How do you know that? Do you have an example program and all its inputs where we cannot in principle determine if it halts?
Many things are non-algorithmic, and thus cannot be done by a computer, yet we can do them (e.g. love someone, enjoy the beauty of a sunset, experience joy or sadness, etc).
I can throw a ton of algorithms that no human alive can hope to decide whether they halt or not. Human minds aren't inherently good at solving halting problems and I see no reason to suggest that they can even decide whether all turing machines with number of states, say, below the number of particles in the observable universe, very much less all possible computers.
Moreover, are you sure that e.g. loving people in non-algorithmic? We can already make chatbots which pretty convincingly act as if they love people. Sure, they don't actually love anyone, they just generate text, but then, what would it mean for a system or even a human to "actually" love someone?
They said - there is no evidence. The reply hence is not supposed to be - how do you know that.
The proposition begs for a counter example, in this case an evidence.
Simply saying - love is non algorithmic - is not evidence, it is just another proposition that has not been proven, so it brings us no closer to an answer i am afraid.
When mathematicians solve the Collatz Conjecture then we'll know. This will likely require creativity and thoughtful reasoning, which are non-algorithmic and can't be accomplished by computers.
We may use computers as a tool to help us solve it, but nonetheless it takes a conscious mind to understand the conjecture and come up with rational ways to reach the solution.
Human minds are ultimately just algorithms running on a wetware computer. Every problem that humans have ever solved is by definition an algorithmic problem.
Oh? What algorithm was executed to discover the laws of planetary motion, or write The Lord of the Rings, or the programs for training the GPT-4 model, for that matter? I'm not convinced that human creativity, ingenuity, and understanding (among other traits) can be reduced to algorithms running on a computer.
They're already algorithms running on a computer. A very different kind of computer where computation and memory are combined at the neuron level and made of wet squishy carbon instead of silicon, but a computer nonetheless.
Many things are non-algorithmic, and thus cannot be done by a computer, yet we can do them (e.g. love someone, enjoy the beauty of a sunset, experience joy or sadness, etc).