How do we determine our actual degree of belief?

Question

The SEP talks about the notion of a degree of belief, or credence in a proposition.

One common way of formalizing this idea is by means of a scale from 0 to 1, where 0 indicates absolute certainty in the falsity of a proposition, 1 indicates absolute certainty in its truth, and .5 indicates that the subject regards the proposition just as likely to be true as false. This number then indicates one’s credence or degree of belief. Standard approaches equate degree of belief with the maximum amount the subject would, or alternatively should, be willing to wager on a bet that pays nothing if the proposition is false and 1 unit if the proposition is true. So, for example, if the subject thinks that the proposition “the restaurant is open” is three times more likely to be true than false, they should be willing to pay no more than $0.75 for a wager that pays nothing if the restaurant is closed and $1 if it is open. Consequently, the subject’s degree of belief is .75, or 75%. Such a formalized approach to degree of belief has proven useful in decision theory, game theory, and economics. Standard philosophical treatments of this topic include Jeffrey (1983) and Skyrms (2000).

So there seems to be two possible ways we assess degree of belief: with the mathematics that lies behind odds, and with actual actions taken in the form of bets. So, in any given situation the odds are merely considered a hypothetical since unless a bet actually is made, we don't know what we believe if haven't decided to bet, right? If we don’t bet, do we know what our actual degree of belief in a proposition is in the first place?

Answer 1

I'm going to answer one aspect of your question:

You ask:

how do we know what our actual degree of belief in a proposition is in the first place?

Two forms of self-knowledge spring to mind: intuition and formalism. That is to say, we can rely on our instincts and the toolbox built from that, and we can also use our formal training. It might help to give an example of each.

When we are dealing with complex phenomena, we might simply intuit our degree of belief. In dealing with a coworker, for instance, we may have very little faith in their ability to complete a task. Thus, we believe they may, but not with a lot of conviction, complete a task. Technically speaking, we are dealing with linguistic epistemic modality as a measure of our belief explicitly by choosing words to represent our inner state. What do we base our choice of words on? Our intuition, instinct, or gut hunch. We might appeal to anecdotes, and a bit of informal reason. It might be a deep fear of the consequences of their poor performance. This would be consistent with the somatic marker hypothesis where our emotional processes.

A second way of determining our degree of belief might be to use statistical methods and formal metrics. Consider how in quality control in manufacturing, we produce a batch of widgets in accordance with some process, and as a follow-up to that process, take a sample of the product, apply measurement, strike out a null hypothesis and then use fancy statistical methods to determine our degree of belief about the quality of the product and our confidence with a confidence interval. Now, we are not just expressing linguistic epistemic modality, but rather relying on the language of mathematics, statistics, and probability distributions to express degree of belief. Consider the language from the WP article on the confidence interval:

"Were this procedure to be repeated on numerous samples, the proportion of calculated 95% confidence intervals that encompassed the true value of the population parameter would tend toward 95%.

That's a lot more precise than "may", "might", or "probably will/won't". But in either case, whether vague natural language or formal statistical language, we are expressing our degree of belief. Ultimately, though, our degree of belief might best be made known, by what sort of action we engage in given the larger framework of our goals and willingness to use the degree of belief to some end, such as winning the bet. In English, we often just use the phrase "put your money where your mouth is" (MW) to convey the idea that one can espouse a degree of belief, but without action, the claim of belief itself might not be accurate.

Answer 2

We do, in a sense, make bets like these frequently. Much of the time we aren't betting money as the anticipated unit of benefit isn't monetary, but sometimes it is. We vote with many things, such as our time and effort, or even our mental consideration. So, we can know what bets we do make. In one sense, the resources we "bet" by expending them in alignment with the expected payouts of those beliefs tells us our degree of confidence in that belief.

That being said, people are not always rational people. Consider an actual bet, like playing the lottery. Rationally, most people would admit that the odds of winning are very low, and even given the large potential payout, the certainty of winning would, according to this metric, call for a person to spend only an amount on a ticket that would be less than the actual cost of a ticket. Emotionally, many people feel an impulse which is not rational and choose to make a bet with a cost greater than their confidence in the likelihood of winning. So, this could be seen as a call to align the actual bets you make with the rational evaluation.

You mentioned belief in God. The famous Pascal's Wager attempts to apply this sort of game theory to the question of that belief. If we sufficiently simplify the question as was presented in the wager and consider the position of non-belief to be subject to the same criteria, then the wager works similarly to the model you mentioned. As such, Pascal would argue that the expected payout of non-belief would be 0 units. Therefore, even if you were 100% confident that there were no god, you should bet 0 units since that would still be 100% of the anticipated payoff. Contrary to that, he would argue that the payoff for positive belief would be infinite units. As such, even if you were only 1% certain that God does exist, you would be rational to bet 1% of infinite units, which would itself still be infinite. Therefore, according to the wager, the only time when you should bet less than infinite units is when you are 100% certain that there is no god.

This actually seems somewhat consistent with how people act and accounts for the "no Atheists in foxholes" mentality. Even given extreme emotional and other impetus to disbelieve, most people do not feel 100% certain that there is no god. Therefore, in a time of distress, when other pressures like social pressure seem less important, they find that there is nothing to lose in calling out to a potentially existing god. They may only be 1% confident, but they see no loss in taking that bet, at least in the moment.

Answer 3

Given that some action didn't actually take place, how do you know what someone would do?

"You ask them. They tell you. Now you know."
"But wait... How do you really know?"
"You ask them again, what would they really do. They tell you. Now you know what they would really do."
"Yeah... but actually? Would they really actually do it?"
"You ask them again. Would they actually do it? Really actually? They ponder, they actually think it over this time. They tell you. Now you know."
"Yeah, well, but can we ever really, actually believe that?"
"You tell me."
"Well, you know, someone could get second thoughts, before they actually do it, right?"
"Sure, but people don't get second thoughts all the time, right? They tell you what they'll do. Now you know what they'll do. If you want to chip away at that -- go ahead, there are tons of assumptions we take for granted. For instance, we assume they were not lying. We assume that an act of God won't intervene and prevent them from actually doing what they said they would do. We assume the world won't end. We assume there minds were not drugged when they told us. We assume they were not under some hypnotic spell. We don't ask them this while they're sleeping (even though they might give a true answer then). Doesn't any of that matter? The assumption that they were not lying and not under hypnosis seems relevant. But we do generally assume that or know it based on other grounds."
"Yeah, but what if we don't actually ever really know? You know, the know know kind of knowledge."
"As Confucius said: 'Rotten wood cannot be carved, a dung wall cannot be painted. At first, I listened to people's words and trusted they'd act accordingly. Now, I listen to what they say and observe what they do.' So, you observe, learn, and adjust if necessary. That's all there is to it. I have no idea what the heck you mean by 'know know kind of knowledge'."
"Yeah, well, that's because you're not an actual real philosopher. You're only a would-be-wannabe. It may be too deep for you, you know?"

Answer 4

The SEP explains that degree of belief, or credence, is often formalized on a scale from 0 to 1, where 0 means certainty in falsehood and 1 means certainty in truth. This can be reflected in a person's willingness to wager on a proposition, with the amount they would bet representing their degree of belief. However, if no bet is made, it raises the question of whether we can truly know our degree of belief, as the odds themselves may only represent a hypothetical belief unless acted upon in a wager.