Many already know that Thomas Huxley first coined the term agnostic, but few know about the principles that he wanted agnostics to follow. Agnosticism was originally meant to be a position against dogmatism (its pejorative sense) and the attitudes associated with it. For an example of a dogmatic person, just think of the Christian pastors that are very assertive when it comes to their moral claims, and then they condemn those that disagree. Also, think of militant atheists that reject anything that isn't in line with metaphysical naturalism. What these two groups have in common is that they have an unwarranted certainty in their beliefs, and they are usually closeminded to anything else. When you have a group of them on a forum, they'll usually boot you out if you disagree with their "orthodoxy". This is precisely the attitude that Huxley was against, and he established principles to keep the agnostic from dogmatism (hence, why he advocated for open-mindedness, freethinking, etc).

I've personally applied these principles, and I believe they've given me a big intellectual boost when it comes to how I approach and think through various subjects in philosophy, religion, and science. Honestly, I find that I shine the most on hot button issues, especially the ones that tend to polarize people. So from time to time, I will share some of his principles of thinking here.

Topical order of agnostic principles:
- On open-mindedness
- On freethinking (edited my explanation on 12/4/2022)
- On nonpartisanship (added on 10/2/2023)
- Huxley's notable views that relate to agnosticism (to serve as an example of the type of conclusions that agnostics would draw)
 
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On open-mindedness:
...the only obligation accepted is to have the mind always open to conviction. Agnost*ics who never fail in carrying out their principles are, I am afraid, as rare as other people of whom the same consistency can be truthfully predicated. But, if you were to meet with such a phœnix and to tell him that you had discovered that two and two make five, he would patiently ask you to state your reasons for that conviction, and express his readiness to [247] agree with you if he found them satisfactory.
Source: Huxley, Thomas. "Agnosticism." Collected Essays V (1889).

To me, this principle means that the agnostic should be open to questioning and exploring anything whether it be something he thinks of or something someone else presents to him. If someone makes a claim about a supernatural claim, don't dismiss it a priori. Be willing to examine it for validity.
 
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On freethinking:
1. Agnosticism is of the essence of science, whether ancient or modern. It simply means that a man shall not say he knows or believes that which he has no scientific grounds for professing to know or believe.
Source: Huxley, Thomas. Agnosticism: A Symposium. The Agnostic Annual (1884)

I question if it's possible to not have any beliefs or opinions at all, especially since they seem to form almost naturally or automatically. I accept that it's possible to lack beliefs towards specific matters (as opposed to not having beliefs on anything at all), like when atheists and agnostics say they lack belief when it comes to God's existence. What I find myself doing is constantly weeding out my beliefs (if there's any) or to make sure that they have no bearing on my views when I'm discussing issues in an intellectual context (check your beliefs at the door, so to speak). And I'm sure others will remind me to do so or to at least acknowledge that they are beliefs, and I'm okay with that. :)
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As I have taken some pains to point out in one of the following essays agnosticism has no creed–in the sense of a statement or conclusions either positive or negative, which the agnostic must hold. It is the method [into] the cause of belief, which[sic] marks the true agnostic, not the results of the intellectual operation conducted according to that method.
[emphasis added]
Source: Thomas Huxley - Agnosticism - A Fragment

From reading the previous statement in this section, we know that the cause of belief for an agnostic should be scientific grounds (a mix of logical reasoning and empirical evidence). This is 100% in line with being a freethinker.

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In matters of the intellect, follow your reason as far as it will take you, without regard to any other consideration
Source: Huxley, Thomas. Agnosticism and Christianity

This is one of my favorite standards. A lot of people that claim to be guided by reason or to be on the reasonable side, only live up to this standard to an extent. These types use reason as far as it can go, but only use it up to the point that it supports their position. The rest they either disregard reason because they want things to be true. Others may try to fill in the gaps in reason/knowledge with their beliefs and then try to pass that off as a reasonable package. I find this in politics, religion, philosophy, and even science.
 
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On being non-partisan (this is more implied by Huxley's actions to steer away from labels):
I trust that I have now made amends for any ambiguity, or want of fulness, in my previous exposition of that which I hold to be the essence of the Agnostic doctrine. Henceforward, I might hope to hear no more of the assertion that we are necessarily Materialists, Idealists, Atheists, Theists, or any other ists, if experience had led me to think that the proved falsity of a statement was any guarantee against its repetition. (source)

Being non-partisan can mean not taking any sides. It can also mean not holding to any side unquestionably. The obvious benefit of this is that it reduces bias or the interest to defending your side vs. getting to the truth (even when your side is wrong).
 
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Notable views
Strictly speaking, I am unaware of any thing that has a right to the title of an "impossibility" except a contradiction in terms. There are impossibilities logical, but none natural. A "round square," a "present past," "two parallel lines that intersect," are impossibilities, because the ideas denoted by the predicates, round, present, intersect, are contradictory of the ideas denoted by the subjects, squared, past, parallel. But walking on water, or turning water into wine, or procreation without male intervention, or raising the dead, are plainly not "impossibilities" in this sense.
Source: Huxley, Thomas. "Possibilities and Impossibilities. Agnostic Annual, 1892.

Huxley offers his standard he'd use to claim something to be an impossibility. This has huge implications when it comes to how open he would be towards accepting metaphysical claims. In contrast, some skeptics would not only dismiss claims just for violating logic, but even for violating the laws of nature as understood by science.
 
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