I realized the reason you have some differences of opinion is that I did not include Tarski. Some methemeticians stated he really should not be left out. So I added a little to the semantics section to allow for theories of classical and modern realism. Also I added a little on ideas of intent influencing causality, as quite a few people raised issues on that; and clarified why causal truth can only be known not to be false by adding Aristotle's law of excluded middle. Beyond that, if I add anything, I would have to remove something else, because it has rather reached a length limit.
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There’s been much discussion about ‘fake news’ recently, resulting rise to a new interest in the definition of truth. In modern philosophy, truth is defined by formal logic upon propositions (statements). There are three basic kinds of truth evaluation, which I here attempt to express in way compatible with the thinking of the modern philosophers Russell, Whitehead, Moore, Wittgenstein, Tarski, Carnap, Strawson, Putnam, Searle, Mendelson, Kripke, Popper, Kuhn, and Davidson.
- Tautological truths within formal systems, such as mathematical equations. These are established by syntactic consistency with core axioms. The core axioms themselves describe the formal systems, and so truths at this level are necessarily true, in accordance with syntactic rules which are themselves defined in formally as logical propositions. These propositional systems can also define rules of deduction and inference without introducing meaningfulness and causality. While the truth evaluation itself requires some semantic definition of ‘truth,’ in order for the proposition to be assessed, the process of evaluating the proposition’s truth value always requires syntactic analysis alone.
- Empirical truths, which are determined via ratification by observation of material objects, states and events, as long as the propositions describing material states and events are logically coherent. If the observation verifies the proposition, then the RESULT of the observation is factually true, but the proposition itself without empirical ratification remains a proposition that is neither true nor false, and is simply an assertion. The specific and exact nature of truth itself depends not only on facts or data, but also on the epistemological factors relating the proposition to the material world in different metaphysical systems, most predominantly in the theories that define the relation of subject and predicate to objects, states, and events in the physical world. These theories add semantics (the meanings of words) to the syntactic relationships described in first-order logic. 'Internal' states, resulting from consciousness, are also evaluated empirically. The nature of consciousness itself is part of the epistemology.
- Causal truths, which again first must be generally consistent within the rules of propositional calculus, and additionally, they must not contain any syntactic fallacies of deduction or inference. These are the most complicated forms of truth, and the basis of science. They are the most complicated because they involve both syntax, semantics, and additional rules. In particular, causal relationships cannot ever be proven necessarily true. They can only be proven not to be false. That is important because, in proposition logic, Aristotle’s law of excluded middle holds that any statement is either true or false; but in real-world language, there need be no excluded middle, hence, proving that a statement is not false does not imply that it is necessarily true. Metaphysical factors also influence the relation of the subject and predicate's in the cause, to the subject and predicate of the result.
Compound, Contractual, and Scientific Truth
While these are the *basic* forms of truth, the truth of many statements rely on combining two or more these forms together. For example, most commonly believe they know that the sun will rise tomorrow. This is based on empirical observations of many prior days where the sun did rise, leading to the simple second-order deduction that it will rise again tomorrow. Logically, one cannot know whether the belief is true that the sun will rise tomorrow until after the event has occurred. But in most cases, when sufficient empirical validation of many prior similar events has occurred, it is loosely assumed true that the same future event will occur again in the same circumstance. This 'axiom of probabilistic certainty' is the foundation of prediction in much scientific theory. The extrapolation of this axiom is the creation of the scientific method, which is designed to define the minimum number of observations necessary to corroborate a theory. As per the rules for causal truth, theories can only be corroborated and not be proven true; but modern science theory might still call a theory true based on the axiom of probabilistic certainty.
Beyond that, there are some other very specific forms of truth in philosophy. For example, there are 'self-generating' truths in linguistics, such as promises, statements of intent, contracts, and some statements of belief, which all become existent by their own statement. One should be aware these kinds of truth have limitations. For example, after making promises, it becomes true that promises were made, but the truth of the promise itself remains an indirect proposition, and still must be determined within the rules for the three basic forms of truth described above.
Truth in theology, morality, ethics, law, and metaphysics
Much confusion about truth has arisen in these fields, but by the above schema, the nature of truth itself is relatively simple. Theological systems make assertions about that which cannot ultimately be proven; morality strives to define that which is good or bad for an individual; ethics defines that which is good or bad for a society; law strives to define that which is right or wrong; and metaphysics strives to define that which is real. In all these cases the absolute truth of the assertions they make is undefinable. However within each of these disciplines, it is possible to evaluate the propositional consistency of statements within formal systems that they define; and from that, to evaluate the truth of their propositions empirically, within the formal systems themselves. so again, when different propositions within, or across, these disciplines contradict each other, it is not possible to evaluate which are true or false in absolute terms. It is only possible to demonstrate whether the claims by each system are coherent.
The Semantics of Truth
According to all modern logicians, truth is the result of evaluating a proposition, but the relation between truth and the proposition itself can be different depending on epistemological considerations. While one might initially believe the nature of truth to be intuitively obvious, the semantics of truth are complex. This starts with the issue as to whether one believes that tautological propositions are true before any person evaluates them; in which case, the truths must exist independently in some abstract space independent of material reality.
That introduces the metaphysical considerations.
Classical realists hold that Platonic ‘ideas’ do exist independent of perception, and truth is simply known by correlation.
Modern realists state only external material reality exists, and abstractions are simply known by common sense (as a result, many modern philosophers refer to classical realism as
idealism).
Dualists hold that there separate domains of physical materiality and conceptual ideas, both of which exist, and some hold tautologies are
a priori true (are still truth regardless whether they are considered).
Monists hold the known reality is only physical, or only exists in the mind, or something else (such as Wittgenstein's idea of
logical positivism, which holds that language is the only thing which can be absolutely known). Such different perspectives change what is actually known when a truth is ‘discovered.’
Regardless whether truth does exist independently of physical reality,
a priori or not, empirical and causal truths may be properties attached to the proposition which are not ‘discovered,’ but rather ‘assessed.’ These latter cases introduce the meaningfulness of incorrect assessments, and how exactly something can be meaningful if its truth is beyond simple binary evaluation, such as for example, propositions which refer to non-existent objects or which contain metaphors. Thus the semantics of truth are not so simple, and become involved with metaphysical decisions defining the nature of reality, meaningfulness, and the definition of knowledge itself.
There are also three separate positions on causality. Some hold that there is no causality without intent, and that it is otherwise simply a logical inference or deduction. The second main position is that intent does not really exist either, but is only an apparent phenomena created by the physical workings of the world. The third main group say one or both of those ideas are reductionist, and so do not give any meaning to the word 'because.' The different positions on intent may also influence truth evaluation of empirical observations on internal states, such as emotions.
Truth and Post Truth
One of the most advanced thinkers on the semantics of truth is Donald Davidson, who is an absolute anomalous monist (there are only ideas, or mind, or matter, or language, but it cannot be known which). Therefore, he states truth is ultimately undefinable, yet through our ability to reason meaningfully, truth can be known, even if people do not know that they know the truth.
For example, people can know that the sun will rise tomorrow; but they do not know that they knew that until after the sun has risen.
Rhetorical misconceptions have arisen from this, whereby people state what they wish to be true as being true, then strive to find facts to prove that truth afterwards, giving rise to the ‘post-truth era.’ While one might attempt to dismiss such efforts as obviously absurd, it is not so easy, because of the complexities of formal definitions of what truth actually is. As things are, we are likely to be stuck with this problem for a very long time, because the framework of formal truth described here, with the resulting complex nature of truth in science, is far beyond that which most people who ‘just want to know the truth’ are ready to learn