Some Notes on A. J. Ayer’s version of Logical Positivism Chapter One of



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Some Notes on A.J. Ayer’s version of Logical Positivism
1. Chapter One of Language Truth and Logic

1.1. Some Important Distinctions


Here we discuss: (1) the analytic/synthetic distinction, the a priori/a posteriori distinction, and (2) in principle verifiability versus verifiability in practice, and weak versus strong verifiability.
  

The following are definitions that we, for now, will take any philosophical account to need to accommodate.  Thus, in a slightly anachronistic way, we will present Kant, Mill, and Ayer as agreeing on these definitions but characterizing the notions defined differently.


(1) A proposition P is analytic if, and only if, P is true (or false) solely in virtue of the meanings of the words in P (and the principles governing the way those words are put together to make P).
One way to test for a sentences being analytically true is to consider if it is possible for the sentence to be false without changing the meaning of any of the words in the sentence.  If it is not possible to do this, then we have good evidence that the sentence is analytically true.
Prima facie examples-
Mathematical truths such as “2 + 2 = 4.”
Linguistic truths such as “All bachelors are unmarried.”
Logical truths such as “Either Jon smokes, or Jon doesn't smoke.”
(Note- This test isn't always sure-fire, as Kant thought mathematical and geometrical truths were synthetic.  Without getting into heavy duty Kant exegesis we’ll see why one might take mathematical and geometrical truths to be synthetic.)
(2) A proposition P is synthetic if, and only if, P is true (or false) in virtue of the meanings of the words in P (and the principles governing the way those words are put together to make P) and the way the world is.
A good test to see whether a sentence is synthetic is to see if it can be made false by the world being different than the way it is when the meaning of the words is held fixed.  Consider the sentence, “George Bush is President.”  This could be false even when the words meant the same as they do now, but the world was such that Dole had gotten elected.
(3) A proposition P is a priori if, and only if, P can’t be proven (or disproven) from experience, even though experience may be needed in order for us to know it
(4) A proposition P is a posteriori if, and only if, P can be proven (or disproven) from experience.
Ayer thought that there were no synthetic/a-priori truths, and no analytic/a-posteriori truths.  That is all truths are either synthetic/a-posteriori or analytic/a-priori.  He also thought that synthetic truths were all verifiable, but we will need to consider some other distinctions to get clear on this claim.  This will be discussed below.
Importantly, the analytic/synthetic distinction is a semantic distinction; it only concerns what makes sentences true or false.  The a-posteriori/a-priori distinction is an epistemological distinction; it concerns what justifies our knowledge of the truth of certain sentences.
 

1.2. Verificationism


Now we can turn to the different senses of verifiability that Ayer works with.  We start with verifiability in practice.
(1) X is verifiable in practice if and only if we can actually verify or falsify X with the means currently at our disposal.
For example, I can currently falsify the sentence “There is a cat on my desk” right now.  I look on my desk and there is no cat.  Thus, the sentence “There is a cat on my desk”  is verifiable in practice.  The sentence, “There is a cat in front of my apartment” is also verifiable in practice, as I currently possess the means to go determine whether or not the sentence is true.

In-principle verifiability is defined in this manner.


(2)  X is in-principle verifiable if and only if, if our capacities and technologies were finitely extended then we could verify X.
The sentence, “The 10 raised to the billionth power raised to the billionth power raised to the billionth powerth even number is the sum of two primes,” is not in practice verifiable, but it is in-principle verifiable.  Or consider sentences about planets in galaxies far away, they are not verifiable in practice but are verifiable in principle.  Every sentence that is verifiable in practice is verifiable in principle, and many sentences that were only verifiable in principle become verifiable in practice as technology and mathematical techniques get better and better.

