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Given P1: that Government controls taxation, and P2: taxation determines what poverty levels will exist, then yes, governments to a degree control poverty levels directly: Modus Ponens - albeit relative to whatever other factors also control poverty, if any.
A direct control does not entail a significant degree of control, if other direct or even indirect factors are more controlling.
But even if controlling taxation was the sole, or even a major factor in controlling poverty, I am not sure I accept P2 in the first place: that taxation determines what poverty levels will exist.
To get the obvious out the way, taxation goes towards services that can counter at least someone’s poverty - only difference here is someone else (in government) is deciding what the money is spent on instead of you if you had not been taxed. Maybe the money goes back into something that makes you better off, maybe it doesn’t. For some people, they are net beneficiaries of tax, others are not. It’s a control to adjust what the market is doing by its own devices.
But this opens up the bigger question of whether or not the government choice on how to spend the money it taxes, instead of leaving it to you, creates poverty. It might make you poorer at the point of taxation, but it may or may not make you richer depending on what it spends it on, compared to what you might have spent it on. It might make society as a whole richer whether or not you individually are poorer or richer. So what purchases make richer and what make poorer?
Investment in a valuable product or service makes richer. Tax can do that, so can you if you are not taxed: tax is independent of richness or poorness - in fact, the correlation between taxation and GDP per capita is probably a negative one: with the countries with least taxation being the poorest, and vice versa. What makes a country rich is the ability to get money to the right people to create value, and to the right people to spend on what they value. The better individuals do this, the less tax they should be charged, and the better government does this, the more tax should be charged.
Therefore it can be moral or immoral for our governments to tax us, depending on the above.
And it is immoral to impose poverty whether it is governments or individuals who compromise the ability to get money to the right people to create value, and to the right people to spend on what they value.