Simply defining Gödel Incompleteness and Tarski Undefinability away V46 [x86 is Turing complete]

[olcott]

An abstract machine having a tape head that can be advanced in 0 to
0xFFFFFFFF increments an unlimited number of times specifies a model of
computation that has access to unlimited memory. The technical name for
memory addressing based on displacement from the current memory address
is relative addressing.

The abstract model of computation specified by the x86 language already
has access to unlimited memory when we assume the implementation detail
that the underlying memory architecture of this abstract model is
organized as an unlimited sequence of adjacent 4GB blocks.

The x86 language has control flow instructions having {8,16,32} bit
signed offsets to the current EIP (instruction pointer) value. It also
has data access instructions having {8,16,32} bit signed offsets to the
base register.

Signed {8,16,32} bit Jumps relative to EIP
; Jump to the first address of the next 4GB block
FFFFFFF0: E90B000000

Signed {8,16,32} offsets relative to Base Register
; Moves a 32-bit integer from the first address of the next 4GB block
e4: BBFFFFFFFF mov ebx, 0xffffffff
f5: 8B4301 mov eax, dword ptr [ebx+0x1]

Because both the control flow and data access instructions of the x86
language have relative addressing the x86 language specifies an abstract
model of computation having access to unlimited memory.


--
Copyright 2020 Pete Olcott

[olcott]

I finally explained myself clearly enough to be understood to be
correct. The intuition of the above words were what were in my mind when
I said that these things are blatantly obvious.

Only in the retrospect of this much clearer explanation can it seen that
that what I am proposing really is blantantly obvious.

[olcott]

Since (at least now) after I have sufficiently explained exactly how the
abstract model of computation defined by the x86 language would have
access to unlimited memory is blatantly obvious, some of the more rude
critiques may seem quite foolish.

"To show that something is Turing-complete, it is enough to show that it
can be used to simulate some Turing-complete system. For example, an
imperative language is Turing-complete if it has conditional branching
(e.g., "if" and "goto" statements, or a "branch if zero" instruction;
see one-instruction set computer) and the ability to change an arbitrary
amount of memory..." https://en.wikipedia.org/wiki/Turing_completeness

When we assume that the above is correct then we can conclude that the
x86 language is fully Turing complete by having control flow and data
access to unlimited memory and conditional branch instructions that can
be executed from anywhere in this memory.