Strong verifiability is defined in this manner:


(3)   X is strongly verifiable if and only if X can be determined to be true or false with certainty.
Ayer holds that very few propositions are strongly verifiable in this manner.  Good examples come from mathematics.
Weak verifiability is defined in this manner
(4)  X is weakly verifiable if and only if there exists evidence which makes the truth or falsity of X more probable.
Most factual claims are weakly verifiable.  Notice that if a proposition  is strongly verifiable then it is also weakly verifiable.
As we study Ayer’s text more we need to see what his account of evidence is such that he can coherently say that metaphysical and ethical claims are not even weakly verifiable.
Now Ayer’s critierion of meaningfulness can be stated clearly.
Principle of Meaningfulness-  An assertoric sentence X is meaningful if and only if it is in-principle, weakly verifiable.
{In the above I have been using “proposition” and “sentence” interchangeably, though we may need to make a distinction between the two in the course of our studies.  In contexts where the distinction is important the principle of meaningfulness will be stated thus:
(Disambiguated) Principle of Meaningfulness-  An assertoric sentence X is meaningful if and only if the proposition corresponding to it is in-principle, weakly verifiable.}
Let’s unpack the principle of meaningfulness so that we don't let Ayer slide with anything later on.  I think what Ayer has in mind is this:
Expanded Principle of Meaningfulness-  An assertoric sentence X is meaningful if and only if, if our capacities and technologies were finitely extended then we could determine whether the existing evidence then available to us makes the truth of X more probable or the falsity of X more probable.
{Again, this could be rephrased in terms of propositions.}
It is this criterion that Ayer will attempt to use to argue that many sentences are not meaningful.
2. The Positivist Denial of the Synthetic a Priori

2.1. Cartoon version of some of Kant's views


Kant notoriously thought that a lot of sentences were both synthetic and a-priori knowable. 
 





A-priori

A-posteriori

Analytic

Logical Truths 
(i.e. instances of “P or not-P”) 
Conceptual Necessities
(i.e.  “All bachelors are unmarried males.”)

 

Synthetic

Scientific Laws
(i.e. “force = mass times acceleration”) 
Mathematical Truths
(i.e. “2 + 2 = 4”) 
Geometrical Truths 
(i.e. “The sum of the interior angles of  a triangle equals 180 degrees”) 
General Moral Truths 
(i.e.  “It is wrong to lie.”) 

Specific factual claims (i.e. “The cat's on the mat.”) 
General non-lawlike claims 
(i.e. “Everyone in this room has seen Star-Trek.”)

Kant’s Divisions

Without belaboring Kant’s specific characterization of analyticity, etcetera, such that he grouped things this way we should see why one might want to have this list of synthetic a-priori truths.  Intuitively all of  Kant’s synthetic claims are true in virtue of meaning and the world because they describe the way the world is in some sense.  When we say that “2 + 2 = 4” this claim is intuitively made true by the plus than and equality relation on the natural numbers.  That is, the natural numbers and the properties they have make the claim true.  (Kant's interesting story of how this works needn”t detain us).  Thus, while the test mentioned above fails for Kant's synthetic/a-priori truths, we can see why Kant didn't want these truths to be analytic. 


2.2  Empiricist rejection of the synthetic a priori


Empiricism is the view that all of our contentful factual knowledge comes through the senses.  That is, all of our evidence for the truth of a claim is sensory evidence. 
Ayer takes himself to be an empiricist.  He takes Hume's arguments to show that correctness of empiricism to entail that there are no synthetic a-priori truths.  The arguments would go like this: 
1. A synthetic a-priori truth would be necessary, since it is a-priori.

2. A synthetic a-priori truth would refer to a matter of fact, since it is synthetic.

3. But truths that refer to matters of fact are by empiricism verified or falsified by sensory evidence.

4. But Hume showed us that no sentence verified or falsified by sensory evidence can ever be necessary, since no matter how many times a sentence is verified in practice, there always remains the possibility that it will be confuted on some future occasion.

