• =?UTF-8?Q?Simply_defining_G=c3=b6del_Incompleteness_and_Tarski_Unde?= =

    From olcott@21:1/5 to All on Wed Aug 19 17:06:51 2020
    XPost: comp.theory, comp.ai.philosophy, sci.lang.semantics

    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

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  • From olcott@21:1/5 to olcott on Wed Aug 19 19:44:44 2020
    XPost: comp.theory, comp.ai.philosophy, sci.lang.semantics

    On 8/19/2020 5:06 PM, olcott wrote:
    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.


    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.


    --
    Copyright 2020 Pete Olcott

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  • From olcott@21:1/5 to olcott on Thu Aug 20 10:23:42 2020
    XPost: comp.theory, comp.ai.philosophy, sci.lang.semantics

    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.

    On 8/19/2020 7:44 PM, olcott wrote:
    On 8/19/2020 5:06 PM, olcott wrote:
    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.


    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.




    --
    Copyright 2020 Pete Olcott

    --- SoupGate-Win32 v1.05
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