Strawman. There is no overlap between theism and atheism (or do you hold they are not mutually exclusive?), and they are sufficiently defined for the point raised in the analogy: that if you believe that Mr.X wears a white hat then you most certainly are part of the group that does not believe Mr.X wears a yellow hat.
I do not at all think that they are sufficiently defined. See below.
That was not the question. The question is to name an atheist belief - as in a belief held by all atheists that distinguishes them from others.
The question was not to list the philosophies that atheists might hold. If you raise a belief that one atheist holds but another doesn't then it is not an atheist belief but a belief of whatever philosophy they hold.
We can collect a list of philosophies that are compatible with atheism, but not compatible with theism. What all atheists have in common is that they hold one or more philosophies from that list.
Compare this with citizens of European countries: they are all Europeans, but per se, they are German, French, Italian, Spanish, Polish etc.
One of the things that distinguishes a German citizen from a Brazilian citizen is that the German citizen is a European, and the Brazilian is not.
There may be no single factor that all Europeans have in common (such as language, nationality, currency, president, ...), other than the qualifier "European", but they all have in common that they are citizens of one of the countries in the geographical entity called "Europe."
Similarly, there may be no single belief that all atheists have in common, other than the qualifier "lack of belief in God", but they all have in common that they hold one or more philosophies from that list.
It's not? Care to summarise why not?
The deist idea that God creates the Universe and everything in it, sets it into motion and then has nothing further to do with it, ever, is an idea compatible with polytheism or a system of demigods, but not with God (capital G).
A human can make a clock, wind it up and let it be, never to care about it again.
A demigod can function by the same principle: make something and let it be (and then another demigod takes over).
God, however, is inextricably bound to everything there is. He cannot not care about it, He cannot let it be. He is always involved.
We consider someone theist if they believe that at least one deity exists. It is the generally accepted definition of the term.
It is also a useless definition, to say the least. Because according to that definition, a person who hates God is a theist!
And also, that Tibetan Buddhists are theists!
That's the only requirement for considering someone a theist.
The only requirement according to whom? The author of a dictionary? People who consider themselves atheists?
Are you suggesting there is an alternative definition of theism, perhaps?
Absolutely.
For an adequate definition of theism, we need to look into theism.
Further, atheism is a reactionary stance to theism, defined by theism, so atheism is only meaningful in relation to theism, while not on its own.
So let's look what a theism may consider to be atheism - the Islamic concept of
kafir:
Types of kufr (disbelief) - Adapted from 'Tafseer ibn Katheer[5] The Qur'an uses the word kufr to denote a person who covers up or hides realities, one who refuses to accept the dominion and authority of God (Allāh). There are several types of Al-Kufr ul Akbar:
1. Kufrul-'Inaad: Disbelief out of stubbornness. This applies to someone who knows the truth and admits to knowing the truth and admits to knowing it with his tongue, but refuses to accept it and refrains from making a declaration. The Qur'an states: "Do ye twain hurl to hell each rebel ingrate?" [6]
2. Kufrul-Inkaar: Disbelief out of denial. This applies to someone who denies with both heart and tongue. The Qur'an states: "They recognize the favor of Allah, yet they deny it, and most of them are ungrateful."[7]
3. Kufrul-Kibr: Disbelief out of arrogance and pride. The disbelief by the devil (Iblees) is an example of this type of kufr.
4. Kufrul-Juhood: Disbelief out of rejection. This applies to someone who acknowledges the truth in his heart, but rejects it with his tongue. This types of kufr is applicable to those who calls themselves Muslims but who reject any necessary and accepted norms of Islam such as Salaat and Zakat. The Qur'an states: "And they denied them, though their souls acknowledged them, for spite and arrogance. Then see the nature of the consequence for the wrong-doers!"[8]
5. Kufrul-Nifaaq: Disbelief out of hypocrisy. This applies to someone who pretends to be a believer but conceals his disbelief. Such a person is called a MUNAFIQ or hypocrite. The Qur'an states: "The Hypocrites will be in the lowest depths of the Fire: no helper wilt thou find for them." [9]
6. Kufrul-Istihlaal: Disbelief out of trying to make HARAM into HALAL. This applies to someone who accepts as lawful (Halal) that which Allah has made unlawful (Haram) like alcohol or adultery. Only Allah has the prerogative to make things Halal and Haram and those who seek to interfere with His right are like rivals to Him and therefore fall outside the boundaries of faith.
7. Kufrul-Kurh: Disbelief out of detesting any of Allah's commands. The Qur'an states: "And those who disbelieve, perdition is for them, and He will make their actions vain; That is because they are averse to that which Allah hath revealed, therefor maketh He their actions fruitless."[10]
8. Kufrul-Istihzaa: Disbelief due to mockery and derision. The Qur'an states: "And if thou ask them (O Muhammad) they will say: We did but talk and jest. Say: Was it at Allah and His revelations and His messenger that ye did scoff; Make no excuse. Ye have disbelieved after your (confession of) belief. If We forgive a party of you, a party of you We shall punish because they have been guilty."[11]
9. Kufrul-I'raadh: Disbelief due to avoidance. This applies to those who turn away and avoid the truth. The Qur'an states: "And who is more unjust than he who is reminded of the communications of his Lord, then he turns away from them and forgets what his two hands have sent before? Surely We have placed veils over their hearts lest they should understand it and a heaviness in their ears; and if you call them to the guidance (Qur'an), they will not ever follow the right course (Islam) in that case."[12]
10. Kufrul-Istibdaal: Disbelief because of trying to substitute Allah's Laws. This could take the form of: (a) Rejection of Allah's law (Sharee'ah) without denying it, (b) denial of Allah's law and therefore rejecting it, or (c) Substituting Allah's laws with "artificial" (i.e. non-Muslim) laws. The Qur'an states: "And if Allah had pleased He would surely have made them a single community, but He makes whom He pleases enter into His mercy, and the unjust it is that shall have no guardian or helper."[13] The Qur'an says: "Truly, Allâh is with those who fear Him (keep their duty unto Him), and those who are doers of good and righteousness." [14]
The stance of a kafir is primarily an ethical stance, not an ontological one.
Or atheism according to a Hindu tradition:
BG 7.15:
Those miscreants who are grossly foolish, who are lowest among mankind, whose knowledge is stolen by illusion, and who partake of the atheistic nature of demons do not surrender unto Me.
Thus four types of what are effectively atheists:
1. people who are grossly foolish
2. people who are the lowest among mankind
3. people who are deluded
4. people with demonic natures
Again, this is not an ontological stance on atheism, but an ethical and practical one.
I conted that theism and atheism are primarily ethical and practical stances:
Theism is a favorable inclination toward God,
atheism is an unfavorable inclination toward God.
Given the common definitions of God (The Creator, Maintainer and Controller of everything, The First Cause, the Summum Bonum) and the common definitions of individual living entities such as humans (fully dependent on God), it would be illogical to take an ontological stance on theism or atheism (such as "I believe / I lack the belief that God exists").
Given the common definitions of God and ourselves, it is pointless to speculate about whether God exists or not and whether we believe one or the other, as such speculation does not apply.
Sure - and if I am seen to be committing such a logical fallacy I would hope that the other person points it out.
But I am not sure of the relevance here - unless you are accusing me of something?
Congratulations on remembering.