5. Therefore, since a synthetic a-priori truth would refer to a matter of fact, it is not necessary.

6. But then, a synthetic a-priori truth would be both necessary and not necessary, which is incoherent.

7. Therefore, there are no synthetic a-priori truths.
It should be noted that Ayer really didn’t need to appeal to empiricism (and open himself up to the accusation of question begging) in this argument. He should have argued along the following lines. 
1. A synthetic a-priori truth would be necessary, since it is a-priori.

2. A synthetic a-priori truth would refer to a matter of fact, since it is synthetic.

3. But truths that refer to matters of fact are not necessary truths; for the facts could always have been different.

4. Therefore, since a synthetic a-priori truth would refer to a matter of fact, it is not necessary.

5. But then, a synthetic a-priori truth would be both necessary and not necessary, which is incoherent.

6. Therefore, there are no synthetic a-priori truths.


It should be noted that the basic way we made sense of a synthetic truth was in terms of whether we could imagine a situation where the sentence was false, without changing the meaning of the sentence. If this is central to our notion of a claim being synthetic, then all synthetic truths are contingent (such that they could have been false), and hence not necessary truths. So Ayer seems to be on good ground here.

2.3.  Cartoon version of some of Mill's views


Ayer presents Mill as holding, in virtue of his (Mill’s) empiricism that all sentences are synthetic/a-posteriori.  In the case of mathematical truths, Mill thinks that they are simply high-level inductive generalizations.   For Mill we experience adding 2 things to 2 things and get 4 things enough times that we end up making this generalization, for all things if you add 2 of them to 2 of them, you get 4 of them, and this is what “2 + 2 = 4” means.  It's as if we see enough white swans and then infer that all swans are white. 
Ayer argues that Mill’s position that Mathematical and Logical truths are synthetic/a-posteriori is itself absurd.  Ayer's argument goes like this:
1. Synthetic a-posteriori truths are contingent (that is, non-necessary)  since they are a-posterioiri.

2. Contingent truths are such that, if they are true, then it is possible that they are false.

3. Mathematical and Logical truths are such that, if they are true, then it is not possible that they are false.

4. Therefore Mathematical and Logical truths are not synthetic a-posteriori.


 

2.4.  Some of Ayer’s views


At this point Ayer has to face the music.  How can an empiricist account for the necessity of mathematics and logic?  Part of the genius of Logical Positivism was to attempt to do this by reshuffling Kant's box this way, and characterizing Analyticity etcetera such that this reshuffling made sense.
 




A-priori

A-posteriori

Analytic

Logical Truths
(i.e. “P or not-P”) 
Conceptual Necessities
(i.e.  “All bachelors are unmarried males.”) 
Mathematical Truths
(i.e. “2 + 2 = 4”) 
Geometrical Truths
(i.e. The Pythagorean Theorem) 




Synthetic




Scientific Laws 
(i.e. “f = m(a)”) 
Specific factual claims
(i.e. “Frank’s on the mat.”) 
General non-lawlike claims 
(i.e. “Everyone in this room has seen Star-Trek.”)

Ayer’s Division

3. Analyticity


Ayer characterizes analytic truths in this manner,
A proposition is analytic if and only if it follows logically from a meaning characterizing definition.
If you want a good idea of what Ayer had in mind, think of your high-school geometry.  You start with some very general definitions concerning point and line, etcetera, and then by following strictly logical reasoning you prove any geometric statement you want to prove.  In Ayer's time, massive world-historical advancements in logic were beginning to be wrought such that  something like this method was beginning to be fruitfully applied to all areas of mathematics (though many of its limitations of this method yet to be discovered), and the idea caught hold in other areas of thought.
Once Ayer gives the above characterization of analyticity, he needs to characterize the meaning-characterizing definitions and the logical inference rules.  His (and other positivists') idea is that the logical deductive inference rules are guaranteed as valid in virtue of the meanings of words such as ``and,'' ``or,'' ``not,'' ``if - then,'' ``all,'' and ``some.''
Then, the initial definitions that correspond to (say in the case of Euclidean Geometry) the postulates of Euclidean geometry for example, are considered to be true in virtue of linguistic convention.  The initial definitions are in some sense considered to be stipulative;  they stipulate what we take the meaning of the terms occurring in the definitions to amount to.
Finally, Ayer has the task of trying to show how analytic truths such as these can be useful in our general theorizing about the world.  For example, a lot of mathematics is part of our physical theories.  If this mathematics is just the result of stipulating meaning of the mathematical terms by picking definitions and then following the logical consequence relation, it is very unclear why, say,  calculus is such an integral part in describing the world with physics.
Note that ethical judgments occur nowhere in Ayer’s boxes.  In Chapter 6 he argues that ethical statements are not even meaningful.
Also notice that scientific laws are now considered to be synthetic/a-posteriori by Ayer.

