The strange world of quantum mechanics seems to have a natural appeal to irrational and foolish people like Postmodernists and others who deny objective empirical truth or the laws of thought.
In arguments with such people when you defend the reality of real objective empirical truths, you will frequently find such people immediately appealing to various weird phenomena in quantum mechanics to defend themselves. “Doesn’t quantum mechanics prove that there is no objective truth?,” they might say.
The use (or, rather, abuse) of quantum theory in this manner is deeply mistaken and fallacious, however, for the simple reason that what is true for, and actually does happen in, the infinitesimally small world of quantum mechanics need not be true at all for large objects in the macroscopic world in which human beings live. Let us take one example: abuse of quantum mechanics in attempts to dismiss the laws of logic.
For example, in the Schrödinger’s cat thought experiment, a cat is imagined as being both alive and dead simultaneously, because it is imagined as being in a state of quantum superposition.
Now, if it were true that a cat could naturally be in such a state, wouldn’t this disprove the Law of Noncontradiction, the law of logic that one cannot assert as true at the same time (1) a proposition p and (2) its negation (¬p) (or, that is to say, one cannot assert p ∧ ¬p without fatal self-contradiction)?
The answer to this lies in asking: how realistic is the Schrödinger’s cat thought experiment? Actually, there is no rational reason to think large macroscopic objects like cats could ever naturally be in a state of quantum superposition at all: the Schrödinger’s cat thought experiment is abstract, unrealistic and not possible in nature (Newton 2000: 166).
To cite some recent research here, some physicists have found evidence that time dilation effects caused by gravity cause the natural collapse of quantum superpositions in objects the size of molecules and larger objects, and that on a system like the Earth (with a given gravity), even with current technology, the size limit for an object in a state of quantum superposition is about a millimetre (which actually seems to be surprisingly large!). Of course, scientists might use better technology to overcome this natural limit in experiments and so create larger objects in a state of quantum superposition, but this is obviously a highly artificial activity that does not – as far as we know – happen in nature.
So the point is: whatever weirdness that happens at quantum scales in nature stays there and does not naturally intrude into our macroscopic world, so that it does not invalidate or refute the laws of logic as applied to the natural macroscopic world. Nor does it refute the arguments for real objective truth or the laws of logic when the latter are carefully restricted to the correct domain in which they operate: the natural macroscopic world of human life and large objects in it.
BIBLIOGRAPHY
Gerry, Christopher C. and Kimberley M. Bruno. 2013. The Quantum Divide: Why Schrödinger’s Cat is either Dead or Alive. Oxford University Press, Oxford.
Newton, Roger G. 2000. Thinking about Physics. Princeton University Press, Princeton, N.J.
Pikovski, Igor, Zych, Magdalena, Costa, Fabio and Časlav Brukner . 2015. “Universal Decoherence due to Gravitational Time Dilation,” Nature Physics
http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3366.html
Showing posts with label Laws of Logic. Show all posts
Showing posts with label Laws of Logic. Show all posts
Sunday, October 4, 2015
Monday, September 9, 2013
The Laws of Thought
The Laws of Thought (or Laws of Logic) are fundamental to good argument, and are often violated or misunderstood, and a fascinating question is: what is their epistemological status?
The Laws of Thought can be set out as follows:
There are of course many other tautologies important for deductive logic, such as De Morgan’s theorems, but the laws of thought remain fundamental.
But, as noted above, what is their epistemological status? Are they simply analytic a priori? And even if we can interpret them in that sense when considered only as pure tautologies, could they also be given an empirical synthetic a posteriori status when asserted as true of the real world? (just as pure geometry and applied geometry each have a different epistemological status.)
For it seems that the law of identity also expresses, or is bound up with, a deep metaphysical truth about existence: existence and identity are closely related concepts, as was stressed by Gottlob Frege and Quine (Scruton 1994: 143).
Indeed, Bertrand Russell gave the laws of logic an ontological interpretation:
That is to say, surely it is not unreasonable to assert that “every thing that exists is identical with itself” is, in the end, an empirical observation of the fundamental nature of the world of human experience. Of course, we cannot even conceive of how it could be false, but then human beings most probably could not conceive of the counter-intuitive truths of quantum mechanics until the 20th century.
