Jon, thank you! A very good example. "There is not a unicorn that is not pink" is true, but "Every unicorn is pink" is not true. This example at last has made me a believer in the relevance of intuitionistic logic.
Best, Helmut
30. Januar 2021 um 20:58 Uhr
"Jon Alan Schmidt" <jonalanschm...@gmail.com>
wrote:
"Jon Alan Schmidt" <jonalanschm...@gmail.com>
wrote:
Helmut, Edwina, List:
There are at least three different ways of translating the natural-language sentence, "a human is a featherless biped," into a proposition in formal logic.
- Some human is a featherless biped.
- Every human is a featherless biped = if something is a human then it is a featherless biped.
- Every human is a featherless biped and every featherless biped is a human = something is a human if and only if it is a featherless biped.
#1 is a "singular description," #2 is a general assertion, and #3 is an _expression_ of complete equivalence. #2 is merely a partial definition since it allows for the possibility of featherless bipeds that are not humans, which are presumably distinguished in some other way; it is only falsified by the existence of a human who is not a featherless biped. Of course, the same is true of "there is not a human who is not a featherless biped," which is why this (scribed as nested ovals) is equivalent to #2 (scribed as a scroll) in classical logic.
However, that is not the case in intuitionistic logic--from "if human then featherless biped" we can infer "not both human and not featherless biped," but not the other way around. Why? If there were no actual humans, then the latter would be true but not necessarily the former. For example, it is true that "there is not a unicorn that is not pink" because there are no actual unicorns, but we cannot infer from this that "every unicorn is pink." On the other hand, since by definition "every unicorn has a single horn," it does follow that "there is not a unicorn that does not have a single horn."
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
On Fri, Jan 29, 2021 at 2:54 PM Helmut Raulien <h.raul...@gmx.de> wrote:
Edwina,yes, "a human is a featherless biped" might be understood as singular description. I meant it as definition, so it is better to say "a human is defined as featherless biped", which is a proposition, a description of a status, and not yet a law. The semiosis of habit-formation goes 1-2-3, and the semiosis of reflexion the other way, so, yes, I agree, that it neither is correct that 2ns is more fundamental than 3ns, nor the other way. But I think logic is reflexion, so in this case 3ns (law, conclusion, the scroll) is primary to 2ns (actuality, proposition, nested ovals). With "more fundamental" I just was refering to the question in this thread about what is primary to what. I still am quibbling with the reason for intuitionalistic logic. But it is somwhat hard to show a primarity that cannot be illustrated with examples, as there is no loss or gain in meaning, merely a by me suspected academic rule, that logic is reflexion, and in reflexion 3ns comes before 2ns. But all in all I am merely suspecting and tentatively trying this and that.Best, HelmutHelmut - if you read Peirce's cosmological outlines [6.203 and 1.412], he begins with 1ns, moves on to the instantiations of 2ns, and then, into the developing habits of 3ns. So, the 'actualization' of the modes in spatiotemporal existence is linear.
But - all three modes are potential and necessary, therefore, I don't think that one can say that any one of them is 'more fundamental'.
And I'm not sure how a singular description of a variable [A human is a featherless biped] can be transformed into a sound deductive argument [IF it is a featherless biped THEN it is human]. As you point out, the connection of the attribute [featherless biped] might not always apply to the variable of 'human'.
Edwina
On Fri 29/01/21 11:02 AM , Helmut Raulien h.raul...@gmx.de sent:All,I think, the difference is not the meaning, but what it is. Though the double negation´s meaning is the same as the conclusion´s meaning, the double negation has the form of a proposition, or a definition, which is secondness: "There is not a featherless biped that is not a human" may be classificationally instantated from exclusion of exclusion to definition: "A human is a featherless biped". The conclusion "If it is a featherless biped then it is a human" may be individually instantated to an argument; "It is a human because it is a featherless biped". It is thirdness, a rule or law. Which of both is more fundamental? Both mean the same, so if one changes, the other changes too. But which is more likely to change? The law "If it is a featherless biped then it is a human" cannot change just so, by itself. But the situation, the secondness, the truth of the proposition "There is not a featherless biped that is not a human" can easily change, and make the law obsolete, e.g. if an ape quits using its arms for walking, or if a dog sadly has two legs amputated, or if a chicken, due to a mutation, is born without feathers. So, is the double negation more fundamental, because it breaks the law? People will say, that the ape is just stupid, the chicken and the dog are just handicapped, exceptions only corrobate the rule, and all people who claim that the law is no longer in charge are heretics. A law (3ns) is more tenacious than actualities (2ns), that first have to prove worthwile one by one to add up to a certain measure, so is it more fundamental?Helmut
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