For Ayer the synthetic truths will be those which are not analytic, but are still meaningful by the principle of meaningfulness given above.  This brings us to Chapter 5 of Ayer's book.


4. Chapter Five of Language, Truth, and Logic
Chapter 5  is perhaps the philosophically richest chapter of Language, Truth, and Logic, so we will only be able to consider a handful of the important arguments Ayer gives.  His purpose in this chapter is to characterize synthetic sentences.
4.1 Ayer on Truth Theories

Ayer wants to argue that a certain view of truth undermines certain philosophical theorizing about truth.  To understand this we need some concept of what traditional truth theories tried to accomplish.  Philosophers prior to Ayer often thought that the proper explanatory task of philosophers was to provide a sweeping characterization of what truth was.  Here are cartoon versions of a couple of such theories.


(1)  Correspondence Theories-  A proposition is true if and only if it corresponds to the facts.
On this conception the philosopher needs to specify what this “correspondence” relation comes to.
For example Plato’s theory of the forms counts as such a specification.  For Plato a proposition is true if the entity named by the subject instantiates the universal named by the predicate.
(2)  Coherence Theories-  A proposition is true if and only if it coheres with (i.e. agrees or is not inconsistent with) the rest of the propositions which we hold true.
On this conception the philosopher needs to specify what this “coherence” relation comes to.   This is a difficult task, as it seems that whole groups of people can believe consistent, yet false beliefs.  For example, people used to believe that the sun orbited around the earth.  This agreed with everything else they believed, yet we now know the belief to be false.
(3)  Pragmatist Theories-  A proposition is true if and only if it is useful for us to believe it.
On this conception the philosopher needs to specify what this “usefulness” relation comes to.  This is a difficult task, as it seems as that there are useful beliefs that are false (e.g. during the Inquisition it was useful for lots of people to believe in witches, as not believing in witches could get you killed by the Inquisition), and true beliefs that are not useful (for most people, knowledge of quantum physics is not very useful).   The American philosopher Charles Pierce tried to spell out usefulness in terms of scientific method.  Thus, he said that a proposition is true if, at a certain point in the ideal evolution of science, it comes to be accepted and is never subsequently rejected.
Ayer, I think, wants to argue that all such approaches are wrong.  In Chapter 5, he is defending a version of what is now called a “redundancy” account of truth.
(4)  Redundancy Thesis-  To say P is true, is merely to say that P.
On this view, the truth predicate doesn't really contribute anything to language.   Somehow, Ayer takes the Redundancy Thesis to make unsupportable the above three projects, and to support the project of asking under what conditions we are justified in asserting P.  What do we mean by “the conditions under which we are justified in asserting P?”  This is a good question, one which Ayer is not totally clear about.  By our normal notion of being justified in asserting something we would take it to be the case that the following sentence is true.
(i)  For some sentence P, it is possible that P is true even though no one will ever be able to be justified in asserting P.
For example, we may never be able to tell how old the universe is.  We may never be justified in the saying “the universe is 15 billion years old,” since we may never be able to know this is true.  For all this, “the universe is 15 billion years old” may be true.  Likewise, by our normal notion of being justified in asserting something, we also take the following to be true.
(ii)  For some sentence P, it is possible that we are justified in asserting P, even though  P is false.
Consider past scientific theories that were entirely justified at the time people believed in them.  Some of these theories, such as Newtonian physics, are now known to be false.   Thus, Ayer's idea of replacing the notion of truth with that of being justified, or warranted, in asserting something seems not better off than the coherence and pragmatic theories of truth.

