: How to use the phrase 'by my undertanding' in a formal essay? Or it is formal already? Is it appropriate to use phrases such as "by my understanding" in a formal setting? If I can't, please

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In a formal essay, the implied context is that everything is "by your understanding." To write that explicitly is to be redundant. Simply state your assertions confidently and give your reader the respect to assume that they're reading your essay critically.

As an aside, you should always read non-fiction with a critical eye. As a reader, the onus is on you to understand that everything you read is the writer's view and not necessarily completely correct. In the extreme case, there are some assertions out there that are simply false. Someone arguing that humans have never landed on the moon, for example, will write just as assertively as someone arguing that the Earth isn't flat, but the former view is completely wrong. But even when you're reading something written in good faith that is largely correct, it's appropriate to read critically. Scientific papers do their best to sell their results as important and trustworthy with the expectation that they'll be read harshly to find where they can be improved. Textbooks will reflect the current understanding of their fields and will eventually have sections that go out of date. News stories, even from the most reputable sources, walk a fine line between editorializing and just reporting the facts.

What all of this means is that reading non-fiction critically is actually respectful to the writers. It gives them the credit of assuming they wrote with the expectation that you would ask questions about their work and with the goal of forming your own views. And it means that when you write, it's only respectful to your reader to assume that they'll read critically. It means that you trust them to engage with your work more deeply than merely taking everything you say at face value.

Given all of this, the implicit context of your essay is that everything you write is your point of view. There's no reason to call attention to that fact; it is already accounted for when someone reads your work.

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Typically you don't include any first person pronouns (such as "my") in formal essays. So instead of saying

x is true by my understanding.

you would say something like,

It appears x is true.

Or instead of appears, there are the words: surmise, deduce, conclude, etc. You would use these in the passive form, however, to eliminate the need for a first person pronoun. "It was surmised that..." instead of "I surmised that..." etc.

Also I would suggest to be careful about stating something in a formal essay that you're not ready to back up, or substantiate with a convincing argument. I wouldn't simply say, in general terms, that you understand something to be true. I would give reasons or examples for why it is true.

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