Does Not Compute
Criticism of p. 37 in The Philosopher’s Toolkit in the section titled ‘Certainty and validity’ the following argument is presented:
1. All humans are mortal
2. Socrates was a human
Therefore, Socrates was mortal
This is an unsound argument. This point is not acknowledged by the authors. The authors only tell us that this argument is deductively valid in that the conclusion follows logically from the premises. A sound argument must have both: true premises and valid logic.
This is technically a valid argument in that the truth of the premises is included in the truth of the conclusion as mentioned by the authors. However, the argument is sound if and only if the premises are also true.
The argument is unsound because the first premise is not true, it cannot be proven to be true, and it cannot be defended. The first premise is really an empirical generalization and should not be used as a premise in a deductive argument as shown by the use of ‘All’ which is a universal quantifier. This type of problem was pointed out by Bertrand Russell in his 1912 book, The Problems of Philosophy.
When the premises are known a priori, deduction is the correct mode of argument. When the premises are based on empirical knowledge, induction is the correct mode of argument. An a priori proposition does not need to be tested with observations to conclude that it is always true. Empirical knowledge is that which is gained through observation and testing. The statement “all humans are mortal” is really an empirical generalization made about all humans. Such a generalization can only be based on observations. However, we have not observed all humans. We do not know what the longevity of a human might be in the future. It does not logically follow that just because every human has died that every human born in the future will die. We cannot defend “all humans are mortal” as a priori knowledge nor can we defend it based on empirical grounds due to our limited number of observations.
We have observed many humans and all of them have turned out to be mortal. We thus have good reason to believe that every single human being who was born has died, we know of no examples to the contrary. If Socrates was human, then we can infer that he was probably mortal. This is actually a stronger argument because we do not have to defend the proposition that “all humans are mortal”. However, we can defend the conclusion that Socrates was probably mortal based on the inference that we can make based on our actual observations. In fact, the probability that Socrates was mortal is actually higher than the probability that “all humans are mortal”. As Bertrand Russell pointed out, any empirical generalization is less certain than the actual individual observations because each of the individual observations can be verified, the generalization cannot be verified. Put another way, we can say that the probability that Socrates was mortal is actually higher than the probability that “all humans are mortal” because it is obvious that if “all humans are mortal”, so was Socrates but if Socrates was mortal it does not follow that “all humans are mortal.”
Here is the argument restated as an inference:
1. All observed humans have been found to be mortal
2. Socrates was a human
Therefore, Socrates was probably mortal
Interestingly, the authors do address the problem of universal claims on P. 48 with the statements “no human is immortal” and “…it always remains logically possible that one of the surviving humans is immortal…” to adduce the argumentative problems created with the use of universal claims but never relate this back as a corrective to the presentation on p. 37.
Criticism of p. 61 in The Philosopher’s Toolkit in the section titled ‘A Complication’:
The author’s engage in misplaced ontological reductionism. It does no good to reduce the objects of common experience to the molecular, atomic or subatomic level because these levels of existence, though real, are not the levels at which we interact with in the everyday world of common experience. They are outside of the relevant range of our common experience. It does no good to say that a table is not really the table as we see it because it is really nothing more than a logical construction based on a collection of atoms or the vibratory patterns of molecules in lattice structure. Our interaction with the table is at our casual level, our level of experience and existence. Our causal level is the same level of existence as where our sense perceptions are operative. We interact with tables as solitary units ascertainable by our sense perceptions. We do not sense at the molecular or atomic level of existence. This sort of ontological reductionism is a mistake and leads us away from dealing with the world at the causal level that is within the relevant range of our common experience. Such reductionism is appropriate to the laboratory, not to our common experience. Such ontological reductionism is an incorrect conflation of different levels of existence that leads to confusion about the nature of existence. A table is not just a logical construction in the way that we can say society is a logical construction made from the existence of individual human beings in a community. This logical construction is sensible in that it is derived from that which already exists at the casual level, human beings, which are within the relevant range of our common experience. It is a mistake to represent the table as a mere logical construction from which it is ultimately made, atoms etc., because atoms do not exist at our causal level or within the range of our common experience. Where does such a logical construction start and stop? Are we to say that the table is a mere local construction of the vibratory patterns of molecules in lattice structure and that these molecules are in turn the logical construction of atoms and that the atoms are in turn a mere logical construction of subatomic particles? If any of these exist, then all of these exist and can be experienced as real at their appropriate level of existence, at their appropriate causal level.
Nor can we think about atoms and quarks as logical constructions of the things that compose our ordinary, common-life world as the authors’ further state. This is the same mistake, in reverse, of representing the table as a mere logical construction of molecules, atoms or subatomic particles as described above, viz., the incorrect conflation of different levels of existence that leads to confusion about the nature of existence and experience. Tables are not the logical construction of, atoms and atoms are not the logical construction of tables. Each exists, but at a different causal level of existence. Each exists, but only within a relevant range of common experience. Atoms, as the mode of existence, is the relevant level of existence for the laboratory and tables, as solitary objects, is the relevant level of existence for the living room.