This is not the end of the story though.  Assume that one can replace the notion of truth with that of warranted assertibility (“P is warrantedly assertible” is another way to say that one would be justified if one asserted P).  Even if one thinks that one needs to theorize about when we are justified in asserting things, as opposed to theorizing about truth, one still can reformulate the earlier truth theories as theories about the nature of evidential warrant.  Consider these:


1.  Correspondence Theories-  A proposition is warrantedly assertible if and only if it corresponds to the facts.
2.  Coherence Theories-  A proposition is warrantedly assertible if and only if it coheres with the rest of the propositions which we hold true.
3.  Pragmatist Theories-  A proposition is warrantedly assertible if and only if it is useful for us to believe it.
Philosophical problems associated with truth don't disappear just because you stop talking about truth. Any debate between the classical truth theorists can simply be reformulated in terms of warranted assertibility.
4. 2  The Quine-Duhem Problem
Ayer has a certain picture of scientific explanation in mind that we can make more specific.   Consider this picture.

scientific laws       description of experimental setting      mathematic/approximations


          \                                   |                                                       /
           \                                 |                                                      /
             \                               |                                                     /
               \                             |                                                    /
                 \_____________ | _________________________/
                               prediction of some observation sentence

Ayer thinks of science as predicting observation sentences via logical relations.  An observation sentence is any sentence which can be determined to be true or false simply by observation.  He seems to think of any scientific theory, that the laws of the theory, conjoined with descriptions of an experimental setting, and perhaps some mathematical theory and approximations, will logically entail a predicted observational outcome of the experiment. Thus, the laws of physics, along with descriptions of a lab experiment involving a ball and a ramp, plus some mathematics, entails a variety of measurable results concerning the ball rolling down the ramp.  Nearly every homework problem in a science class describes an experimental setting and asks you to determine the truth of some observation sentence (such as “The ball is rolling at eight kilometers an hour 3 seconds after it is released”).  You have to figure out how to use the scientific laws and mathematics to logically derive the correct observation sentence.  The only difference between your homework assignment and what scientists do is that they go on to test the theory by seeing if the predicted observation sentence actually does turn out to be true when the experiment is run.

This picture of science gives rise to what people today call the “Quine/Duhem hypothesis” (though some hold that Jules Henri Poincare was the first to think of it).  The pre-Quine/Duhemian thought would be that if your theory predicted an observation sentence that was falsified by the experiment (say you predicted a dial in the laboratory would read 7, and it actually reads 5 when you do the experiment), then one of your scientific laws would be falsified. However if you look at the above schema you can see that it might have been either a faulty description of the experimental setting or faulty mathematics that caused you to come up with a false prediction.  Thus, the scientific laws might be true, and the other theoretical apparatus involved in generating the prediction might be what went wrong.  Thus, when you get a falsified prediction, you have a choice, you are only forced to reject either the scientific laws, the description of the experiment, or the mathematics used.  The Quine-Duhem hypothesis, in effect, states a pessimistic conclusion about there being a fact of the matter about which of the three you have to do in such a situation.
Quine-Duhem hypothesis- No set of observations can ever compel us to abandon a hypothesis.
The thought is that if we want to hold onto a belief badly enough we can always hold that belief true and make compensatory adjustments elsewhere to explain why our observations didn't accord with our predictions.

In a couple of extremely interesting passages (around p. 90-95) , Ayer argues that the Quine-Duhem hypothesis holds of sentences that describe observations.


