symmetrical in shape.
(-X) The universe is Asymmetrical in shape.

(X) There is a car on Jupiter.
(-X) There is no car on Jupiter.

(X) Dave will win the lottery this weekend.
(-X) Dave will not win the lottery this weekend.

(X) There is only one star in the universe.
(-X) There is not only one star in the universe.

If someone is void of rational reasons (whether knowingly or not) for believing either proposition is more likely true than its opposite, that same person is rationally obligated to hold to a 50/50 agnosticism between both competing propositions (on which is more likely true); however, this is not to say one can not believe a proposition as true for non-inferential reasons, but the circumstances in which that non-inferential belief is held have to be based on the rational deliverances of reason (and this will depend on which epistemic model one holds to).

If someone claims one proposition is more likely true than its opposite they are making a positive knowledge statement and have a burden of proof to show this to be the case.

I will now move on to three ways in which reasoning can be shown to rationally support a proposition over its competing opposite...

----------FIRST WAY: Direct Inferential/non-Inferential evidence/reason----------

The first way a proposition can be shown to have a rational reason for belief over its opposite, is by giving direct inferential (or non-inferential) evidence/argumentation.

So between these two competing and opposite propositions below...

(X) Dave murdered Sally.
(-X) Dave did not murder Sally.

...an example of a direct piece of inferential evidence would be something like: I believe proposition (X) is more likely true than proposition (-X) because Dave was found in possession of the murder weapon.

Between these two competing and opposite propositions below...

(X) The sun exists (a big bright light above the earth).
(-X) The sun does not exist (a big bright light above the earth).

...an example of a direct non-inferential reason would be something like: I believe proposition (X) is more likely true than proposition (-X) because I see the sun in the sky. This is a non-inferential reason grounded directly in experience (depending on ones epistemology, this will dictate which non-inferential beliefs are rationally valid, and therefore, which non-inferential beliefs can/could be used to directly show/support a proposition as more likely true over its competing opposite).

----------SECOND WAY: Absence of evidence can be evidence of absence----------

The second way a proposition can be shown to have a rational reason for belief over its opposite proposition (which is normally used falsely, but I will get to that), is by claiming there is no evidence for the opposite proposition and that leads to evidence of absence.

For example, someone could say something like:
"I believe (-X) is more likely true because there is no evidence for (X)."

But the problem is that it is no good to just say there is no evidence for (X), as that is no evidence for (-X) to be more likely true (the same argument could be made but in the reverse order: "I believe (X) is more likely true because there is no evidence for (-X)").

The absence of evidence is NOT NECESSARILY evidence of absence. The only time the absence of evidence is evidence of absence, is if we should expect to have more evidence for (X) --or vice versa-- than what we do have; therefore the absence of evidence in this case would be evidence of absence.

Take these two propositions below for example...

(X) The stars in the universe are even in number.
(-X) The stars in the universe are uneven in number.

...now the absence of evidence for proposition (X) being true is no evidence that it is more likely false (and that proposition (-X) is more likely true). That is because there is no expected evidence for (X) that we should have --if (X) were true-- which we do not have.

Now for example, take these two propositions below...

(X) There is a planet the size of Texas between the earth and the moon.
(-X) There is no planet the size of Texas between the earth and the moon.

...this time the absence of evidence for (X) is evidence of absence (and thus evidence for proposition (-X) being more likely true). If (X) were true we would expect to find evidence of people being able to see it, NASA/news outlets informing us of it and that it would cause certain effects on nature (like the tide to change) etc... all of which we do not find.

So if one wanted to support a proposition over its opposite with the reason of lack of evidence leading to evidence of absence, one has to state what evidence we would expect to find if proposition (X) --or vice versa-- were true and then show that we do not find that evidence.

----------THIRD WAY: Circumstantial chance----------

The third way a proposition can be shown to have a rational reason for belief over its opposite, is via the chance of such a proposition being true based on certain background data.

