The guy in the video likely didn't even read the book he's "reviewing" and gives opinions that in are in no way supported by the book and its author, Soccio, and in no way can be inferred from it, either.
I was also assigned "Archetypes of Wisdom" for a philosophy class I took, and it is one of the best books I've ever read, not just in philosophy.
The book is a textbook that has in the margins quotes and musings from famous philosophers, as well as cartoons and so on (like the wonderful Calvin and Hobbes series) that are in some way connected to the material discussed in the relevant chapter.
Everything that guy quotes are either from the margins or, like in the case of the quote from Buddha, are on the opening chapter pages. All of his quotes are from the first part of the book, which isn't even about Western philosophy in the first place, but about Eastern philosophy. In fact, the guy must have only flipped through chapter one and the opening of chapter two.
Anyway, he's wrong about Buddha as well. If one bothered to read the book, or to stay awake during the course, he'd note that Buddha was not in any way a "misanthrope." A misanthrope has an overall negative view of humanity, that is in a way, doomed, and no faith in individual choices.
However, as the book notes, the Buddha's beliefs were the exact opposte (page 49-50):
"Among the insights Buddha gained during his arduous search for enlightenment, three 'realities' command our attention: impermanence, suffering, and egolessness. In simplistic, contemporary terms, we can sum up this part of Buddha's teaching like this: 'Although nothing lasts, suffering is everywhere, and the 'me' that suffers isn't even real.'
"At the core of the Buddha's doctrine is the concept of the primal unsatisfactoriness (dukka) generated by the perilousness of the human condition and by the inescapability of physical suffering and sickness, psychological conflict, anxiety, and anguish. As if this is not enough, Buddha reminds us that beneath our dissatisfaction lies a profounder insight: the insubstantiality of existence.
"Awareness of insubstantiality is related to the Buddhist doctrines of impermanence (ever-change) and egolessness... Out of ignorance, we project a sense of 'permanence' onto impermanent conditions. Because all is in flux, we are inevitably disappointed by change, destruction, and loss.
"Failing to see the true nature of the complex web of conditions and reactions that we think of as 'an individual,' our illusory 'self' remains subject to suffering and perpetual dissatisfaction. We compound suffering whenever we insist on projecting (excepting and anticipating) the possibility of a continuous life of pleasure, joy, and stability for our individual selves. While in a state of projection, we find it difficult to accept that we are subject to sickness, grief, and suffering. We resist the deeper insight by engaging in repression, aggression, greed, lust (consuption), denial, and anger. So it is that a fundamental 'human condition' or 'predicament' is our heritage. As one translation of Buddha's First Noble Truth poetically puts it, 'When we are born, suffering comes with us.'
"Is this vision of the fundamental human condition pessimistic? Perhaps it would be, if Buddha had nothing more to teach. But Buddha promised that through a discipline of meditation, we can learn to control unruly desires and realizes what happiness is possible given the facts -- not our projections -- of the human condition.
"Thus, we see that central to Buddha's teaching is a notion of free will, a belief that we can control our thoughts, attitudes, and behavior and that thoughts, attitudes, and behavior have consequences. These consequences, their causes, and their control are called karma."
(emphasis mine.)
He goes on to state that
karma really isn't the same thing as fate. In the first instance, not everything happens because of Karma, as different laws govern "natural change, physical phenomena, certain psychological processes" and so on. And second, because if karma alone acted for the human condition, a person with good karma would always be good and a person with bad karma would always be bad.
Rather, karma comes because of an individual's actions, which Buddha believed that a change in either our actions, thoughts, or feelings always has an affect on the other.
I post all this to give some context, and because there is nothing misanthropic about this. It's merely an opinion of the existence of humanity, and one that is not overall negative, as Buddha quite clearly seemed to believe we could overcome these problems.
As for the definition of "true belief" and "belief," the author is talking about that in the context of epistemology. Epistemology is a branch of philosophy that deals with knowledge and whether or not it is even possible.
What he's saying is not anti-science, as science doesn't deal in absolute truth in the first place. There is no such thing as absolutism in real science, and you cannot even prove that the ground exists or existed definitely five minutes ago. For instance, one could claim that the world sprang up five minutes ago, with all of human consciousness in tact. This is obviously ridiculous but it is not logically refutable. This is the argument some creationists give against evolution, that God created the world 6,000 years ago only to "test our faith."
What science is about that is having a theory that is capable of being proven wrong, yet all empirical evidence points to it being true. This could be considered a scientific "fact" or a "true belief," swuch as evolution. Scientists have an inherent self-interest in being honest because there usually isn't a "second chance" after someone is exposed as being a complete fraud in the field.
It's not appropriate to claim that philosophy is "anti-science" based on excerpts you read from a discussion on Eastern philosophy in chapter one of a textbook, that isn't even the mainpoint of the discussion. I guess it could be seen as confusing to put Eastern philosophy in an introduction to philosophy that is primarily an introduction to Western philsoophy, but really even the interpretations of Eastern concepts is not accurate. The book, in the discussion of Western philosophy, covers many Western philosophers who were not only important to philosophy but to the advancement of science and scientific philosophy as well, such as Descartes, Locke, Berkeley, and Hume (as well as aristotle etc., some might say it helps to understand science if you understand how past scientists viewed the world, and how their views, like Aristotelian physics, came to be disproven).