6

Abstract mathematics doesn't have to be related to physics. There are many things that mathematicians routinely consider (such as non-measurable sets, etc) that cannot possibly exist in the physical world. In particular, the laws of the physical world have no bearing on the P=NP problem.


5

This would wildly depend on how one would exactly define "complexity" and how it would be quantified. Equally one would have to develop some objective metric for "self consciousnesses" as well. The specific answers would depend largely on the specific metrics. However most reasonable metrics for complexity would likely be "monotonic", i.e. the complexity of ...


4

This line of thought has a rich tradition in philosophy. One potential way to gain empirical evidence one way or another is through the famous Turing Test, which challenges a computer to successfully imitate the perceptible output of human thought processes effectively enough that a human being would be unable to tell the difference. To the extent that a ...


4

Arthur Schopenhauer is probably the most notable example of a Western philosopher who praised ideas from the Buddhist tradition. He explicitly compared his own theory of the human will to the "Four Noble Truths" of Buddhism. While American Transcendentalism was more of a cultural than a philosophical movement, that might be another case where prominent ...


3

It's very hard to understand what a connection between the analytic/synthetic distinction and computational complexity could mean. As an example objection to the idea: if you are saying that synthetic statements are somehow equivalent to an NP-complete question, how would you handle the statement: New Orleans is the largest city in Louisiana. What is NP-...


3

Positivism is a form of empiricism, and as such, is antithetical to rationalism and Plato's theory of forms, and eventually with any system that asserts the existence of a reality independent of and beyond the senses. More recently, in the 20th century, several schools, such as phenomenology, existentialism, sturcturalism, postmodernism, and (...


3

A deterministic universe might not be a quantum universe, in which case algorithms like Shor's algorithm would be impossible; whether there will be a quantum or post-quantum method for solving NP problems in P-time is unknown. Suppose that there is. This won't mean that P = NP; Shor's algorithm is in complexity class BQP: bounded error quantum polynomial ...


3

I had some heated arguments with “emergentists”, who tend to define strong emergence as something like: Strong emergence (definition 1): a property of the system that can not be derived from the properties of its parts and their effects on each other when so combined. Of course, using this definition, strong emergence would obviously exist. But in my ...


2

Compare this with the question: what makes something heavy? If someone can eventually, in a small amount of time, lift it, is it no longer heavy? Obviously some people can lift heavier things than others. The key word is heavier. There may not be an absolute property of heaviness, but there is certainly a relative one, which corresponds more or less to how ...


2

Compare the complexity classes BQP (quantum) and BPP (classical). You might be more acquainted with P vs. NP; note that BPP ⊆ BQP and we don't know how BPP relates to NP. BPP is a probabilistic version of P. According to the BQP model of quantum computation, quantum computers are merely faster at solving some kinds of problems. I mean two things by using the ...


2

Arguably, the historical importance of the argument from design has been distorted by its centrality in the writings of biologist and anti-theologian Richard Dawkins, who has been vocal about his belief that it is unanswerable outside of the Theory of Evolution. It's far from clear that either the religious or the scientific establishment of the time gave ...


2

'Jobermark' got it right when the question is answered within philosophy of science. Kuhn's revolutionary view of scientific progress is the opposite to the linear view of logical positivists (or logical empiricists). Logical positivist theories (e.g., Carnap's confirmationism and Popper's falsificationism) shared the idea that science progresses in a ...


1

In quantum mechanics we describe waves of probability or probability distributions. Does this have to or should it be conceptualized as more of an abstract principal or can we intuit that the probability distributions exist in an already computed (So to speak) form that is superposition? What you are touching upon here is the issue of scientific realism vs ...


1

Quantum complexity theory exists and it is one of the fastest growing fields in computer science. The answer to how this occurs will come out of an elaboration on your first question, the question of how do we treat the ontological status of probability amplitudes. In quantum mechanics we deal with what are called probability amplitudes. Probability ...


1

I think it's crucial to see here that all computational problems whether be in any classified complexity are always analytical. Well defined mathematical problems (that can be computed) need to be tautological in the sense linguistic expressions are, just as the provided example of bachelors. Whether it be prime factoring or addition their algorithms are ...


1

Just because we evolve, does not mean the evolution is happening due to random chance. There could be force of divine mind behind the evolution. I for one am not convinced that anything in the universe is truly random unless it was specifically designed to be so ( to make it more interesting ) Remember randomness is just a perspective - in other words it ...


1

Finally, I found what I was looking for. That's Evolutionary Epistemology.


1

Swami Vivekananda (late 19th century) commenting on the Design Theory (Complete Works, V6, pp 97-98; available here under the heading Notes of Class Talks and Lectures, subheading The Design Theory - http://cwsv.belurmath.org/volume_6/vol_6_frame.htm): The idea that nature in all her orderly arrangements shows design on the part of the Creator of the ...


1

There are several meanings for "reductionism" that people apply. However, in philosophy "reductionism" typically means "ontological reductionism," the idea that A is B. For this particular meaning, computational complexity does not figure into their thinking. Either A reduces to B, or it doesn't (such as if the reduction would require a computational ...


1

I am responding in a general way to your question and subsequent comments. Though I am not sure how well defined "complexity" and "systems theory" really are, one philosopher who may interest you is Nicholas Luhmann. He develops a "systems-based" ontology in which his fundamental terms are System/Environment. He employs this largely in descriptions of social ...


1

As I now understand your comments your intention is to consider philosophy as a whole and to investigate the characteristics of this discipline. Such enterprise belongs to the domain of philosophy of science. I would break down your original question about the essence of philosophy into the following subitems: What are main questions philosophers deal ...


1

Firstly, Complexity means approaching a problem from a higher-level (i.e. higher-order) perspective, much like economists look at the economy: detached and analytical. Unfortunately, it's prone to the same problems of that field -- excessive application of purely mental modes of understanding. Secondly, Complexity expresses an interest of how complexity ...


1

Saying 'computers can think', meaning: thinking is really just mechanical. Or else, meaning: computers are becoming really sophisticated, having near human behaviour. Neither of these things is really true. Thinking, thoughtfulness is by definition not mechanical. And no matter how sophisticated or advanced we consider computer behaviour, can you even ...


1

1) I highly recommend reading the book "Intelligence" by Jeff Hawkins 2) As for the Turing Test, it said nothing about how the computer performed the actions and it had nothing to do with emotions. It was simply whether or not a judge could discern between a computer (a "machine") and a human based on answers to questions. 2a) In practice (...and I've ...


1

The question whether P=NP has no bearing on whether processes are deterministic are not, only on the relative amount of effort that deterministic vs. nondeterministic stepwise processes may take to arrive at solutions to particular types of problems. The nondeterminism considered is always limited to a finite, enumerable choice of alternatives, so for any of ...


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