In this case, the proposition is not looked at specifically, but assessed based on generality. I will explain fully what I mean.

For example, look at these two propositions below...

(X) There is a tea pot on the backside of Mars.
(-X) There is no tea pot on the backside of Mars.

...now most people intuitively believe it is more rational to hold proposition (-X) as more likely true than proposition (X). Why is this though?

Well, let us look at the first way: there is no direct evidence/reason for (-X) being more likely true than (X). How about the second way: there is no absence of evidence for (X) leading to evidence of absence (there is no expected evidence we should find if (X) were true which we do not find). So that leaves us with this third way: circumstantial chance/probability.

Basically, we have a series of background beliefs/data/information about reality which inform us that the contingent possibility of (X) happening to be true by chance is far less likely than (-X) happening to be true by chance (there is no direct evidence proving one way or the other, and there is no expected evidence which we are missing; however given certain background beliefs --if these background beliefs are true-- they inform us that the probability of (X) happening to be true by chance is far more likely than (-X) happening to be true by chance).

This way we are not assessing the content specifically but rather assessing it by a generality. For example, look at these two propositions below:

(X) The car on this authors drive way has fuel in the tank.
(-X) The car on this authors drive way has no fuel in the tank.

Now, most people reading this probably don't know me personally and therefore have no idea (directly) about the nature of the case. However, most people reading this know that generally most people's cars have fuel in the tank when they are sat on their drive ways; therefore taking this general case (background data) one can/could apply it to my specific case and have a rational reason for believing (X) is less likely true than (-X).

So, to show (X) --or vice versa-- to be more likely true than its opposite via this third way, one has to state the background information we have (if true) which would inform us that the contingent possibility of (X) happening to be true by chance is far less likely than (-X) happening to be true by chance.

----------SUMMARY OF THE THREE WAYS----------

Firstly, if you are going to say a proposition is more likely true than its opposite you are making a positive knowledge statement and have a burden of proof.

Secondly, to show a proposition to be more likely than its opposite you have to:

(1) Show direct evidence for proposition (X) being more likely true than (-X).
(2) Show that we would have more evidence for (-X) than we currently have if (-X) were true; thus the absence of evidence for (-X) is evidence for (X) being more likely true.
(3) Show based on certain background information/data/beliefs (X) is more likely to happen to be true by chance than (-X) happening to be true by chance.

----------ASSESSING THE PROPOSITION 'GOD EXISTS' OVER ITS OPPOSITE----------

-----FIRST EXAMPLE-----

Classical Theism is a belief in God, yes, but more specifically it is a belief about the nature of Ultimate Reality. It is the belief that Ultimate Reality is Personal (not to be confused with 'Relational') in nature, rather than Ultimate Reality being Impersonal in nature (i.e. atheism - as this is the antithesis to Theism).

I am going to post a link on a debate which was based on these two propositions below...

(X) God exists (i.e. Ultimate Reality is Personal).
(-X) God does not exist (i.e. Ultimate Reality is Impersonal).

...I will post the link at the end, after I state some issues concerning the debate.

The debate was between Christian Theist philosopher Dr William Craig (supporting (X) ) VS the late infamous anti-theist Christopher Hitchens (supporting (-X) ).

In the debate Craig gave four inferential arguments/reasons to support proposition (X) --mostly via deductive syllogisms-- and one non-inferential argument/reason to support proposition (X).

Hitchens on the other hand gave no inferential arguments to support proposition (-X), rather he made a lot of rhetorical jabs; like religion is the cause of lots of evil acts through out history etc... If Hitchens wanted to turn these rhetorical jabs into actual arguments/reasons to support proposition (-X) over (X), he would of had to add some minor premises to the major premises to allow for the rational conclusion of 'therefore, (-X) is true;' but Hitchens did not do this. Also, Hitchens did not attempt any serious rebuttals of Dr Craig's arguments for (X) being true.