Even in the realm of the laws of thought, when these laws are asserted as truths of the real world, they arguably must be considered empirical.
Links
“Law of Thought,” Wikipedia
http://en.wikipedia.org/wiki/Three_classical_laws_of_thought#Aristotle
“Law of Noncontradiction,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_noncontradiction
“Law of Identity,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_identity
“Law of Excluded Middle,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_Excluded_Middle
BIBLIOGRAPHY
Scruton, R. 1994. Modern Philosophy: An Introduction and Survey. Penguin Books, London.
Quine, W. V. 1986. Philosophy of Logic (2nd edn.). Harvard University Press, Cambridge, Mass.
The Laws of Thought can be set out as follows:
(1) the Law of IdentityIt is also generally believed that laws (1) and (3) are tautologies.
This can be stated simply as the idea that any entity x is identical with itself (or x = x). With respect to propositions, it means that, if a proposition p is true, then it is true (or p → p).
A violation of the Law of Identity is the informal logical fallacy of equivocation: changing the meaning of terms in an argument or using the same term in different senses.
(2) Law of Noncontradiction
This can be stated as the idea that one cannot assert as true a proposition p and its negation at the same time (or p ∧ ¬p is false). Such a statement is self-contradictory. That is to say, the proposition p and its negation (¬p) asserted as true at the same time are mutually exclusive.
The source of the Law of Noncontradiction is Aristotle’s Metaphysics, although he gives three versions of the law, in (1) an ontological, (2) psychological and (3) logical sense.
(3) the Law of Excluded Middle
This states that every meaningful proposition is either true or false. There is no third option. Put another way, either the proposition p is true or its negation (¬p) is true. Symbolically, this means that p ∨ ¬p must be true.
There are of course many other tautologies important for deductive logic, such as De Morgan’s theorems, but the laws of thought remain fundamental.
But, as noted above, what is their epistemological status? Are they simply analytic a priori? And even if we can interpret them in that sense when considered only as pure tautologies, could they also be given an empirical synthetic a posteriori status when asserted as true of the real world? (just as pure geometry and applied geometry each have a different epistemological status.)
For it seems that the law of identity also expresses, or is bound up with, a deep metaphysical truth about existence: existence and identity are closely related concepts, as was stressed by Gottlob Frege and Quine (Scruton 1994: 143).
Indeed, Bertrand Russell gave the laws of logic an ontological interpretation:
(1) law of identity: ‘whatever is, is.’Russell thought that these were “self evident logical principles,” but the possibility that the law of excluded middle may not apply to certain quantum mechanical phenomena (Quine 1986: 86–87) should alert us to the idea that the laws of thought are ultimately empirical statements derived from human experience of the macroscopic world. (And this does not falsify the law of excluded middle with respect to the macroscopic world at all, but confines or limits it as a truth to that domain.)
(2) the law of contradiction: ‘nothing can both be and not be.’
(3) the law of excluded middle: ‘everything must either be or not be.’
That is to say, surely it is not unreasonable to assert that “every thing that exists is identical with itself” is, in the end, an empirical observation of the fundamental nature of the world of human experience. Of course, we cannot even conceive of how it could be false, but then human beings most probably could not conceive of the counter-intuitive truths of quantum mechanics until the 20th century.
Even in the realm of the laws of thought, when these laws are asserted as truths of the real world, they arguably must be considered empirical.
Links
“Law of Thought,” Wikipedia
http://en.wikipedia.org/wiki/Three_classical_laws_of_thought#Aristotle
“Law of Noncontradiction,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_noncontradiction
“Law of Identity,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_identity
“Law of Excluded Middle,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_Excluded_Middle
BIBLIOGRAPHY
Scruton, R. 1994. Modern Philosophy: An Introduction and Survey. Penguin Books, London.
Quine, W. V. 1986. Philosophy of Logic (2nd edn.). Harvard University Press, Cambridge, Mass.
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