Given the Quine-Duhem hypothesis, a central question concerns what good reasons there are for abandoning a hypothesis, and what experiments can be taken to confirm hypotheses. We can think of these questions in these ways: (1) When is an experimental result that doesn't jive with an experimental prediction taken to disconfirm a scientific law rather than disconfirm the description of the experimental apparatus or the mathematics used?  (2)  When do a set of experiments that do jive with the experimental predictions of a theory + experimental description + math provide good evidence that the theory is correct?


These issues are important because Ayer seems to want to treat all synthetic propositions in the way we may intuitively treat scientific hypotheses.  He states that the purpose of a synthetic proposition is to, “anticipate the course of sensations, that is to make accurate predictions.”
This might seem intuitively plausible with scientific laws such as E = MC2.  Using Einstein's law, we can correctly predict the orbit of the planets, while the prior Newtonian equations generated false predictions for the orbit of Mercury (for example).
However, Ayer wants to say that all synthetic propositions have this predictive role, even such commonplace sentences such as “Fido is a dog.”  There is something to this view.  For example if I believe that Fido is a dog, then I expect that in all of my future encounters with Fido, Fido will behave in characteristic dog-like ways.  The most important thing here is to realize that it is in virtue of the predictive function of sentences that they can be talked about as being verifiable.  If, every time I see Fido, he does characteristic dog-like things then the predictions that followed from my classifying Fido as a dog are verified.  If, however, Fido talks to me next time I see him, I would have evidence for the claim that Fido is not a dog.
When the predictions that follow from the assertion of a proposition are observed, then the probability of the propositions is increased. Ayer holds, however, that the probability of a proposition holding can never attain 100%. Further evidence may overturn the proposition.  On p. 101 Ayer writes that an increase in probability is an increase in “the degree of confidence with which it is rational to entertain the hypothesis.” These rational standards will be those which are used by scientists, not the ones we always use in practice. This issue of which standards are correct bears directly on the Quine-Duhem hypothesis; since it is only whole groups of sentences together that contradict observations.  When a prediction is refuted by evidence, we always need further standards other than logic to tell us which sentence in the set of sentences (that entailed the wrong prediction) to take as false.
While Ayer doesn’t specifically discuss rational standards of science, a common rap about these standards starts by stressing certain theoretical virtues that good scientific theories have.  For example, some traditional virtues of scientific theories can be given thus:
1. Simplicity-  When choosing between two theories, all other things being equal, the simpler is to be preferred.

2. Familiarity of Principle- When choosing between two theories, all other things being equal, the one that preserves the most hypotheses already held true is to be preferred.

3.  Scope-  When choosing between two theories, all other things being equal, the one that implies a wider array of testable consequences is to be preferred.

4.  Fecundity-  When choosing between two theories, all other things being equal, the one that can be more successfully extended is to be preferred.

5.  Level of Confirmation-  When choosing between two theories, all other things being equal, the one which has had more of its predictions verified and less of its predictions falsified is to be preferred.
Thus, even though falsified predictions do not uniquely tell us how to adjust our theory that gave rise to them, there are often good reasons that scientists have for picking one new theory rather than another.  Note- all of the above theoretical virtues are notoriously difficult to make precise sense of when looking at actual scientific theories.  As far as I know, no one has yet sucessfully characterized them in a manner which is non-vague and true to scientific practice.
5. Chapter Six of Language, Truth, and Logic - A Positivist Critique of Ethics
Much of Ayer’s discussion hinges on the claim that normative properties are not definable.  To understand Ayer's discussion we must first look at what he took a good definition to be, and then examine some traditional definitions of moral predicates.
It is common in philosophical culture to take a good definition to provide necessary and sufficient conditions for the occurence of the term being defined.
We say A is necessary for B if and only if it is not possible for B to be true and A to be false.  For example, it is not possible for something to be three sided and not a triangle.  Thus ``x is three sided'' is necessary for ``x is a triangle.''
We say A is sufficient for B if and only if it is not possible for A to be true and B to be false.  For example, it is not possible for something to be a triangle and not be three sided. (Notice that A is necessary for B if and only if B is sufficient for A).
In mathematical contexts we often have necessary and sufficient conditions. For example, a two dimensional figure is a triangle if and only if the sum of the interior angles of that figure is 180 degrees.  Having the sum of one's interior angles being equal to 180 degrees is both necessary and sufficient for a two dimensional figure's being a triangle.