Here is a short video highlighting some of the issues of the debate:
https://www.youtube.com/watch?v=L0qQoJjsBWs

Here is a link to the full debate:
https://www.youtube.com/watch?v=0tYm41hb48o

Of this debate, Commonsenseatheism..com stated: "Frankly, Craig spanked Hitchens like a foolish child..."

-----SIDE NOTE (Beginning)-----

I have a reason for why I emphasize belief in God being recognized as a belief about the nature of Ultimate Reality. The reason is misconception.

A lot of people think of God as being like some kind of super hero (Superman for example): that God is just some being who exists within reality, being subject/subservient to reality and just a part of it; yet with incredible powers and abilities.

The problem with this belief is that when people think about the probability of the proposition 'God exists' they sub-consciously see it as less likely than 50/50 (even if they have no reasons based on the first and second way) because of the third way.

For example, the chance of someone making up the story of superman and a being contingently just happening to exist which has all the properties of superman, seems very unlikely (given all the possible contingent possibilities of reality - so the third way makes the proposition 'Superman exists' less likely).

This is sub-consciously how people think of the proposition 'God exists' I believe, however, when it is framed in its proper context (being about the nature of Ultimate Reality) people realize that the third way can not be applied in this case (there is no possible background information which can be applied to the very nature of Ultimate Reality happening to be a s certain way by chance).

-----SIDE NOTE (Ending)-----

-----SECOND EXAMPLE-----

In this second exchange (link below) Dr Craig is debating Dr Shook. The debate is based on these two competing propositions below:

(X) The natural world is all that exists (i.e. Naturalism).
VS
(-X) The natural world is not all that exists (i.e. Super-naturalism).

However, in this exchange Dr John Shook seems to be arguing a straw-man. He seems to approach the debate as if the two competing propositions are:

(S) The natural world exists.
VS
(-S) The natural and supernatural world exist.

To prove (X) is more likely true Dr Shook has to show evidence/argument/reason for this based on what we know from reality. It is no good to just show evidence the natural world exists (the straw-man argument -- since both sides believe the natural world exists), rather he has to show some evidence/argument/reason from the natural world (or via some other means) which shows it is more likely to be the only thing which exists in reality.

Now, for either proposition (X) or (-X) to be rationally shown as more likely true than its equal and opposite proposition, requires reasoning based on what we know about reality. Let me give a similar scenario to demonstrate this:

(A) There are no more than 230,000 species of fish in the sea (230,000 is the most recent estimate to date I believe for the amount of differing fish species we have found).
VS
(-A) There are more than 230,000 species of fish in the sea.

Now if some one wants to rationally show one proposition is more likely true than the its opposite, it has to be based on reasoned argument from what we know.

For example somebody could make an argument for (-A) like: "Well, there is so much more ocean yet to discover which we have not been able to access so far, and based on what we know of life, if it can exist anywhere it will exist; therefore it is more likely there are more types of fish species in the sea yet to discover."

An example argument for (A) could be something like:
"Well, all the sea left to discover which we have not accessed yet is under too much pressure for a fish to survive based on what we know via fish biology; therefore it is less likely there are anymore types of fish in the sea."

The bottom line is this, if you want to show a claim as more likely true than its opposite you need a reasoned argument for that based on what we know via reality.

Here is a short video highlighting the issues in the debate:
https://www.youtube.com/watch?v=XcnZRctcleM

Here is a link to the full debate:
https://www.youtube.com/watch?v=jRp3ERk8Tho

----------RELATED LINKS----------

RELATED LINKS BELOW:

>>>Is there Good Evidence for Atheism?<<<
https://www.youtube.com/watch?v=5T76Rp6pS4I

>>>God Is Not Merely Interested In Getting People to Believe In Him<<<
https://www.youtube.com/watch?v=A1iWk3KYhGA

>>>The Presumption of Atheism<<<
https://www.youtube.com/watch?v=nGG5uuNW8q0