Again, interestingly the authors do hint at this problem on P. 129 with the statements “The liquidity of water is not apparent in its microstructure, but that does not mean that the description of water as H2O is inadequate or mistaken…” and further “…because to ascribe a chemical structure to water is not to deny water’s liquidity – liquidity not being a property of atoms.” These statements are precisely correct but never related back as a corrective to the presentation on p. 61. These statements implicitly recognize that a material thing can have existence that is relevant at different levels of existence-perception and that any given level of existence-perception is not the mere logical construction of a different level of existence-perception. Each is real, but only at its appropriate and relevant range of common experience.
On page 173 it is stated “– the law of excluded middle – which holds that a statement must be either true or false, but not some third alternative (see 3.3).” From reading section 3.3, the statements on page 173 seems to be a statement of bivalence, or a conflation of bivalence and the excluded middle.
From 3.3:
Excluded middle rule: For any P, P or not-P must be true
Bivalence rule: Every statement is true or false.
On p. 173, would not be better to state that the fundamental principle of rationality is that of bivalence, not the excluded middle? As stated in section 3.3, “Note that the principles of excluded middle and bivalence are not equivalent, since the former involves the concept of (‘not’), whereas the latter does not.”
Section 4.4:
Can we further distinguish ontological objectivity and subjectively from epistemological objectivity and subjectively? As pointed out in the text, many people will state that politics or mortality or ethics is entirely subjective and there can be no objective answers and that only science is objective. It seems to me that the concept of ‘intersubjectivity’ may perhaps rest on the confusion between ontological objectivity and subjectively with epistemological objectivity and subjectively. There very well may be an equivocation in that the terms objective and subjective are used to mean ontology at one point and then epistemology at another point in such statements.
Ontology is about existence. Epistemology is about knowledge, or what we know about what exists. There are ontologically objective phenomena that are observer independent such as the material reality of the world, e.g., the existence of particles, atoms, mountains, lakes etc. Ontologically subjective phenomena are also things that do exist but are observer dependent such as, pain, happiness, love. Morality, ethics, politics are ontologically subjective. They exist but they are observer dependent. For example, pain is real but it is ontologically subjective, it is a subjective experience. Does this mean that we can know say nothing or do nothing objectively about pain? Pain is still epistemologically objective. This is the basis on anesthesiology. Therefore, it does not follow that ontologically subjective subjects are also epistemologically subjective. Epistemology is about knowledge and we can thus come to know objective facts about ontologically subjective subjects such as politics, ethics and pain.
We can have epistemologically objective knowledge, facts and analysis, about things that are ontologically subjective such as politics, morality and ethics. The social sciences and humanities cannot be dismissed as purely subjective because they are ontologically subjective. Human choice is a subjective reality (ontology) about which we can derive objective knowledge (epistemology).
Section 5.6, Leibniz Law:
The law is correctly stated as: “X is identical with Y, if and only if every property of X is a property of Y and every property of Y is a property of X”. This is found on page 205. It is further stated on page 205, “In any case, for most practical purposes the principles seem obviously true, and do similar work.”
I do not believe that it we should be so quick to state that Leibniz Law is obviously true. I am not sure what is meant by “…for most practical purposes…”
Here is the problem:
Leibniz Law: “X is identical with Y, if and only if every property of X is a property of Y and every property of Y is a property of X.”
From Leibniz Law it follows that X can be substituted for Y and Y can be substituted for X.
Leibniz law is essentially one of substitutability of co-referential statements. However, there are examples of where the basic principle of substitutability fails. Sometimes expressions referring to the same object are not substitutable as it follows from Leibniz law. If the truth of a statement is dependent on how an object id referred to, the principle of substitutability will fail. W.V.O. Quine referred to the failure of substitutability as referential opacity.
Here is an example of how the principle of substitutability fails from John Searle:
Statement 1: The number of planets is eight
Statements 2: Eight is greater than seven
By substitution of the subject from Statement 1, “The numbers of plants” for the subject of statement 2, “Eight” it necessarily follows that the number of planets is greater than seven.
Actually, this does not follow. There is nothing necessary about the number of planets being eight. It just so happens to be the case that the number of plants is eight, but it is not necessarily so. Until recently the number of plants was nine and we would have falsely concluded, via this same principle, that there must necessarily be nine planets.
Statement 1: The number of planets is nine
Statements 2: Nine is greater than eight
By substitution of the subject from Statement 1, “The numbers of plants” for the subject of statement 2, “nine” it necessarily follows that the number of planets is greater than eight.
My own example,
Bruce Wayne is identical with Batman. Every property of Bruce Wayne is a property of Batman and every property of Batman is a property of Bruce Wayne.
Just because Batman is Bruce Wayne it does not follow that Commissioner Gordon, Chief O’Hara, The Joker, The Riddler, The Penguin and the rest of the hoard believe that Batman is Bruce Wayne. Batman cannot be substituted for Bruce Wayne and Bruce Wayne cannot be substituted for Batman for this hoard of characters as it is the case for Alfred. In this case, the expression referring to the thing is not substitutable. Batman cannot be substituted for Bruce Wayne. No one knows that the properties of Batman and Bruce Wayne are identical. Since they do not know that Bruce Wayne is Batman, substitutability does not hold thus Leibniz Law cannot be said to hold or be applicable in this case. Bruce Wayne and Batman remain two different individuals with different properties for the Commissioner Gordon, et. al. The separate identities of Bruce Wayne and Batman depend on the failure of the principle of substitutability and if we can say that the principle of substitutability is the main requirement for identity within Leibniz Law, can say that Leibniz Law does not hold?