Note that the calculator cannot consciously distinguish between which thoughts are perceptions, concepts, or memories. It is only conscious of what is shown within its ten visible digits.

Due to the fact that the calculator has only twelve "working" digits and thirteen possible locations for the decimal place, it has a finite number of possible conscious thoughts, with many of these come at by different ways of thinking. Let's call these its "library". In fact, any of its conscious thoughts can be either a memory, a perception, or a concept arrived at by many different unconscious calculations. The numbers shown before calculating and those shown after calculating cannot be given a necessarily one-to-one relationship.

Let's look at one such unconscious process: the method of calculating square roots. In order to do this, a number is either keyed in, used from a previous calculation, or brought up from memory; in which case, there is the initial conscious thought which is the number for which its square root is to be calculated. Then, when the square root key is used, there is a fully determined set of actions performed which end when twelve digits are arrived at which do not change after more calculating. The first ten of these twelve are shown; the conscious thought which the calculator recognizes as the square root.

Here, we have what might be considered a problem, because not all square roots of the numbers within the calculator's library have (only) ten, or even twelve, actual digits. In fact, most are not even rational; they have an infinite number of actual digits. Perhaps we are given an extra notation, a dash set above one or more terminating digits in the visible field which denotes that all digits after the ten shown repeat those under the dashes. Even given this, the library is still of finite length, and there are non-repeating square roots which the calculator cannot show.

In this sense, the calculator is inherently consciously erroneous in some of its calculations. We might say that it is "flawed". This flaw or others are possible to show in any of its kinds of calculations. If one were to add 5000000000 to 5000000000, perhaps a special light could be shown which designates the result as a number which it not within the calculator's library. A similar multiplication would give the same result. If a non-repeating square root is found, however, the calculator only shows the ten digit approximation for the actual number. Unless the light is shown for every answer that is only a ten-digit approximation of a longer number or the repeating-decimal notation can be correctly used, the calculator cannot be conscious of its error in calculating the square root.

Let's now change scope and consider the human mind. For argument's sake, let's accept the view that the mind has a subjective "I" within it that perceives through the bodies senses, its memories, or from unconscious thinking.

This "I" can neither experience a sensual perception outside of the scope of the body's senses, remember something which is not held in the body's memories, nor have a thought which is beyond the body's ability to conceptualize. "I" can neither see in the ultraviolet range, remember the sinking of the Titanic, nor imagine a square circle. In this sense, the "I" of the mind is bounded, if not finite. Certainly, the number of possible conscious thoughts which a mind can have in the lifetime of its body is finite.

If we equate a single thought experienced by the "I" of the mind with the visible digits on our calculator, then we can say that this "I" is also inherently consciously erroneous in some of its thinking. This is inevitable when we only consider the mind trying to do the calculations of a calculator. "I" can never find the complete square root of 2, for instance. No matter how many digits of the number that can be memorized or calculated, what is perceived finally by the mind as the square root of 2 is always only an approximation for the actual number.

If we take the calculator as an example of a machine using pure mathematical logic to come to conclusions, we can say that no calculator can come to always true conclusions or that all calculators must end their calculations at some point and allow an approximation for a true value.

Likewise, even if the "I" of the mind can use pure reasoning to come to conscious conclusions, we can say that no mind can come to always true conclusions or that all minds must end their unconscious conceptualization and allow an approximation for a true conclusion. In fact, given that the mind is never conscious of the difference between things which it can experience and those things which it cannot, there are thoughts of which it cannot be conscious of its approximation as an error.

At best, when given numbers with fewer than ten digits and calculations that do not raise the number of significant digits of the answer beyond ten, a calculator can give true answers.

Likewise, when given perceptions or ideas within the scope of the body's senses, memories, or concepts and logical processes of conceptualization; a mind can perceive true thoughts.

It is the problem of finding the scope of the body's senses, memories, and concepts and defining acceptable logical processes of conceptualization which can give us the knowledge of what thoughts are true. The mind (more exactly, the "I" of the mind) can never be trusted in itself to know whether its thoughts are true.