I interpret the Axiom of choice to be a 'prayer to nature' to send me the desired object already made. The axiom refers to my opponents choices that a...
A non-computable real number r refers to a truly random infinite process, and yet the distinction between a truly random infinite process and a pseudo...
Unless 'Living within a simulation' is defined in such a way as to be falsifiable, the hypothesis is meaningless. And yet it is imaginable that the fa...
But what about ontics? If the meaning of a proper noun, say "Elvis Presley", is considered to be a family-resemblance of uses across partially over-la...
In the example of sqrt(2), Alice creates a computer program f(n) for calculating sqrt(2) to n decimal places and sends f(n) to Bob. Bob receives f(n),...
When irrationals are identified as being rational-number generating algorithms, irrationals are obviously well-defined. But of course we are rarely in...
IMO, the heart of the problem is that the notations of both classical and constructive logic do not explicitly demark the analytic or a priori uses of...
Pure and unapplied logic makes no empirical claims and only expresses linguistic rules for rewriting a term. All logically valid sentences are reducib...
In practice, a "non-computable" process, that is to say a truly random process, is indistinguishable from an unknown pseudo-random process, since we c...
The stance that 'knowledge consists of instructions and the ability to follow them' is the epistemological philosophy known as constructivism. In my v...
Recall that the proofs of Godel and Cantor correspond to Turing-computable algorithms. Are you meaning to suggest that a deterministic machine can fol...
Computability isn't a mathematical assumption, rather computability refers to the very activity of construction by following rules. Since mathematical...
A topologically structured set that only possesses the notion of "neighbouring" elements does not in itself possess 'holes', regardless of the finiten...
Well obviously in each case, the terms on the left and right side do not possess the same sense, so are not practically substitutable, so are only sub...
Your intuition is constructively valid, since constructivists identify the real reals with the computable binary sequences, that is to say, the binary...
Identicality isn't a description of appearances, it is an adopted convention that grants the inter-substitution of two or more distinguishable things ...
This expression sounds very anti-realist to my ears. Namely that the past is deducible i.e. in some sense a living construction out of present sense-d...
That only holds if one is a realist about the past who believes that the object of history is an unknowable reality in being unobservable and transcen...
Sort of, yes. Consider the statement "All objects have a temperature at or above zero Kelvin". Interpreted from a realist's perspective, the sentence ...
An anti-realist with respect to time, might say that "nothing can travel faster than the speed of light" is a statement about the grammar of special r...
Is stoicism really a personal philosophy? One of the things i find ironic about conservatives, and especially the more radical christian conservatives...
I think you would be clearer by referring only to the syntactical notion of derivability, since the diagonal lemma does not refer to truth, and neithe...
Whether or not a particular Turing test is appropriate in a given situation is largely a question concerning the breadth of the test. For example, if ...
Yes the Turing test is anthropomorphic, but why is that a problem in the absence of an 'objective' alternative? Not even a logical language can be ide...
Recall that in the Turing Test, a human evaluator has to decide purely on the basis of reading or hearing a natural language dialogue between two part...
The very definition of 'alien' is in terms of the respective entity's tendency or capacity to mirror and predict our stimulus-responses for it's own s...
Self-negation, or perhaps to state more accurately, the potential for self-negation, is a common property of negative universal propositions of meta-l...
In Godel's incompleteness theorem f is taken to be ~Prov('s'), the negative of the 'provability predicate'. It is easy to show via the construction of...
That depends on your notion of truth. Classically, you're right; for truth is not traditionally considered to be the property of a sentence or of it's...
The liar paradox has multiple interpretations and resolutions. For instance, if 'this sentence' is interpreted syntactically as being recursive self-q...
Assertions of change are relative to a notion of identity, which is terminological. For example, suppose that every waking moment is labelled by the c...
Personally, what I think the p-zombie thought experiment demonstrates is that my own feelings, imagination and judgements constitute a substantial par...
What is the relationship between defined subjective beliefs and undefined or unknown physical probabilities? Consider an urn containing N balls, each ...
Probability theory is fraught with problems when interpreted to refer to epistemic uncertainty. Unless one is a psychologist whose object of study is ...
Ghost-in-the-machine metaphysical problems are what happens when a plurality of different phenomenological senses are (mis)interpreted as a plurality ...
The hard problem only exists for naturalists, because they consider the concepts they use to describe the world to be semantically divorced from sense...
Popper might have done better to have restricted the notion of an empirical proposition to one whose domain of realisation is finite and closed rather...
Any purported factual distinction between determinism and randomness isn't clear, in light of the problem of induction and the difficulty in defending...
There exists disagreement as to the extent to which Hume considered the problem of induction to be epistemological versus metaphysical. Considered epi...
It's remarkable that when it comes to simple AI agents such as Amazon Alexa, we tend to avoid attributing beliefs to them because we are confident in ...
To that, one might want to add a long list philosophers who have rejected epistemological foundationalism on the basis of either phenomenological or c...
Any absolute or all encompassing notion of inscrutability is self-inconsistent,something that Quine was presumably aware of. We can only understand th...
What makes you think that subjectivity/objectivity isn't also a property of propositions? Let us suppose that society never spoke of abstract pain, an...
"The observer is the observed", as with a Metaphysical assertion, shouldn't be interpreted as being a report or proposition. Rather, these sorts of st...
The biblical meaning of "Good and Evil" as in 'The Tree of Knowledge of Good and Evil' can be interpreted to mean everything that exists, rather than ...
No. 1 expresses the limitless discursive activity of rational analysis, which can sometimes be represented compactly via an infinite loop like in No. ...
Wittgenstein briefly entertained a somewhat similar idea in the blue book, when he said "apparently it didn't occur to Socrates to enumerate everythin...
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