Now we can look at some definitions of “the good” from traditional philosophy.


Deontological theories of ethics attempt to define the goodness of an action in terms of whether that action follows from a moral law.  One version of deontological ethics gives this definition for the good:
An action x is good if and only if x is such that in performing it the agent (which performs x) treats others as ends rather than as means.
 Consequentialist theories attempt to define the goodness of an action in terms of whether or not that action produces the best consequences.  One version of consequentialist ethics gives this definiiton for the good,
An action x is good if and only if x is such that in performing it the agent helps to bring about the greatest amount of pleasure for the greatest number of people.

When Ayer claims that normative predicates such as “good” are undefinable he says that for any definition of the good it will not be contradictory to disagree with the definition.  This is, at best, unclear.  I take it that what he has in mind is that for any proposed definition of a predicate such as “good” there will always be (at least possible) counterexamples to the definitions.


With the above definitions we need only imagine situations where either it is good to perform an action and the definition doesn't hold for the action (making the definition non-necessary), or imagine situations where it is not good to perform the action and the definition does hold of the action (making the definition non-sufficient). [As an exercise, think of the examples we came up with in class and determine whether or not they show the above definitions to be non-necessary or non-sufficient.]
Now, weirdly, Ayer thinks that the indefinability of ethics forces us to conclude that ethical propositions such as “that was a good thing he did” are meaningless.  To see how weird this is, if you pick any definition in the dictionary you will find that it is not necessary and sufficient in the way that Ayer wants ethical definitions to be.  For example, the definition of “dog” will be something like the following.
Dog- four legged member of the species canine, traditionally used for hunting, often used as pets today.
This definition certainly doesn’t specify necessary conditions for doghood, since there are plenty of dogs which have three legs.  Ayer might say that the dictionary writers are sloppy and they really should write.
Dog- member of the species canine, traditionally used for hunting, often used as pets today.
This doesn't seem to specify sufficient conditions though.  We can certainly imagine biologists deciding to classify Cocker Spaniels as non-canines for certain theoretical reasons, while we still keep calling Cocker Spaniels dogs.  Or we can imagine discovering new breeds of dogs that don't qualify as canine by the specifications for being in the species canine by biologists.
Maybe in this case Ayer would say that once we start calling non-canines dogs we have changed the meaning of the word “dog.”  If he's willing to say this, then his point about normative definitions could be that any definition of a normative term will have counterexamples where the meaning of the normative term hasn't intuitively changed.
Thus when we call non-canines dogs we have changed the meaning of “dog,” but when we say that it is good for a person to lie to Nazis (thus treating the Nazi as a mean and not an end) we have not changed the meaning of the word “good.”  Rather the purported definition failed to specify necessary and sufficient conditions for the goodness of an act.
At this point in the argument Ayer asks how we can possibly know whether an action is good if we can’t define what it is for an act to be good.  His thought is that if we can't provide such a definition then we can't say what it would be to verify the claim that an action is good, for if we can really verify moral claims we must have reasons by which to verify these claims. These reasons would be given by a definition of a good act, but since there is no definition there is no procedure by which to verify moral claims.  Then, since moral claims aren’t (for Ayer) even weakly, in-principle verifiable they are not synthetic.  And, since they don't follow logically from stipulative definitions, they aren't analytic.  Thus, they are meaningless.
 



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