So you take away from this sentence... "And ‘note that problem solving, in this context, has to do with a problem to be solved by the character, not a problem (such as How do I role-play this situation?) to be solved by the player."... that the player makes all decisions using his own knowledge. Which of course completely ignores the part I bolded.
I'm not ignoring the part that you bolded. The player has inserted him-/herself into the situation of the character - and hence has the problem to solve.
The question of what knowledge the player should use is not addressed at all in Gygax's essay, is it? I know that it was pretty common in the early days of D&D for players to memorise the Monster Manual - that's one of the reason why new monsters (and new trap ideas, and new spells, and new magic items, . . .) are so important to the game, at least in that period. They are a way of surprising players, and presenting them with a problem to solve - rather than expecting players to
pretend to be surprised when they actually are not (eg pretending to be surprised by trolls' regeneration, when in fact they're familiar with it), and to
pretend to solve a problem to which they already actually know the solution (eg pretending to try to hit upon fire as a solution to the troll problem, when in fact they already know that fire is the key).
This goes to the contrast that Gygax draws between
role playing (in effect, acting) and
role assumption. Here are what I think are some key passages from the essay in this respect:
A role-playing game should be such that players begin the personification portion as role play, and then as they progress the activity should evolve into something akin to role assumption. This does away with stilted attempts to act the part of some character. In place of this, players should try to become that person they are imagining during the course of the game, and conduct the actions of their characters accordingly. . . .
Combat, survival amidst threatening conditions, or stalking an opponent are typical means of adding excitement and suspense into the whole. These are action oriented portions of the game activity which call for little role playing but a fair amount of role assumption. The magic-user character (and thus, the player of that character) must know his or her spells and how to utilize them efficiently. The explorer must know outdoor craft. Whatever the situation, setting, or character being played, skill not theatrics is what is called for here. . . .
Role-playing games are different from other games in that they allow participants to create a game persona, develop this character, and enhance his or her skills and abilities. While some considerable amount of acting is most beneficial to play, this is by no means the sole objective or purpose. The fun of such gaming includes all the other elements mentioned, plus the interactive relationships which develop between the various characters of the players participating. In the well-balanced game, role playing should quickly become role assumption . . .
Not every game of this sort must be completely balanced with regard to all of these aspects. Such a decision is entirely in the hands of the game master and the players. If a particular group desires to stress acting, or combat, or problem solving, or any other singular feature of the whole, that is strictly up to the individuals concerned. How they enjoy gaming, and what constitutes fun, is theirs alone to decide. . . .
Play of the game is the thing. Play includes development of the character and personification thereof, role assumption and role playing, and the rest.
There are a few interesting things here. First, he emphasises the breadth of feasible approaches - a greater emphasis on his preferred style (of player skill-based "role assumption") or on his less-preferred style (of player theatrics or "role playing", which would include pretending to be surprised by trolls when one actually knows what their abilitiies are). Although Gygax has strong preferences, he is not stating a purist position about what he thinks is the only way to play D&D.
Second, look at what he says about combat. In combat, theatrics do not loom large. But a skilled player is able to assume the role of the MU, by knowing the spell list and making sensible choices. Likewise, he assumes that a player of a ranger ("explorer") will actually draw upon knowledge of outdoor craft to solve ingame problems (eg thinking of ways to use trees to make rafts, or vines to make ropes, or to signal via fire and smoke, etc). This is his preferred approach. (Though, I stress again as he himself does, not the only viable approach.)
Third, and following on from the second, player skill in role assumption ("skill not theatrics is what is called for here") means that knowing your suite of resources, and understanding how they fit into the fictional position of the character, is key (eg do I need rope? are there vines? am I carrying a knife? am I able to tell strong, healthy vines from rotting ones? etc). If a character has low INT, that will manifest itself in the answers to these questions - it is one of the things the GM has regard to in informing the player of relevant information (and it can do this in multiple ways: knowledge of languages; a roll to decipher blurred handwriting; a roll to recognise a healthy vine; etc). But there is no suggestion that the player is meant to
pretend to be stupid. That is the sort of theatrics that Gygax is skeptical of (while recognising that other RPGers might value it more than he does). That is framing the problem as one for the
player alone ("How do I roleplay a stupid PC") rather than as one for the character, which the player him-/herself then engages via "role assumption".
When playing in Gygax's preferred style, if it important to the table that 5 INT matter to character decision making beyond the language rules and INT checks, then the GM should be filtering information provided to the different players on the basis of character INT, so that when the player takes on the situation of the PC, the fictional position is true to the PC's INT.
As far as the bigger discussion in this thread is concerned, I think that this essay from Gygax shows that there are conceptions of RPGing that are very different from the one which gives rise to the question "How do I roleplay a 5 INT character" - and I think this is why [MENTION=6787503]Hriston[/MENTION] posted the essay.
I also think it reminds us that there are
multiple ways to do RPGing, and it shows us an author with a strong preference nevertheless acknowledging that others will enjoy doing it other ways (and even recommending that modules, tournament sessions etc advise prospective purchasers/participants which playstyle they are suited to). In this respect, I think it fits with [MENTION=97077]iserith[/MENTION]'s position in this thread, that to insist that a character having 5 INT
must give rise to a question of "How do I roleplay that" is to take one preferred approach (broadly, the one that Gygax identifies as theatrics/"role playing" in the narrow sense) and dismiss other completely legitimate and viable approaches (such as Gygax's preferred "role assumption" approach).
My take way is that when role playing you make decisions based solely on character knowledge and exp and your still considered roleplaying without having to improv act out everything.
When Gygax talks about "theatrics", I don't think he is just getting at literal improv acting. He is getting at the idea that playing one's PC means self-consciously adopting another persona and posing the question "What would this other person do?".
Hence his call for "role playing" to quickly become "role assumption" - the persona of the PC is developed fairly quickly, and the PC is oriented in some sort of challenging fictional situation, and now the player's job - having put him-/herself imaginatively into that situation - is to solve the challenge using the resources that the game makes available to him/her.
If your PC's INT is 5, that's one resource you don't have. Your PC's 5 INT might also have contributed when you took the early steps of establishing a personality for your character, which helps shape the PC's goals and methods, and hence helps give content to the character's fictional position. But other than these ways, Gygax is not expecting that the 5 INT should be a constant consideration in making action declarations for your PC. Because that would be engaging the situation from the point of view of a
player ("How do I, this real person in the real world, roleplay a 5 INT") rather than from the point of view of the
character ("How do I, Thrud the Magnificent, solve this problem that confronts me?").
Again, if it's important for the table that Thrud's 5 INT contribute to the way Thrud (and hence Thrud's player) encounters that problem, that falls onto the GM to factor it into the way information is dispensed.
Speaking now for myself rather than as a Gygax interpreter, I think it's enough that Thrud's player doesn't have INT to draw on as a resource, and hence can't declare knowledge check, certain sorts of investigation or perception checks, etc, with much prospect of success. I don't also see the need for the GM to factor into his/her framing of Thrud's situation. But if I wanted the INT 5 to matter in that respect, I would absolutely put it onto the GM, not the player - as I have repeatedly stated upthread.