(This answer mostly has its roots in a course some time ago with Prof. David Bain - apologies if I am misrepresenting an otherwise interesting position!)
One way we might start looking at your question is with a deceptively simple semantic clarification: "what do you mean by External World"?
If you mean something like "the totality of stuff that isn't just perceptual data", then the question presumes something like a Cartesian Philosophy of Mind - we have the stuff "in here", and that's the domain of the mind, and we have the stuff that's "out there", and that's the domain of bodies.
That's an intuitive place to start when it comes to looking at solipsistic, skeptical hypotheses, because that is of course where Descartes himself started. On the one hand, we appear to have a very clear sense of the thoughts we experience being "our thoughts", as presented to us in the fact of experience, and on the other we recognize that the content of these thoughts might be mistaken in as much as we take them to describe a world that sits beyond the boundaries of that phenomenal, inner experience. The question we ask ourselves as a Cartesian skeptic is how do we determine, as observing subjects of the world, whether we might be subject to deception by a malevolent spirit about what the reality our world is projecting towards us is actually like.
One way philosophers have tried to address the Cartesian challenge is to challenge the dualism at work in this philosophical starting point. The skeptic is trying to make the case that Internal and External might not align; one response, which has emerged somewhat recently in the history of philosophy, is to argue that (at least some of) the classically "Internal" stuff is really part of the "External" domain, and that maybe this view of "minds as internal" and "bodies as external" that the skeptic banks so much argumentative capital over doesn't quite hold true (at least not all of the time).
Externalism (Stanford Encyclopedia of Philosophy) is a family resemblance of views that when a subject uses their cognitive faculties to form propositions about the world, at least some of what they are doing involves aspects of the world that extend beyond their biological boundaries. One example of such a view is the Extended Mind hypothesis; that a complete and accurate account of someone's thought processes might essentially require involving objects or agencies external to their person as part of their physical or computational operation (such as a notebook, mobile phone or social support network). Another is Content Externalism, which is that what it means to "have this or that thought", to identify and individuate thoughts, is dependent on facts or things sitting outside the biological organism "having the thought".
It might seem clear to us now, in the age of social media and the mass manipulation of facts and information, that human cognition has contingently become dependent on devices and technologies external to our physical selves (and that the Extended Mind hypothesis explains a really important fact about how smaller-scale skepticisms are powerful tools for any kind of epistemic agent in the present context).
But the involvement of our outer worlds in the individuation of thoughts is a more subtle and far-reaching observation. If we think thoughts follow a structure and ontology that essentially maps on to the way we learn to use Language, as many both philosophers and non-philosophers do, then variations in our linguistic community give rise to variations in how we think, and thus those external variations we ought to say form a proper part of the thoughts themselves.
In his paper "Individualism and the Mental", Tyler Burge draws this idea out in a thought experiment about how we come to acquire descriptive understandings of our experience of pain. Someone who has come to understand themselves as having "Arthritis in my thigh" is, in our current world, misattributing the joint condition Arthritis to their current experiential state. However, that it is a misattributation is the kind of fact that is entirely related to social conditions. Since we could conceive of a reality in which someone with exactly the same personal and physical history themselves might live in a community in which this wasn't a misattributation, where the meaning of "arthritis" as speakers have come to use it also includes pains that can occur outside the joints, this has consequences for the actual meaning of "arthritis", and thus for the mental content of thoughts involving the concept of arthritis. Even in our actual world in which people have thoughts about arthritis, their thoughts can't be determined by personal, "Internal" facts, or even physical ones about their own bodies.
So, to the cartesian point: What does it mean for an agent to have the thought "I am being manipulated by an evil demon"? If "being an evil demon" is importantly like "Arthritis" in the sense in which Burge describes, then to have the thought is to engage in the practices of a linguistic community. The question, then, is whether we might reasonably entertain that hypothesis without at the same time withdrawing from the practices of the community that ground the hypothesis being meaningful. It's not correct to see the individual as a distinct mind, and the community as just providing that mind simply with data - rather, the mind as such has to be understood within that sociolinguistic context, and this challenges the prior "internal/external" distinction that the Cartesian idea relies on to argue that skepticism might simply be true simpliciter.
The interesting takeaway from this is that whether it might be logical to believe you are being controlled by an evil demon is actually a contingent matter, depending on the community in which you find yourself! In some communities (I'm thinking particularly of hardline protestant Christianity or the whole "redpill" idea) this kind of solipsistic collapse might be entirely coherent with their practices. In others, we might suggest that something fundamental is lost when a member disengages from shared experiences to indulge in solipsism.
Either way, it forms the basis of a potential argument for the practice of Scientific epistemology that the totalizing radical skepticism of Descartes is just a category mistake. That's not to say that it's a bad idea to doubt the contents of your phenomenal experience, and to take a critical lens to the prima facie nature of how things seem to be structured from your perspective; simply that the extreme forms of such skepticism involve separating yourself from the basis that makes your experience meaningful, that this to some degree collapses into absurdity, and that consequently our theories of psychology and epistemology don't have to start by justifying the first principles of the possibility of reality at all.