[quote=@ZAVAZggg]
How do we know logic, like time, isn't just a construct our minds?
[/quote]

Because it's our only way to even perceive reality. You could claim logic to be false, but it undermines our entire ability to perceive, evaluate, or even interact with reality. You would have to accept the fabric of reality around you to be unrepresentative of the actual truth of the world (but even that conclusion relies on me taking the claim to its logical ends). Ultimately, you can deny anything you want, but if you don't choose to accept logic, whatever system is put in its place (or lack thereof) will have no predictive or analytic power to do anything, really. It's like if I had a computer and denied that ADDI R1, R0, 5 would place the number 5 in register 1. I can claim absolutely anything I want, but I can't accomplish anything that doesn't abide by logical rules.